https://wiki.swarma.org/api.php?action=feedcontributions&user=Wei&feedformat=atom集智百科 - 复杂系统|人工智能|复杂科学|复杂网络|自组织 - 用户贡献 [zh-cn]2024-03-28T22:51:48Z用户贡献MediaWiki 1.35.0https://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29516逆概率加权2022-03-24T10:57:35Z<p>Wei:</p>
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'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref>{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}</ref>。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref>{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}</ref>。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
<br />
一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
<br />
当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref>{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}</ref>。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
<br />
== 逆概率加权估计量 ==<br />
<br />
<br />
<br />
当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE)可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中 <br />
* <math> X \in \mathbb{R}^{p} </math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
<br />
目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
<br />
=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> , 其中 <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math>;<br />
# 使用任何倾向性模型(通常是逻辑回归模型)构建 <math>\hat{p}_{n}(a|x)</math> 或 <math>p(a|x)</math> ;<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math>。<br />
在计算出各处理组的平均数后,可以用统计学上的t检验或方差检验(ANOVA test)来判断组间平均数的差异,并确定处理效果的统计显著性。<br />
<br />
==== 假设 ====<br />
回顾对于协变量<math>X</math>,操作<math>A</math>和响应量<math>Y</math>的联合概率模型。当已知<math>X</math>和<math>A</math>分别为<math>x</math>和<math>a</math>时,响应量<math> Y(X=x,A=a)=Y(x,a)</math>的分布为<br />
<math>\begin{aligned}Y(x,a)\sim {\frac {P(x,a,\cdot )}{\int P(x,a,y)\,dy}}\end{aligned}</math>。<br />
<br />
我们做出以下假设:<br />
* ('''A1''')一致性(Consistency): <math>Y = Y^{*}(A)</math><br />
* ('''A2''') 没有未观测的混淆因子: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math>。更正式地说,对于每个有界和可测函数<math>f</math>和<math>g</math>,<br />
<math>{\begin{aligned}\qquad \mathbb {E} _{(A,Y)}\left[f(Y(X,a))\,g(A)\,|\,X\right]=\mathbb {E} _{Y}\left[f(Y(X,a))\,|\,X\right]\,\mathbb {E} _{A}\left[g(A)\,|\,X\right]\end{aligned}}</math>。<br />
<br />
这意味着治疗分配只基于协变量数据,与潜在结果无关。<br />
* ('''A3''') 正值性(Positivity): 对于所有的 <math>a</math> 和 <math>x</math>,<math>P(A=a|X=x)>0 </math> 。<br />
<br />
==== 缺点 ====<br />
逆概率加权估计器(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么逻辑回归模型可能在尾部附近变得不稳定,导致逆概率加权估计器也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
另一种估计方法是增广逆概率加权估计器(Augmented Inverse Probability Weighted Estimator,AIPWE) 。它融合了基于回归的估计和逆概率加权估计的性质。因此,它是一种“双重稳健”的方法。因为它只需要正确指定倾向或结果模型,而不是同时指定。这种方法增强了逆概率加权估计,以减少了变异性并提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref>。<br />
<br />
=== 估计器公式 ===<br />
<br />
<math><br />
\begin{align}<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
符号定义如下:<br />
# <math>1_{A_{i}=a}</math> 是一个示性函数 ([[indicator function]]),指示受试者 i 是治疗组 a 的一部分(或不是)。<br />
# 对于某个个体i,基于协变量<math>X</math> 和处理 <math>A</math>,构建回归估计器 <math>\hat{Q}_n(x,a)</math> 去预测结果 <math>Y</math>。例如,使用普通最小二乘([[ordinary least squares]])回归。<br />
# 构建倾向(概率)估计 <math>\hat{p}_n(A_i|X_i)</math>. 例如,使用逻辑回归([[logistic regression]])。<br />
# 在AIPWE中结合得到 <math>\hat{\mu}^{AIPWE}_{a,n}</math>。<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
公式的后面重排有助于揭示基本思想:我们的估计器是基于使用模型的平均预测结果的(即<math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>)。然而,那么模型的残差就不会(在完整的治疗组<math>a</math>)大约为0。 我们可以通过增加模型的平均残差(<math>Q</math>)与结果(<math>Y</math>)的真实值的额外项来纠正这种潜在的偏差(即<math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). 因为我们有<math>Y</math>的缺失值,所以我们给予权重,以提高每个残差的相对重要性(这些权重是基于看到每个个体观测值的反倾向性,也就是逆概率)。(参见文献<ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>的第10页).<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(即可能是<math>\hat{Q}_n(X_i,a)</math>或<math>\hat{p}_{n}(A_{i}|X_{i})</math>, 或两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均的残差很好地估计(并修正)<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref>。<br />
<br />
双重稳健估计器的偏差被称为'''二阶偏差''',它取决于差分<math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math>和差分<math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref>。<br />
<br />
==参见==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29493逆概率加权2022-03-23T14:27:04Z<p>Wei:</p>
<hr />
<div><br />
'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref>{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}</ref>。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref>{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}</ref>。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
<br />
一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
<br />
当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref>{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}</ref>。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
<br />
== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
<br />
<br />
当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中 <br />
* <math> X \in \mathbb{R}^{p} </math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
<br />
目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
<br />
=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> , 其中 <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math>;<br />
# 使用任何倾向性模型(通常是逻辑回归模型)构建 <math>\hat{p}_{n}(a|x)</math> 或 <math>p(a|x)</math> ;<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math>。<br />
在计算出各处理组的平均数后,可以用统计学上的t检验或方差检验(ANOVA test)来判断组间平均数的差异,并确定处理效果的统计显著性。<br />
<br />
==== 假设 ====<br />
回顾对于协变量<math>X</math>,操作<math>A</math>和响应量<math>Y</math>的联合概率模型。当已知<math>X</math>和<math>A</math>分别为<math>x</math>和<math>a</math>时,响应量<math> Y(X=x,A=a)=Y(x,a)</math>的分布为<br />
<math>\begin{aligned}Y(x,a)\sim {\frac {P(x,a,\cdot )}{\int P(x,a,y)\,dy}}\end{aligned}</math>。<br />
<br />
我们做出以下假设:<br />
* ('''A1''')一致性(Consistency): <math>Y = Y^{*}(A)</math><br />
* ('''A2''') 没有未观测的混淆因子: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math>。更正式地说,对于每个有界和可测函数<math>f</math>和<math>g</math>,<br />
<math>{\begin{aligned}\qquad \mathbb {E} _{(A,Y)}\left[f(Y(X,a))\,g(A)\,|\,X\right]=\mathbb {E} _{Y}\left[f(Y(X,a))\,|\,X\right]\,\mathbb {E} _{A}\left[g(A)\,|\,X\right]\end{aligned}}</math>。<br />
<br />
这意味着治疗分配只基于协变量数据,与潜在结果无关。<br />
* ('''A3''') 正值性(Positivity): 对于所有的 <math>a</math> 和 <math>x</math>,<math>P(A=a|X=x)>0 </math> 。<br />
<br />
==== 缺点 ====<br />
逆概率加权估计器(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么逻辑回归模型可能在尾部附近变得不稳定,导致逆概率加权估计器也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
另一种估计方法是增广逆概率加权估计器(Augmented Inverse Probability Weighted Estimator,AIPWE) 。它融合了基于回归的估计和逆概率加权估计的性质。因此,它是一种“双重稳健”的方法。因为它只需要正确指定倾向或结果模型,而不是同时指定。这种方法增强了逆概率加权估计,以减少了变异性并提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref>。<br />
<br />
=== 估计器公式 ===<br />
<br />
<math><br />
\begin{align}<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
符号定义如下:<br />
# <math>1_{A_{i}=a}</math> 是一个示性函数 ([[indicator function]]),指示受试者 i 是治疗组 a 的一部分(或不是)。<br />
# 对于某个个体i,基于协变量<math>X</math> 和处理 <math>A</math>,构建回归估计器 <math>\hat{Q}_n(x,a)</math> 去预测结果 <math>Y</math>。例如,使用普通最小二乘([[ordinary least squares]])回归。<br />
# 构建倾向(概率)估计 <math>\hat{p}_n(A_i|X_i)</math>. 例如,使用逻辑回归([[logistic regression]])。<br />
# 在AIPWE中结合得到 <math>\hat{\mu}^{AIPWE}_{a,n}</math>。<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
公式的后面重排有助于揭示基本思想:我们的估计器是基于使用模型的平均预测结果的(即<math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>)。然而,那么模型的残差就不会(在完整的治疗组<math>a</math>)大约为0。 我们可以通过增加模型的平均残差(<math>Q</math>)与结果(<math>Y</math>)的真实值的额外项来纠正这种潜在的偏差(即<math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). 因为我们有<math>Y</math>的缺失值,所以我们给予权重,以提高每个残差的相对重要性(这些权重是基于看到每个个体观测值的反倾向性,也就是逆概率)。(参见文献<ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>的第10页).<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(即可能是<math>\hat{Q}_n(X_i,a)</math>或<math>\hat{p}_{n}(A_{i}|X_{i})</math>, 或两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均的残差很好地估计(并修正)<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref>。<br />
<br />
双重稳健估计器的偏差被称为'''二阶偏差''',它取决于差分<math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math>和差分<math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref>。<br />
<br />
==参见==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29492逆概率加权2022-03-23T14:24:16Z<p>Wei:</p>
<hr />
<div><br />
'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref>Robins, JM; Rotnitzky, A; Zhao, LP (1994). "Estimation of regression coefficients when some regressors are not always observed". Journal of the American Statistical Association. 89 (427): 846–866. doi:10.1080/01621459.1994.10476818.</ref>。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref>Breslow, NE; Lumley, T; et al. (2009). "[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2768499 Using the Whole Cohort in the Analysis of Case-Cohort Data]". Am J Epidemiol. 169 (11): 1398–1405. [https://doi.org/10.1093%2Faje%2Fkwp055 doi:10.1093/aje/kwp055]. PMC [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2768499 2768499]. PMID [https://pubmed.ncbi.nlm.nih.gov/19357328 19357328]</ref>。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
<br />
一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
<br />
当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref>Hernan, MA; Robins, JM (2006). "Estimating Causal Effects From Epidemiological Data". J Epidemiol Community Health. 60 (7): 578–596. CiteSeerX 10.1.1.157.9366. doi:10.1136/jech.2004.029496. PMC 2652882. PMID 16790829.</ref>。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
<br />
== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
<br />
<br />
当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中 <br />
* <math> X \in \mathbb{R}^{p} </math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
<br />
目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
<br />
=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> , 其中 <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math>;<br />
# 使用任何倾向性模型(通常是逻辑回归模型)构建 <math>\hat{p}_{n}(a|x)</math> 或 <math>p(a|x)</math> ;<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math>。<br />
在计算出各处理组的平均数后,可以用统计学上的t检验或方差检验(ANOVA test)来判断组间平均数的差异,并确定处理效果的统计显著性。<br />
<br />
==== 假设 ====<br />
回顾对于协变量<math>X</math>,操作<math>A</math>和响应量<math>Y</math>的联合概率模型。当已知<math>X</math>和<math>A</math>分别为<math>x</math>和<math>a</math>时,响应量<math> Y(X=x,A=a)=Y(x,a)</math>的分布为<br />
<math>\begin{aligned}Y(x,a)\sim {\frac {P(x,a,\cdot )}{\int P(x,a,y)\,dy}}\end{aligned}</math>。<br />
<br />
我们做出以下假设:<br />
* ('''A1''')一致性(Consistency): <math>Y = Y^{*}(A)</math><br />
* ('''A2''') 没有未观测的混淆因子: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math>。更正式地说,对于每个有界和可测函数<math>f</math>和<math>g</math>,<br />
<math>{\begin{aligned}\qquad \mathbb {E} _{(A,Y)}\left[f(Y(X,a))\,g(A)\,|\,X\right]=\mathbb {E} _{Y}\left[f(Y(X,a))\,|\,X\right]\,\mathbb {E} _{A}\left[g(A)\,|\,X\right]\end{aligned}}</math>。<br />
<br />
这意味着治疗分配只基于协变量数据,与潜在结果无关。<br />
* ('''A3''') 正值性(Positivity): 对于所有的 <math>a</math> 和 <math>x</math>,<math>P(A=a|X=x)>0 </math> 。<br />
<br />
==== 缺点 ====<br />
逆概率加权估计器(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么逻辑回归模型可能在尾部附近变得不稳定,导致逆概率加权估计器也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
另一种估计方法是增广逆概率加权估计器(Augmented Inverse Probability Weighted Estimator,AIPWE) 。它融合了基于回归的估计和逆概率加权估计的性质。因此,它是一种“双重稳健”的方法。因为它只需要正确指定倾向或结果模型,而不是同时指定。这种方法增强了逆概率加权估计,以减少了变异性并提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref>。<br />
<br />
=== 估计器公式 ===<br />
<br />
<math><br />
\begin{align}<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
符号定义如下:<br />
# <math>1_{A_{i}=a}</math> 是一个示性函数 ([[indicator function]]),指示受试者 i 是治疗组 a 的一部分(或不是)。<br />
# 对于某个个体i,基于协变量<math>X</math> 和处理 <math>A</math>,构建回归估计器 <math>\hat{Q}_n(x,a)</math> 去预测结果 <math>Y</math>。例如,使用普通最小二乘([[ordinary least squares]])回归。<br />
# 构建倾向(概率)估计 <math>\hat{p}_n(A_i|X_i)</math>. 例如,使用逻辑回归([[logistic regression]])。<br />
# 在AIPWE中结合得到 <math>\hat{\mu}^{AIPWE}_{a,n}</math>。<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
公式的后面重排有助于揭示基本思想:我们的估计器是基于使用模型的平均预测结果的(即<math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>)。然而,那么模型的残差就不会(在完整的治疗组<math>a</math>)大约为0。 我们可以通过增加模型的平均残差(<math>Q</math>)与结果(<math>Y</math>)的真实值的额外项来纠正这种潜在的偏差(即<math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). 因为我们有<math>Y</math>的缺失值,所以我们给予权重,以提高每个残差的相对重要性(这些权重是基于看到每个个体观测值的反倾向性,也就是逆概率)。(参见文献<ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>的第10页).<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(即可能是<math>\hat{Q}_n(X_i,a)</math>或<math>\hat{p}_{n}(A_{i}|X_{i})</math>, 或两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均的残差很好地估计(并修正)<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref>。<br />
<br />
双重稳健估计器的偏差被称为'''二阶偏差''',它取决于差分<math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math>和差分<math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref>。<br />
<br />
==参见==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29491逆概率加权2022-03-23T14:20:31Z<p>Wei:</p>
<hr />
<div><br />
'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref>Robins, JM; Rotnitzky, A; Zhao, LP (1994). "Estimation of regression coefficients when some regressors are not always observed". Journal of the American Statistical Association. 89 (427): 846–866. doi:10.1080/01621459.1994.10476818.</ref>。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref>Breslow, NE; Lumley, T; et al. (2009). "Using the Whole Cohort in the Analysis of Case-Cohort Data". Am J Epidemiol. 169 (11): 1398–1405. doi:10.1093/aje/kwp055. PMC 2768499. PMID 19357328</ref>。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
<br />
一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
<br />
当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref>Hernan, MA; Robins, JM (2006). "Estimating Causal Effects From Epidemiological Data". J Epidemiol Community Health. 60 (7): 578–596. CiteSeerX 10.1.1.157.9366. doi:10.1136/jech.2004.029496. PMC 2652882. PMID 16790829.</ref>。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
<br />
== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
<br />
<br />
当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中 <br />
* <math> X \in \mathbb{R}^{p} </math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
<br />
目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
<br />
=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> , 其中 <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math>;<br />
# 使用任何倾向性模型(通常是逻辑回归模型)构建 <math>\hat{p}_{n}(a|x)</math> 或 <math>p(a|x)</math> ;<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math>。<br />
在计算出各处理组的平均数后,可以用统计学上的t检验或方差检验(ANOVA test)来判断组间平均数的差异,并确定处理效果的统计显著性。<br />
<br />
==== 假设 ====<br />
回顾对于协变量<math>X</math>,操作<math>A</math>和响应量<math>Y</math>的联合概率模型。当已知<math>X</math>和<math>A</math>分别为<math>x</math>和<math>a</math>时,响应量<math> Y(X=x,A=a)=Y(x,a)</math>的分布为<br />
<math>\begin{aligned}Y(x,a)\sim {\frac {P(x,a,\cdot )}{\int P(x,a,y)\,dy}}\end{aligned}</math>。<br />
<br />
我们做出以下假设:<br />
* ('''A1''')一致性(Consistency): <math>Y = Y^{*}(A)</math><br />
* ('''A2''') 没有未观测的混淆因子: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math>。更正式地说,对于每个有界和可测函数<math>f</math>和<math>g</math>,<br />
<math>{\begin{aligned}\qquad \mathbb {E} _{(A,Y)}\left[f(Y(X,a))\,g(A)\,|\,X\right]=\mathbb {E} _{Y}\left[f(Y(X,a))\,|\,X\right]\,\mathbb {E} _{A}\left[g(A)\,|\,X\right]\end{aligned}}</math>。<br />
<br />
这意味着治疗分配只基于协变量数据,与潜在结果无关。<br />
* ('''A3''') 正值性(Positivity): 对于所有的 <math>a</math> 和 <math>x</math>,<math>P(A=a|X=x)>0 </math> 。<br />
<br />
==== 缺点 ====<br />
逆概率加权估计器(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么逻辑回归模型可能在尾部附近变得不稳定,导致逆概率加权估计器也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
另一种估计方法是增广逆概率加权估计器(Augmented Inverse Probability Weighted Estimator,AIPWE) 。它融合了基于回归的估计和逆概率加权估计的性质。因此,它是一种“双重稳健”的方法。因为它只需要正确指定倾向或结果模型,而不是同时指定。这种方法增强了逆概率加权估计,以减少了变异性并提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref>。<br />
<br />
=== 估计器公式 ===<br />
<br />
<math><br />
\begin{align}<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
符号定义如下:<br />
# <math>1_{A_{i}=a}</math> 是一个示性函数 ([[indicator function]]),指示受试者 i 是治疗组 a 的一部分(或不是)。<br />
# 对于某个个体i,基于协变量<math>X</math> 和处理 <math>A</math>,构建回归估计器 <math>\hat{Q}_n(x,a)</math> 去预测结果 <math>Y</math>。例如,使用普通最小二乘([[ordinary least squares]])回归。<br />
# 构建倾向(概率)估计 <math>\hat{p}_n(A_i|X_i)</math>. 例如,使用逻辑回归([[logistic regression]])。<br />
# 在AIPWE中结合得到 <math>\hat{\mu}^{AIPWE}_{a,n}</math>。<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
公式的后面重排有助于揭示基本思想:我们的估计器是基于使用模型的平均预测结果的(即<math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>)。然而,那么模型的残差就不会(在完整的治疗组<math>a</math>)大约为0。 我们可以通过增加模型的平均残差(<math>Q</math>)与结果(<math>Y</math>)的真实值的额外项来纠正这种潜在的偏差(即<math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). 因为我们有<math>Y</math>的缺失值,所以我们给予权重,以提高每个残差的相对重要性(这些权重是基于看到每个个体观测值的反倾向性,也就是逆概率)。(参见文献<ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>的第10页).<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(即可能是<math>\hat{Q}_n(X_i,a)</math>或<math>\hat{p}_{n}(A_{i}|X_{i})</math>, 或两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均的残差很好地估计(并修正)<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref>。<br />
<br />
双重稳健估计器的偏差被称为'''二阶偏差''',它取决于差分<math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math>和差分<math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref>。<br />
<br />
==参见==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29490逆概率加权2022-03-23T14:18:00Z<p>Wei:</p>
<hr />
<div><br />
<br />
'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref>Robins, JM; Rotnitzky, A; Zhao, LP (1994). "Estimation of regression coefficients when some regressors are not always observed". Journal of the American Statistical Association. 89 (427): 846–866. doi:10.1080/01621459.1994.10476818.</ref>。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref></ref>。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
<br />
<br />
一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
<br />
<br />
当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref></ref>。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
<br />
== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
<br />
<br />
当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中 <br />
* <math> X \in \mathbb{R}^{p} </math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
<br />
目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
<br />
=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> , 其中 <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math>;<br />
# 使用任何倾向性模型(通常是逻辑回归模型)构建 <math>\hat{p}_{n}(a|x)</math> 或 <math>p(a|x)</math> ;<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math>。<br />
在计算出各处理组的平均数后,可以用统计学上的t检验或方差检验(ANOVA test)来判断组间平均数的差异,并确定处理效果的统计显著性。<br />
<br />
==== 假设 ====<br />
回顾对于协变量<math>X</math>,操作<math>A</math>和响应量<math>Y</math>的联合概率模型。当已知<math>X</math>和<math>A</math>分别为<math>x</math>和<math>a</math>时,响应量<math> Y(X=x,A=a)=Y(x,a)</math>的分布为<br />
<math>\begin{aligned}Y(x,a)\sim {\frac {P(x,a,\cdot )}{\int P(x,a,y)\,dy}}\end{aligned}</math>。<br />
<br />
我们做出以下假设:<br />
* ('''A1''')一致性(Consistency): <math>Y = Y^{*}(A)</math><br />
* ('''A2''') 没有未观测的混淆因子: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math>。更正式地说,对于每个有界和可测函数<math>f</math>和<math>g</math>,<br />
<math>{\begin{aligned}\qquad \mathbb {E} _{(A,Y)}\left[f(Y(X,a))\,g(A)\,|\,X\right]=\mathbb {E} _{Y}\left[f(Y(X,a))\,|\,X\right]\,\mathbb {E} _{A}\left[g(A)\,|\,X\right]\end{aligned}}</math>。<br />
<br />
这意味着治疗分配只基于协变量数据,与潜在结果无关。<br />
* ('''A3''') 正值性(Positivity): 对于所有的 <math>a</math> 和 <math>x</math>,<math>P(A=a|X=x)>0 </math> 。<br />
<br />
==== 缺点 ====<br />
逆概率加权估计器(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么逻辑回归模型可能在尾部附近变得不稳定,导致逆概率加权估计器也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
另一种估计方法是增广逆概率加权估计器(Augmented Inverse Probability Weighted Estimator,AIPWE) 。它融合了基于回归的估计和逆概率加权估计的性质。因此,它是一种“双重稳健”的方法。因为它只需要正确指定倾向或结果模型,而不是同时指定。这种方法增强了逆概率加权估计,以减少了变异性并提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref>。<br />
<br />
=== 估计器公式 ===<br />
<br />
<math><br />
\begin{align}<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
符号定义如下:<br />
# <math>1_{A_{i}=a}</math> 是一个示性函数 ([[indicator function]]),指示受试者 i 是治疗组 a 的一部分(或不是)。<br />
# 对于某个个体i,基于协变量<math>X</math> 和处理 <math>A</math>,构建回归估计器 <math>\hat{Q}_n(x,a)</math> 去预测结果 <math>Y</math>。例如,使用普通最小二乘([[ordinary least squares]])回归。<br />
# 构建倾向(概率)估计 <math>\hat{p}_n(A_i|X_i)</math>. 例如,使用逻辑回归([[logistic regression]])。<br />
# 在AIPWE中结合得到 <math>\hat{\mu}^{AIPWE}_{a,n}</math>。<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
公式的后面重排有助于揭示基本思想:我们的估计器是基于使用模型的平均预测结果的(即<math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>)。然而,那么模型的残差就不会(在完整的治疗组<math>a</math>)大约为0。 我们可以通过增加模型的平均残差(<math>Q</math>)与结果(<math>Y</math>)的真实值的额外项来纠正这种潜在的偏差(即<math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). 因为我们有<math>Y</math>的缺失值,所以我们给予权重,以提高每个残差的相对重要性(这些权重是基于看到每个个体观测值的反倾向性,也就是逆概率)。(参见文献<ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>的第10页).<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(即可能是<math>\hat{Q}_n(X_i,a)</math>或<math>\hat{p}_{n}(A_{i}|X_{i})</math>, 或两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均的残差很好地估计(并修正)<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref>。<br />
<br />
双重稳健估计器的偏差被称为'''二阶偏差''',它取决于差分<math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math>和差分<math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref>。<br />
<br />
==参见==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29489逆概率加权2022-03-23T14:04:18Z<p>Wei:</p>
<hr />
<div><br />
<br />
'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref name="refname2" />。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref name="refname3" />。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
<br />
<br />
一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
<br />
<br />
当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref name="refname1" />。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
<br />
== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
<br />
<br />
当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中 <br />
* <math> X \in \mathbb{R}^{p} </math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
<br />
目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
<br />
=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> , 其中 <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math>;<br />
# 使用任何倾向性模型(通常是逻辑回归模型)构建 <math>\hat{p}_{n}(a|x)</math> 或 <math>p(a|x)</math> ;<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math>。<br />
在计算出各处理组的平均数后,可以用统计学上的t检验或方差检验(ANOVA test)来判断组间平均数的差异,并确定处理效果的统计显著性。<br />
<br />
==== 假设 ====<br />
回顾对于协变量<math>X</math>,操作<math>A</math>和响应量<math>Y</math>的联合概率模型。当已知<math>X</math>和<math>A</math>分别为<math>x</math>和<math>a</math>时,响应量<math> Y(X=x,A=a)=Y(x,a)</math>的分布为<br />
<math>\begin{aligned}Y(x,a)\sim {\frac {P(x,a,\cdot )}{\int P(x,a,y)\,dy}}\end{aligned}</math>。<br />
<br />
我们做出以下假设:<br />
* ('''A1''')一致性(Consistency): <math>Y = Y^{*}(A)</math><br />
* ('''A2''') 没有未观测的混淆因子: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math>。更正式地说,对于每个有界和可测函数<math>f</math>和<math>g</math>,<br />
<math>{\begin{aligned}\qquad \mathbb {E} _{(A,Y)}\left[f(Y(X,a))\,g(A)\,|\,X\right]=\mathbb {E} _{Y}\left[f(Y(X,a))\,|\,X\right]\,\mathbb {E} _{A}\left[g(A)\,|\,X\right]\end{aligned}}</math>。<br />
<br />
这意味着治疗分配只基于协变量数据,与潜在结果无关。<br />
* ('''A3''') 正值性(Positivity): 对于所有的 <math>a</math> 和 <math>x</math>,<math>P(A=a|X=x)>0 </math> 。<br />
<br />
==== 缺点 ====<br />
逆概率加权估计器(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么逻辑回归模型可能在尾部附近变得不稳定,导致逆概率加权估计器也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
另一种估计方法是增广逆概率加权估计器(Augmented Inverse Probability Weighted Estimator,AIPWE) 。它融合了基于回归的估计和逆概率加权估计的性质。因此,它是一种“双重稳健”的方法。因为它只需要正确指定倾向或结果模型,而不是同时指定。这种方法增强了逆概率加权估计,以减少了变异性并提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref>。<br />
<br />
=== 估计器公式 ===<br />
<br />
<math><br />
\begin{align}<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
符号定义如下:<br />
# <math>1_{A_{i}=a}</math> 是一个示性函数 ([[indicator function]]),指示受试者 i 是治疗组 a 的一部分(或不是)。<br />
# 对于某个个体i,基于协变量<math>X</math> 和处理 <math>A</math>,构建回归估计器 <math>\hat{Q}_n(x,a)</math> 去预测结果 <math>Y</math>。例如,使用普通最小二乘([[ordinary least squares]])回归。<br />
# 构建倾向(概率)估计 <math>\hat{p}_n(A_i|X_i)</math>. 例如,使用逻辑回归([[logistic regression]])。<br />
# 在AIPWE中结合得到 <math>\hat{\mu}^{AIPWE}_{a,n}</math>。<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in <ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>).<br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: \frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: \frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. link for the paper).<br />
<br />
公式的后期重新排列有助于揭示基本思想: 我们的估计是基于使用该模型的平均预测结果(即。: frac {1}{ n } sum { i = 1} ^ n Biggl (hat { q } _ n (x _ i,a) Biggr)).然而,如果模型是偏倚的,那么模型的残差将不会(在完整的治疗组 a)大约0。我们可以通过将模型的平均残差(q)与结果的真实值(y)相加的额外项来纠正这种潜在的偏差。: frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q _ n (x _ i,a) Biggr))).因为我们有 y 的缺失值,所以我们给出权值来膨胀每个剩余值的相对重要性(这些权值基于反向倾向,也就是 a。观察到每个主题的概率)(见 Kang,Joseph DY 和 Joseph l. Schafer 的第10页。去神秘化的双重稳健性: 从不完全数据估计人口平均值的替代策略的比较统计科学22.4(2007) : 523-539. 论文链接)。<br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either <math>\hat{Q}_n(X_i,a)</math> or <math>\hat{p}_{n}(A_{i}|X_{i})</math>, or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref><br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either \hat{Q}_n(X_i,a) or \hat{p}_{n}(A_{i}|X_{i}), or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. link to the paperSeaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. link to the paper<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(hat { q } _ n (xi,a)或 hat { p } _ { n }(a _ { i } | x _ { i }) ,或者两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均数残差很好地估计(并修正)。和 David Haziza。调查抽样中缺失数据的双重稳健推断24.1(2014) : 375-394. link to the paperSeaman,Shaun r. ,and Stijn Vansteelandt.“不完整数据的双重稳健方法介绍”统计科学: 数理统计研究所的评论杂志33.2(2018) : 184. 链接到论文<br />
<br />
The bias of the doubly robust estimators is called a '''second-order bias''', and it depends on the product of the difference <math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math> and the difference <math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>. This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using [[machine learning]] estimators (instead of parametric models).<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref><br />
<br />
The bias of the doubly robust estimators is called a second-order bias, and it depends on the product of the difference \frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})} and the difference \hat{Q}_n(X_i,a) - Q_n(X_i,a). This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using machine learning estimators (instead of parametric models).Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. link to the book - page 179<br />
<br />
双重稳健估计的偏差称为二阶偏差,它取决于差分 frac {1}{ hat { p }{ n }(a _ { i } | x _ { i })}-frac {1}{ p }{ n }(a _ { i } | x _ { i })}和差分{ q } _ n (x _ i,a)-q _ n (x _ i,a)的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差。米格尔 · a · 埃尔南和詹姆斯 · m · 罗宾斯。”因果推理”(2010) : 2. 链接到书-页179<br />
<br />
==参见==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}<br />
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[[Category:Survey methodology]]<br />
[[Category:Epidemiology]]<br />
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[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29488逆概率加权2022-03-23T14:01:49Z<p>Wei:/* 估计器公式 */</p>
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'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref name="refname2" />。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref name="refname3" />。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
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一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
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当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref name="refname1" />。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
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== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
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当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中 <br />
* <math> X \in \mathbb{R}^{p} </math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
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目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
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=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
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==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> , 其中 <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math>;<br />
# 使用任何倾向性模型(通常是逻辑回归模型)构建 <math>\hat{p}_{n}(a|x)</math> 或 <math>p(a|x)</math> ;<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math>。<br />
在计算出各处理组的平均数后,可以用统计学上的t检验或方差检验(ANOVA test)来判断组间平均数的差异,并确定处理效果的统计显著性。<br />
<br />
==== 假设 ====<br />
回顾对于协变量<math>X</math>,操作<math>A</math>和响应量<math>Y</math>的联合概率模型。当已知<math>X</math>和<math>A</math>分别为<math>x</math>和<math>a</math>时,响应量<math> Y(X=x,A=a)=Y(x,a)</math>的分布为<br />
<math>\begin{aligned}Y(x,a)\sim {\frac {P(x,a,\cdot )}{\int P(x,a,y)\,dy}}\end{aligned}</math>。<br />
<br />
我们做出以下假设:<br />
* ('''A1''')一致性(Consistency): <math>Y = Y^{*}(A)</math><br />
* ('''A2''') 没有未观测的混淆因子: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math>。更正式地说,对于每个有界和可测函数<math>f</math>和<math>g</math>,<br />
<math>{\begin{aligned}\qquad \mathbb {E} _{(A,Y)}\left[f(Y(X,a))\,g(A)\,|\,X\right]=\mathbb {E} _{Y}\left[f(Y(X,a))\,|\,X\right]\,\mathbb {E} _{A}\left[g(A)\,|\,X\right]\end{aligned}}</math>。<br />
<br />
这意味着治疗分配只基于协变量数据,与潜在结果无关。<br />
* ('''A3''') 正值性(Positivity): 对于所有的 <math>a</math> 和 <math>x</math>,<math>P(A=a|X=x)>0 </math> 。<br />
<br />
==== 缺点 ====<br />
逆概率加权估计器(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么逻辑回归模型可能在尾部附近变得不稳定,导致逆概率加权估计器也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
另一种估计方法是增广逆概率加权估计器(Augmented Inverse Probability Weighted Estimator,AIPWE) 。它融合了基于回归的估计和逆概率加权估计的性质。因此,它是一种“双重稳健”的方法。因为它只需要正确指定倾向或结果模型,而不是同时指定。这种方法增强了逆概率加权估计,以减少了变异性并提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref>。<br />
<br />
=== 估计器公式 ===<br />
<br />
<math><br />
\begin{align}<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
符号定义如下:<br />
# <math>1_{A_{i}=a}</math> 是一个示性函数 ([[indicator function]]),指示受试者 i 是治疗组 a 的一部分(或不是)。<br />
# 对于某个个体i,基于协变量<math>X</math> 和处理 <math>A</math>,构建回归估计器 <math>\hat{Q}_n(x,a)</math> 去预测结果 <math>Y</math>。例如,使用普通最小二乘([[ordinary least squares]])回归。<br />
# 构建倾向(概率)估计 <math>\hat{p}_n(A_i|X_i)</math>. 例如,使用逻辑回归([[logistic regression]])。<br />
# 在AIPWE中结合得到 <math>\hat{\mu}^{AIPWE}_{a,n}</math>。<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in <ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>).<br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: \frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: \frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. link for the paper).<br />
<br />
公式的后期重新排列有助于揭示基本思想: 我们的估计是基于使用该模型的平均预测结果(即。: frac {1}{ n } sum { i = 1} ^ n Biggl (hat { q } _ n (x _ i,a) Biggr)).然而,如果模型是偏倚的,那么模型的残差将不会(在完整的治疗组 a)大约0。我们可以通过将模型的平均残差(q)与结果的真实值(y)相加的额外项来纠正这种潜在的偏差。: frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q _ n (x _ i,a) Biggr))).因为我们有 y 的缺失值,所以我们给出权值来膨胀每个剩余值的相对重要性(这些权值基于反向倾向,也就是 a。观察到每个主题的概率)(见 Kang,Joseph DY 和 Joseph l. Schafer 的第10页。去神秘化的双重稳健性: 从不完全数据估计人口平均值的替代策略的比较统计科学22.4(2007) : 523-539. 论文链接)。<br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either <math>\hat{Q}_n(X_i,a)</math> or <math>\hat{p}_{n}(A_{i}|X_{i})</math>, or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref><br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either \hat{Q}_n(X_i,a) or \hat{p}_{n}(A_{i}|X_{i}), or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. link to the paperSeaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. link to the paper<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(hat { q } _ n (xi,a)或 hat { p } _ { n }(a _ { i } | x _ { i }) ,或者两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均数残差很好地估计(并修正)。和 David Haziza。调查抽样中缺失数据的双重稳健推断24.1(2014) : 375-394. link to the paperSeaman,Shaun r. ,and Stijn Vansteelandt.“不完整数据的双重稳健方法介绍”统计科学: 数理统计研究所的评论杂志33.2(2018) : 184. 链接到论文<br />
<br />
The bias of the doubly robust estimators is called a '''second-order bias''', and it depends on the product of the difference <math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math> and the difference <math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>. This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using [[machine learning]] estimators (instead of parametric models).<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref><br />
<br />
The bias of the doubly robust estimators is called a second-order bias, and it depends on the product of the difference \frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})} and the difference \hat{Q}_n(X_i,a) - Q_n(X_i,a). This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using machine learning estimators (instead of parametric models).Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. link to the book - page 179<br />
<br />
双重稳健估计的偏差称为二阶偏差,它取决于差分 frac {1}{ hat { p }{ n }(a _ { i } | x _ { i })}-frac {1}{ p }{ n }(a _ { i } | x _ { i })}和差分{ q } _ n (x _ i,a)-q _ n (x _ i,a)的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差。米格尔 · a · 埃尔南和詹姆斯 · m · 罗宾斯。”因果推理”(2010) : 2. 链接到书-页179<br />
<br />
==See also==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}<br />
<br />
[[Category:Survey methodology]]<br />
[[Category:Epidemiology]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29487逆概率加权2022-03-23T13:53:47Z<p>Wei:</p>
<hr />
<div><br />
<br />
'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref name="refname2" />。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref name="refname3" />。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
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一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
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当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref name="refname1" />。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
<br />
== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
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当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中 <br />
* <math> X \in \mathbb{R}^{p} </math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
<br />
目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
<br />
=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> , 其中 <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math>;<br />
# 使用任何倾向性模型(通常是逻辑回归模型)构建 <math>\hat{p}_{n}(a|x)</math> 或 <math>p(a|x)</math> ;<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math>。<br />
在计算出各处理组的平均数后,可以用统计学上的t检验或方差检验(ANOVA test)来判断组间平均数的差异,并确定处理效果的统计显著性。<br />
<br />
==== 假设 ====<br />
回顾对于协变量<math>X</math>,操作<math>A</math>和响应量<math>Y</math>的联合概率模型。当已知<math>X</math>和<math>A</math>分别为<math>x</math>和<math>a</math>时,响应量<math> Y(X=x,A=a)=Y(x,a)</math>的分布为<br />
<math>\begin{aligned}Y(x,a)\sim {\frac {P(x,a,\cdot )}{\int P(x,a,y)\,dy}}\end{aligned}</math>。<br />
<br />
我们做出以下假设:<br />
* ('''A1''')一致性(Consistency): <math>Y = Y^{*}(A)</math><br />
* ('''A2''') 没有未观测的混淆因子: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math>。更正式地说,对于每个有界和可测函数<math>f</math>和<math>g</math>,<br />
<math>{\begin{aligned}\qquad \mathbb {E} _{(A,Y)}\left[f(Y(X,a))\,g(A)\,|\,X\right]=\mathbb {E} _{Y}\left[f(Y(X,a))\,|\,X\right]\,\mathbb {E} _{A}\left[g(A)\,|\,X\right]\end{aligned}}</math>。<br />
<br />
这意味着治疗分配只基于协变量数据,与潜在结果无关。<br />
* ('''A3''') 正值性(Positivity): 对于所有的 <math>a</math> 和 <math>x</math>,<math>P(A=a|X=x)>0 </math> 。<br />
<br />
==== 缺点 ====<br />
逆概率加权估计器(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么逻辑回归模型可能在尾部附近变得不稳定,导致逆概率加权估计器也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
另一种估计方法是增广逆概率加权估计器(Augmented Inverse Probability Weighted Estimator,AIPWE) 。它融合了基于回归的估计和逆概率加权估计的性质。因此,它是一种“双重稳健”的方法。因为它只需要正确指定倾向或结果模型,而不是同时指定。这种方法增强了逆概率加权估计,以减少了变异性并提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref>。<br />
<br />
=== 估计器公式 ===<br />
<math><br />
\begin{align}<br />
<br />
<math><br />
\begin{align}<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
如果你想要的话,你可以选择<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
Frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q } _ n (x _ i,a) Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
符号定义如下:<br />
# <math>1_{A_{i}=a}</math> 是一个示性函数 ([[indicator function]]),指示受试者 i 是治疗组 a 的一部分(或不是)。<br />
# 对于某个个体i,基于协变量<math>X</math> 和处理 <math>A</math>,构建回归估计器 <math>\hat{Q}_n(x,a)</math> 去预测结果 <math>Y</math>。例如,使用普通最小二乘([[ordinary least squares]])回归。<br />
# 构建倾向(概率)估计 <math>\hat{p}_n(A_i|X_i)</math>. 例如,使用逻辑回归([[logistic regression]])。<br />
# 在AIPWE结合得到 <math>\hat{\mu}^{AIPWE}_{a,n}</math>。<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in <ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>).<br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: \frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: \frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. link for the paper).<br />
<br />
公式的后期重新排列有助于揭示基本思想: 我们的估计是基于使用该模型的平均预测结果(即。: frac {1}{ n } sum { i = 1} ^ n Biggl (hat { q } _ n (x _ i,a) Biggr)).然而,如果模型是偏倚的,那么模型的残差将不会(在完整的治疗组 a)大约0。我们可以通过将模型的平均残差(q)与结果的真实值(y)相加的额外项来纠正这种潜在的偏差。: frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q _ n (x _ i,a) Biggr))).因为我们有 y 的缺失值,所以我们给出权值来膨胀每个剩余值的相对重要性(这些权值基于反向倾向,也就是 a。观察到每个主题的概率)(见 Kang,Joseph DY 和 Joseph l. Schafer 的第10页。去神秘化的双重稳健性: 从不完全数据估计人口平均值的替代策略的比较统计科学22.4(2007) : 523-539. 论文链接)。<br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either <math>\hat{Q}_n(X_i,a)</math> or <math>\hat{p}_{n}(A_{i}|X_{i})</math>, or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref><br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either \hat{Q}_n(X_i,a) or \hat{p}_{n}(A_{i}|X_{i}), or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. link to the paperSeaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. link to the paper<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(hat { q } _ n (xi,a)或 hat { p } _ { n }(a _ { i } | x _ { i }) ,或者两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均数残差很好地估计(并修正)。和 David Haziza。调查抽样中缺失数据的双重稳健推断24.1(2014) : 375-394. link to the paperSeaman,Shaun r. ,and Stijn Vansteelandt.“不完整数据的双重稳健方法介绍”统计科学: 数理统计研究所的评论杂志33.2(2018) : 184. 链接到论文<br />
<br />
The bias of the doubly robust estimators is called a '''second-order bias''', and it depends on the product of the difference <math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math> and the difference <math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>. This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using [[machine learning]] estimators (instead of parametric models).<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref><br />
<br />
The bias of the doubly robust estimators is called a second-order bias, and it depends on the product of the difference \frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})} and the difference \hat{Q}_n(X_i,a) - Q_n(X_i,a). This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using machine learning estimators (instead of parametric models).Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. link to the book - page 179<br />
<br />
双重稳健估计的偏差称为二阶偏差,它取决于差分 frac {1}{ hat { p }{ n }(a _ { i } | x _ { i })}-frac {1}{ p }{ n }(a _ { i } | x _ { i })}和差分{ q } _ n (x _ i,a)-q _ n (x _ i,a)的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差。米格尔 · a · 埃尔南和詹姆斯 · m · 罗宾斯。”因果推理”(2010) : 2. 链接到书-页179<br />
<br />
==See also==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}<br />
<br />
[[Category:Survey methodology]]<br />
[[Category:Epidemiology]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29485逆概率加权2022-03-23T13:44:06Z<p>Wei:</p>
<hr />
<div><br />
<br />
'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref name="refname2" />。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref name="refname3" />。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
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一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
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当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref name="refname1" />。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
<br />
== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
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当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中 <br />
* <math> X \in \mathbb{R}^{p} </math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
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目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
<br />
=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> , 其中 <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math>;<br />
# 使用任何倾向性模型(通常是逻辑回归模型)构造 <math>\hat{p}_{n}(a|x)</math> 或 <math>p(a|x)</math> ;<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math>。<br />
在计算出各处理组的平均数后,可以用统计学上的t检验或方差检验(ANOVA test)来判断组间平均数的差异,并确定处理效果的统计显著性。<br />
<br />
==== 假设 ====<br />
回顾对于协变量<math>X</math>,操作<math>A</math>和响应量<math>Y</math>的联合概率模型。当已知<math>X</math>和<math>A</math>分别为<math>x</math>和<math>a</math>时,响应量<math> Y(X=x,A=a)=Y(x,a)</math>的分布为<br />
<math>\begin{aligned}Y(x,a)\sim {\frac {P(x,a,\cdot )}{\int P(x,a,y)\,dy}}\end{aligned}</math>。<br />
<br />
我们做出以下假设:<br />
* ('''A1''')一致性(Consistency): <math>Y = Y^{*}(A)</math><br />
* ('''A2''') 没有未观测的混淆因子: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math>。更正式地说,对于每个有界和可测函数<math>f</math>和<math>g</math>,<br />
<math>{\begin{aligned}\qquad \mathbb {E} _{(A,Y)}\left[f(Y(X,a))\,g(A)\,|\,X\right]=\mathbb {E} _{Y}\left[f(Y(X,a))\,|\,X\right]\,\mathbb {E} _{A}\left[g(A)\,|\,X\right]\end{aligned}}</math>。<br />
<br />
这意味着治疗分配只基于协变量数据,与潜在结果无关。<br />
* ('''A3''') 正值性(Positivity): 对于所有的 <math>a</math> 和 <math>x</math>,<math>P(A=a|X=x)>0 </math> 。<br />
<br />
==== 缺点 ====<br />
逆概率加权估计量(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么逻辑回归模型可能在尾部附近变得不稳定,导致逆概率加权估计量也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<br />
<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<br />
<br />
另一种估计方法是增广逆概率加权估计(Augmented Inverse Probability Weighted Estimator,AIPWE) 。它融合了基于回归的估计和逆概率加权估计的性质。因此,它是一种“双重稳健”的方法。因为它只需要正确指定倾向或结果模型,而不是同时指定。这种方法增强了逆概率加权估计,以减少了变异性并提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref>。<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
<math><br />
\begin{align}<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
如果你想要的话,你可以选择<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
Frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q } _ n (x _ i,a) Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
With the following notations:<br />
# <math>1_{A_{i}=a}</math> is an [[indicator function]] if subject i is part of treatment group a (or not).<br />
# Construct regression estimator <math>\hat{Q}_n(x,a)</math> to predict outcome <math>Y</math> based on covariates <math>X</math> and treatment <math>A</math>, for some subject i. For example, using [[ordinary least squares]] regression.<br />
# Construct propensity (probability) estimate <math>\hat{p}_n(A_i|X_i)</math>. For example, using [[logistic regression]].<br />
# Combine in AIPWE to obtain <math>\hat{\mu}^{AIPWE}_{a,n}</math><br />
<br />
With the following notations:<br />
# 1_{A_{i}=a} is an indicator function if subject i is part of treatment group a (or not).<br />
# Construct regression estimator \hat{Q}_n(x,a) to predict outcome Y based on covariates X and treatment A, for some subject i. For example, using ordinary least squares regression.<br />
# Construct propensity (probability) estimate \hat{p}_n(A_i|X_i). For example, using logistic regression.<br />
# Combine in AIPWE to obtain \hat{\mu}^{AIPWE}_{a,n}<br />
<br />
用下面的符号: # 1{ a { i } = a }是一个指示函数,如果主体 i 是治疗组 a 的一部分(或不是)。# 基于协变量 x 和处理 a 构造回归估计量{ q } _ n (x,a)来预测结果 y。例如,使用一般最小平方法回归。# 构造倾向(概率)估计{ p } _ n (a _ i | x _ i)。例如,使用 Logit模型。# 在 AIPWE 中组合以获得 hat { mu } ^ { AIPWE } _ { a,n }<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in <ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>).<br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: \frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: \frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. link for the paper).<br />
<br />
公式的后期重新排列有助于揭示基本思想: 我们的估计是基于使用该模型的平均预测结果(即。: frac {1}{ n } sum { i = 1} ^ n Biggl (hat { q } _ n (x _ i,a) Biggr)).然而,如果模型是偏倚的,那么模型的残差将不会(在完整的治疗组 a)大约0。我们可以通过将模型的平均残差(q)与结果的真实值(y)相加的额外项来纠正这种潜在的偏差。: frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q _ n (x _ i,a) Biggr))).因为我们有 y 的缺失值,所以我们给出权值来膨胀每个剩余值的相对重要性(这些权值基于反向倾向,也就是 a。观察到每个主题的概率)(见 Kang,Joseph DY 和 Joseph l. Schafer 的第10页。去神秘化的双重稳健性: 从不完全数据估计人口平均值的替代策略的比较统计科学22.4(2007) : 523-539. 论文链接)。<br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either <math>\hat{Q}_n(X_i,a)</math> or <math>\hat{p}_{n}(A_{i}|X_{i})</math>, or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref><br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either \hat{Q}_n(X_i,a) or \hat{p}_{n}(A_{i}|X_{i}), or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. link to the paperSeaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. link to the paper<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(hat { q } _ n (xi,a)或 hat { p } _ { n }(a _ { i } | x _ { i }) ,或者两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均数残差很好地估计(并修正)。和 David Haziza。调查抽样中缺失数据的双重稳健推断24.1(2014) : 375-394. link to the paperSeaman,Shaun r. ,and Stijn Vansteelandt.“不完整数据的双重稳健方法介绍”统计科学: 数理统计研究所的评论杂志33.2(2018) : 184. 链接到论文<br />
<br />
The bias of the doubly robust estimators is called a '''second-order bias''', and it depends on the product of the difference <math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math> and the difference <math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>. This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using [[machine learning]] estimators (instead of parametric models).<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref><br />
<br />
The bias of the doubly robust estimators is called a second-order bias, and it depends on the product of the difference \frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})} and the difference \hat{Q}_n(X_i,a) - Q_n(X_i,a). This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using machine learning estimators (instead of parametric models).Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. link to the book - page 179<br />
<br />
双重稳健估计的偏差称为二阶偏差,它取决于差分 frac {1}{ hat { p }{ n }(a _ { i } | x _ { i })}-frac {1}{ p }{ n }(a _ { i } | x _ { i })}和差分{ q } _ n (x _ i,a)-q _ n (x _ i,a)的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差。米格尔 · a · 埃尔南和詹姆斯 · m · 罗宾斯。”因果推理”(2010) : 2. 链接到书-页179<br />
<br />
==See also==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}<br />
<br />
[[Category:Survey methodology]]<br />
[[Category:Epidemiology]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29484逆概率加权2022-03-23T13:40:25Z<p>Wei:</p>
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<div><br />
<br />
'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref name="refname2" />。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref name="refname3" />。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
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一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
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当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref name="refname1" />。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
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== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
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当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中 <br />
* <math> X \in \mathbb{R}^{p} </math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
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目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
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=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> , 其中 <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math>;<br />
# 使用任何倾向性模型(通常是逻辑回归模型)构造 <math>\hat{p}_{n}(a|x)</math> 或 <math>p(a|x)</math> ;<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math>。<br />
在计算出各处理组的平均数后,可以用统计学上的t检验或方差检验(ANOVA test)来判断组间平均数的差异,并确定处理效果的统计显著性。<br />
<br />
==== 假设 ====<br />
回顾对于协变量<math>X</math>,操作<math>A</math>和响应量<math>Y</math>的联合概率模型。当已知<math>X</math>和<math>A</math>分别为<math>x</math>和<math>a</math>时,响应量<math> Y(X=x,A=a)=Y(x,a)</math>的分布为<br />
<math>\begin{aligned}Y(x,a)\sim {\frac {P(x,a,\cdot )}{\int P(x,a,y)\,dy}}\end{aligned}}</math>。<br />
<br />
我们做出以下假设:<br />
# ('''A1''')一致性(Consistency): <math>Y = Y^{*}(A)</math><br />
# ('''A2''') 没有未观测的混淆因子: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math>。更正式地说,对于每个有界和可测函数<math>f</math>和<math>g</math>,<br />
<math>{\begin{aligned}\qquad \mathbb {E} _{(A,Y)}\left[f(Y(X,a))\,g(A)\,|\,X\right]=\mathbb {E} _{Y}\left[f(Y(X,a))\,|\,X\right]\,\mathbb {E} _{A}\left[g(A)\,|\,X\right].\end{aligned}}</math><br />
这意味着治疗分配只基于协变量数据,与潜在结果无关。<br />
# ('''A3''') 正值性(Positivity): 对于所有的 <math>a</math> 和 <math>x</math>,<math>P(A=a|X=x)>0 </math> 。<br />
<br />
==== 缺点 ====<br />
逆概率加权估计量(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么逻辑回归模型可能在尾部附近变得不稳定,导致逆概率加权估计量也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<br />
<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<br />
<br />
另一种估计方法是增广逆概率加权估计(Augmented Inverse Probability Weighted Estimator,AIPWE) 。它融合了基于回归的估计和逆概率加权估计的性质。因此,它是一种“双重稳健”的方法。因为它只需要正确指定倾向或结果模型,而不是同时指定。这种方法增强了逆概率加权估计,以减少了变异性并提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref>。<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
<math><br />
\begin{align}<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
如果你想要的话,你可以选择<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
Frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q } _ n (x _ i,a) Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
With the following notations:<br />
# <math>1_{A_{i}=a}</math> is an [[indicator function]] if subject i is part of treatment group a (or not).<br />
# Construct regression estimator <math>\hat{Q}_n(x,a)</math> to predict outcome <math>Y</math> based on covariates <math>X</math> and treatment <math>A</math>, for some subject i. For example, using [[ordinary least squares]] regression.<br />
# Construct propensity (probability) estimate <math>\hat{p}_n(A_i|X_i)</math>. For example, using [[logistic regression]].<br />
# Combine in AIPWE to obtain <math>\hat{\mu}^{AIPWE}_{a,n}</math><br />
<br />
With the following notations:<br />
# 1_{A_{i}=a} is an indicator function if subject i is part of treatment group a (or not).<br />
# Construct regression estimator \hat{Q}_n(x,a) to predict outcome Y based on covariates X and treatment A, for some subject i. For example, using ordinary least squares regression.<br />
# Construct propensity (probability) estimate \hat{p}_n(A_i|X_i). For example, using logistic regression.<br />
# Combine in AIPWE to obtain \hat{\mu}^{AIPWE}_{a,n}<br />
<br />
用下面的符号: # 1{ a { i } = a }是一个指示函数,如果主体 i 是治疗组 a 的一部分(或不是)。# 基于协变量 x 和处理 a 构造回归估计量{ q } _ n (x,a)来预测结果 y。例如,使用一般最小平方法回归。# 构造倾向(概率)估计{ p } _ n (a _ i | x _ i)。例如,使用 Logit模型。# 在 AIPWE 中组合以获得 hat { mu } ^ { AIPWE } _ { a,n }<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in <ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>).<br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: \frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: \frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. link for the paper).<br />
<br />
公式的后期重新排列有助于揭示基本思想: 我们的估计是基于使用该模型的平均预测结果(即。: frac {1}{ n } sum { i = 1} ^ n Biggl (hat { q } _ n (x _ i,a) Biggr)).然而,如果模型是偏倚的,那么模型的残差将不会(在完整的治疗组 a)大约0。我们可以通过将模型的平均残差(q)与结果的真实值(y)相加的额外项来纠正这种潜在的偏差。: frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q _ n (x _ i,a) Biggr))).因为我们有 y 的缺失值,所以我们给出权值来膨胀每个剩余值的相对重要性(这些权值基于反向倾向,也就是 a。观察到每个主题的概率)(见 Kang,Joseph DY 和 Joseph l. Schafer 的第10页。去神秘化的双重稳健性: 从不完全数据估计人口平均值的替代策略的比较统计科学22.4(2007) : 523-539. 论文链接)。<br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either <math>\hat{Q}_n(X_i,a)</math> or <math>\hat{p}_{n}(A_{i}|X_{i})</math>, or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref><br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either \hat{Q}_n(X_i,a) or \hat{p}_{n}(A_{i}|X_{i}), or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. link to the paperSeaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. link to the paper<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(hat { q } _ n (xi,a)或 hat { p } _ { n }(a _ { i } | x _ { i }) ,或者两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均数残差很好地估计(并修正)。和 David Haziza。调查抽样中缺失数据的双重稳健推断24.1(2014) : 375-394. link to the paperSeaman,Shaun r. ,and Stijn Vansteelandt.“不完整数据的双重稳健方法介绍”统计科学: 数理统计研究所的评论杂志33.2(2018) : 184. 链接到论文<br />
<br />
The bias of the doubly robust estimators is called a '''second-order bias''', and it depends on the product of the difference <math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math> and the difference <math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>. This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using [[machine learning]] estimators (instead of parametric models).<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref><br />
<br />
The bias of the doubly robust estimators is called a second-order bias, and it depends on the product of the difference \frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})} and the difference \hat{Q}_n(X_i,a) - Q_n(X_i,a). This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using machine learning estimators (instead of parametric models).Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. link to the book - page 179<br />
<br />
双重稳健估计的偏差称为二阶偏差,它取决于差分 frac {1}{ hat { p }{ n }(a _ { i } | x _ { i })}-frac {1}{ p }{ n }(a _ { i } | x _ { i })}和差分{ q } _ n (x _ i,a)-q _ n (x _ i,a)的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差。米格尔 · a · 埃尔南和詹姆斯 · m · 罗宾斯。”因果推理”(2010) : 2. 链接到书-页179<br />
<br />
==See also==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}<br />
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[[Category:Survey methodology]]<br />
[[Category:Epidemiology]]<br />
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[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29483逆概率加权2022-03-23T13:26:12Z<p>Wei:</p>
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<div><br />
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'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref name="refname2" />。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref name="refname3" />。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
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一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
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当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref name="refname1" />。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
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== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
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当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
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假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中 <br />
* <math> X \in \mathbb{R}^{p} </math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
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目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
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=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
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==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> , 其中 <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math>;<br />
# 使用任何倾向性模型(通常是逻辑回归模型)构造 <math>\hat{p}_{n}(a|x)</math> 或 <math>p(a|x)</math> ;<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math>。<br />
在计算出各处理组的平均数后,可以用统计学上的t检验或方差检验(ANOVA test)来判断组间平均数的差异,并确定处理效果的统计显著性。<br />
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==== 假设 ====<br />
回顾对于协变量,操作和响应量的联合概率模型。当已知分别为,响应量的分布为<br />
<br />
<br />
我们做出以下假设:<br />
# (A1)一致性(Consistency): <math>Y = Y^{*}(A)</math><br />
# (A2) 没有未观测的混淆因子: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math>。更正式地说,对于每个有界和可测函数 <br />
#* 这意味着治疗分配只基于协变量数据,与潜在结果无关。<br />
# (A3) 正值性(Positivity): 对于所有的 <math>a</math> 和 <math>x</math>,<math>P(A=a|X=x)>0 </math> 。<br />
<br />
==== 缺点 ====<br />
逆概率加权估计量(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么逻辑回归模型可能在尾部附近变得不稳定,导致逆概率加权估计量也变得不稳定。<br />
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== 增广逆概率加权估计器 ==<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<br />
<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<br />
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另一种估计方法是增广逆概率加权估计(Augmented Inverse Probability Weighted Estimator,AIPWE) 。它融合了基于回归的估计和逆概率加权估计的性质。因此,它是一种“双重稳健”的方法。因为它只需要正确指定倾向或结果模型,而不是同时指定。这种方法增强了逆概率加权估计,以减少了变异性并提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref>。<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
<math><br />
\begin{align}<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
如果你想要的话,你可以选择<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
Frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q } _ n (x _ i,a) Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
With the following notations:<br />
# <math>1_{A_{i}=a}</math> is an [[indicator function]] if subject i is part of treatment group a (or not).<br />
# Construct regression estimator <math>\hat{Q}_n(x,a)</math> to predict outcome <math>Y</math> based on covariates <math>X</math> and treatment <math>A</math>, for some subject i. For example, using [[ordinary least squares]] regression.<br />
# Construct propensity (probability) estimate <math>\hat{p}_n(A_i|X_i)</math>. For example, using [[logistic regression]].<br />
# Combine in AIPWE to obtain <math>\hat{\mu}^{AIPWE}_{a,n}</math><br />
<br />
With the following notations:<br />
# 1_{A_{i}=a} is an indicator function if subject i is part of treatment group a (or not).<br />
# Construct regression estimator \hat{Q}_n(x,a) to predict outcome Y based on covariates X and treatment A, for some subject i. For example, using ordinary least squares regression.<br />
# Construct propensity (probability) estimate \hat{p}_n(A_i|X_i). For example, using logistic regression.<br />
# Combine in AIPWE to obtain \hat{\mu}^{AIPWE}_{a,n}<br />
<br />
用下面的符号: # 1{ a { i } = a }是一个指示函数,如果主体 i 是治疗组 a 的一部分(或不是)。# 基于协变量 x 和处理 a 构造回归估计量{ q } _ n (x,a)来预测结果 y。例如,使用一般最小平方法回归。# 构造倾向(概率)估计{ p } _ n (a _ i | x _ i)。例如,使用 Logit模型。# 在 AIPWE 中组合以获得 hat { mu } ^ { AIPWE } _ { a,n }<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in <ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>).<br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: \frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: \frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. link for the paper).<br />
<br />
公式的后期重新排列有助于揭示基本思想: 我们的估计是基于使用该模型的平均预测结果(即。: frac {1}{ n } sum { i = 1} ^ n Biggl (hat { q } _ n (x _ i,a) Biggr)).然而,如果模型是偏倚的,那么模型的残差将不会(在完整的治疗组 a)大约0。我们可以通过将模型的平均残差(q)与结果的真实值(y)相加的额外项来纠正这种潜在的偏差。: frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q _ n (x _ i,a) Biggr))).因为我们有 y 的缺失值,所以我们给出权值来膨胀每个剩余值的相对重要性(这些权值基于反向倾向,也就是 a。观察到每个主题的概率)(见 Kang,Joseph DY 和 Joseph l. Schafer 的第10页。去神秘化的双重稳健性: 从不完全数据估计人口平均值的替代策略的比较统计科学22.4(2007) : 523-539. 论文链接)。<br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either <math>\hat{Q}_n(X_i,a)</math> or <math>\hat{p}_{n}(A_{i}|X_{i})</math>, or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref><br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either \hat{Q}_n(X_i,a) or \hat{p}_{n}(A_{i}|X_{i}), or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. link to the paperSeaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. link to the paper<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(hat { q } _ n (xi,a)或 hat { p } _ { n }(a _ { i } | x _ { i }) ,或者两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均数残差很好地估计(并修正)。和 David Haziza。调查抽样中缺失数据的双重稳健推断24.1(2014) : 375-394. link to the paperSeaman,Shaun r. ,and Stijn Vansteelandt.“不完整数据的双重稳健方法介绍”统计科学: 数理统计研究所的评论杂志33.2(2018) : 184. 链接到论文<br />
<br />
The bias of the doubly robust estimators is called a '''second-order bias''', and it depends on the product of the difference <math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math> and the difference <math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>. This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using [[machine learning]] estimators (instead of parametric models).<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref><br />
<br />
The bias of the doubly robust estimators is called a second-order bias, and it depends on the product of the difference \frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})} and the difference \hat{Q}_n(X_i,a) - Q_n(X_i,a). This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using machine learning estimators (instead of parametric models).Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. link to the book - page 179<br />
<br />
双重稳健估计的偏差称为二阶偏差,它取决于差分 frac {1}{ hat { p }{ n }(a _ { i } | x _ { i })}-frac {1}{ p }{ n }(a _ { i } | x _ { i })}和差分{ q } _ n (x _ i,a)-q _ n (x _ i,a)的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差。米格尔 · a · 埃尔南和詹姆斯 · m · 罗宾斯。”因果推理”(2010) : 2. 链接到书-页179<br />
<br />
==See also==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}<br />
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[[Category:Survey methodology]]<br />
[[Category:Epidemiology]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29482逆概率加权2022-03-23T13:07:13Z<p>Wei:</p>
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<div><br />
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'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref name="refname2" />。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref name="refname3" />。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
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一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
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当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref name="refname1" />。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
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== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
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当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
Suppose observed data are <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math> drawn [[Independent and identically distributed random variables|i.i.d ()]] from unknown distribution P, where<br />
* <math>X \in \mathbb{R}^{p}</math> covariates<br />
* <math>A \in \{0, 1\}</math> are the two possible treatments.<br />
* <math>Y \in \mathbb{R}</math> response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, <math>Y^{*}\bigl(a\bigr)</math>, that would be observed if the subject were assigned treatment <math>a</math>. Then compare the mean outcome if all patients in the population were assigned either treatment: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>. We want to estimate <math>\mu_a</math> using observed data <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>.<br />
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Suppose observed data are \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1} drawn i.i.d (independent and identically distributed) from unknown distribution P, where<br />
* X \in \mathbb{R}^{p} covariates<br />
* A \in \{0, 1\} are the two possible treatments.<br />
* Y \in \mathbb{R} response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, Y^{*}\bigl(a\bigr), that would be observed if the subject were assigned treatment a. Then compare the mean outcome if all patients in the population were assigned either treatment: \mu_{a} = \mathbb{E}Y^{*}(a). We want to estimate \mu_a using observed data \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}.<br />
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假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中 <br />
* <math> X \in \mathbb{R}^{p} </math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
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目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
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=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
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\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}<br />
<br />
==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> where <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math><br />
# construct <math>\hat{p}_{n}(a|x)</math> or <math>p(a|x)</math> using any propensity model (often a logistic regression model)<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math><br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
# \mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)} where p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}<br />
# construct \hat{p}_{n}(a|x) or p(a|x) using any propensity model (often a logistic regression model)<br />
# \hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}<br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
= = = = = = = # mu { a } = mathbb { e } frac { mathbf {1}{ a = a } y }{ p (a | x)}其中 p (a | x) = frac { p (a = a,x = x)}{ p (x = x)}}{ p (x = x)}} # construct hat { p }{ n }(a | x)或 p (a | x)使用任意模型(通常是 Logit模型模型) # 帽子{ mu } ^ { IPWE } _ { a,n } = sum ^ { n } _ { i = 1} frac { y { i }1 _ { a _ { i } = a }{ n hat { p } _ { n }(a _ { i } | x { i })计算每个治疗组的平均值,方差分析和统计 t 检验可以用来判断治疗效果的差异,并确定治疗效果的统计显著性。<br />
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==== 假设 ====<br />
# Consistency: <math>Y = Y^{*}(A)</math><br />
# No unmeasured confounders: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math> <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: <math>P(A=a|X=x)>0 </math> for all <math>a</math> and <math>x</math><br />
<br />
# Consistency: Y = Y^{*}(A)<br />
# No unmeasured confounders: \{Y^{*}(0), Y^{*}(1)\} \perp A|X <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: P(A=a|X=x)>0 for all a and x<br />
<br />
= = = = = = = = = = # 一致性: y = y ^ { <br />
* }(a) # 不存在未测量的混杂因素: { y ^ { <br />
* }(0) ,y ^ { <br />
* }(1)} a/p | x # <br />
* 治疗分配完全基于协数据,与潜在结果无关。# 正性: p (a = a | x = x) > 0表示所有 a 和 x<br />
<br />
==== Limitations ====<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
= = = = 极限 = = = = = 反概率加权估计量(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么 Logit模型模型可能在尾部附近变得不稳定,导致 IPWE 也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref><br />
<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<br />
<br />
另一种估计是增广逆概率加权估计(Augmented Inverse Probability Weighted Estimator,AIPWE) ,它综合了基于回归的估计和逆概率加权估计的性质。因此,这是一个双重稳健的方法,因为它只需要正确指定倾向或结果模型,而不是两者都要求。这种方法增强了 IPWE,减少了变异性,提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件。<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
<math><br />
\begin{align}<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
如果你想要的话,你可以选择<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
Frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q } _ n (x _ i,a) Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
With the following notations:<br />
# <math>1_{A_{i}=a}</math> is an [[indicator function]] if subject i is part of treatment group a (or not).<br />
# Construct regression estimator <math>\hat{Q}_n(x,a)</math> to predict outcome <math>Y</math> based on covariates <math>X</math> and treatment <math>A</math>, for some subject i. For example, using [[ordinary least squares]] regression.<br />
# Construct propensity (probability) estimate <math>\hat{p}_n(A_i|X_i)</math>. For example, using [[logistic regression]].<br />
# Combine in AIPWE to obtain <math>\hat{\mu}^{AIPWE}_{a,n}</math><br />
<br />
With the following notations:<br />
# 1_{A_{i}=a} is an indicator function if subject i is part of treatment group a (or not).<br />
# Construct regression estimator \hat{Q}_n(x,a) to predict outcome Y based on covariates X and treatment A, for some subject i. For example, using ordinary least squares regression.<br />
# Construct propensity (probability) estimate \hat{p}_n(A_i|X_i). For example, using logistic regression.<br />
# Combine in AIPWE to obtain \hat{\mu}^{AIPWE}_{a,n}<br />
<br />
用下面的符号: # 1{ a { i } = a }是一个指示函数,如果主体 i 是治疗组 a 的一部分(或不是)。# 基于协变量 x 和处理 a 构造回归估计量{ q } _ n (x,a)来预测结果 y。例如,使用一般最小平方法回归。# 构造倾向(概率)估计{ p } _ n (a _ i | x _ i)。例如,使用 Logit模型。# 在 AIPWE 中组合以获得 hat { mu } ^ { AIPWE } _ { a,n }<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in <ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>).<br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: \frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: \frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. link for the paper).<br />
<br />
公式的后期重新排列有助于揭示基本思想: 我们的估计是基于使用该模型的平均预测结果(即。: frac {1}{ n } sum { i = 1} ^ n Biggl (hat { q } _ n (x _ i,a) Biggr)).然而,如果模型是偏倚的,那么模型的残差将不会(在完整的治疗组 a)大约0。我们可以通过将模型的平均残差(q)与结果的真实值(y)相加的额外项来纠正这种潜在的偏差。: frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q _ n (x _ i,a) Biggr))).因为我们有 y 的缺失值,所以我们给出权值来膨胀每个剩余值的相对重要性(这些权值基于反向倾向,也就是 a。观察到每个主题的概率)(见 Kang,Joseph DY 和 Joseph l. Schafer 的第10页。去神秘化的双重稳健性: 从不完全数据估计人口平均值的替代策略的比较统计科学22.4(2007) : 523-539. 论文链接)。<br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either <math>\hat{Q}_n(X_i,a)</math> or <math>\hat{p}_{n}(A_{i}|X_{i})</math>, or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref><br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either \hat{Q}_n(X_i,a) or \hat{p}_{n}(A_{i}|X_{i}), or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. link to the paperSeaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. link to the paper<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(hat { q } _ n (xi,a)或 hat { p } _ { n }(a _ { i } | x _ { i }) ,或者两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均数残差很好地估计(并修正)。和 David Haziza。调查抽样中缺失数据的双重稳健推断24.1(2014) : 375-394. link to the paperSeaman,Shaun r. ,and Stijn Vansteelandt.“不完整数据的双重稳健方法介绍”统计科学: 数理统计研究所的评论杂志33.2(2018) : 184. 链接到论文<br />
<br />
The bias of the doubly robust estimators is called a '''second-order bias''', and it depends on the product of the difference <math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math> and the difference <math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>. This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using [[machine learning]] estimators (instead of parametric models).<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref><br />
<br />
The bias of the doubly robust estimators is called a second-order bias, and it depends on the product of the difference \frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})} and the difference \hat{Q}_n(X_i,a) - Q_n(X_i,a). This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using machine learning estimators (instead of parametric models).Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. link to the book - page 179<br />
<br />
双重稳健估计的偏差称为二阶偏差,它取决于差分 frac {1}{ hat { p }{ n }(a _ { i } | x _ { i })}-frac {1}{ p }{ n }(a _ { i } | x _ { i })}和差分{ q } _ n (x _ i,a)-q _ n (x _ i,a)的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差。米格尔 · a · 埃尔南和詹姆斯 · m · 罗宾斯。”因果推理”(2010) : 2. 链接到书-页179<br />
<br />
==See also==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}<br />
<br />
[[Category:Survey methodology]]<br />
[[Category:Epidemiology]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29481逆概率加权2022-03-23T13:05:02Z<p>Wei:</p>
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<div><br />
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'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref name="refname2" />。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref name="refname3" />。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
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一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
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当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref name="refname1" />。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
<br />
== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
<br />
<br />
当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
Suppose observed data are <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math> drawn [[Independent and identically distributed random variables|i.i.d ()]] from unknown distribution P, where<br />
* <math>X \in \mathbb{R}^{p}</math> covariates<br />
* <math>A \in \{0, 1\}</math> are the two possible treatments.<br />
* <math>Y \in \mathbb{R}</math> response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, <math>Y^{*}\bigl(a\bigr)</math>, that would be observed if the subject were assigned treatment <math>a</math>. Then compare the mean outcome if all patients in the population were assigned either treatment: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>. We want to estimate <math>\mu_a</math> using observed data <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>.<br />
<br />
Suppose observed data are \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1} drawn i.i.d (independent and identically distributed) from unknown distribution P, where<br />
* X \in \mathbb{R}^{p} covariates<br />
* A \in \{0, 1\} are the two possible treatments.<br />
* Y \in \mathbb{R} response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, Y^{*}\bigl(a\bigr), that would be observed if the subject were assigned treatment a. Then compare the mean outcome if all patients in the population were assigned either treatment: \mu_{a} = \mathbb{E}Y^{*}(a). We want to estimate \mu_a using observed data \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}.<br />
<br />
假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中 <br />
* <math>X \in \mathbb{R}^{p}</math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
<br />
目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
<br />
=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}<br />
<br />
==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> where <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math><br />
# construct <math>\hat{p}_{n}(a|x)</math> or <math>p(a|x)</math> using any propensity model (often a logistic regression model)<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math><br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
# \mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)} where p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}<br />
# construct \hat{p}_{n}(a|x) or p(a|x) using any propensity model (often a logistic regression model)<br />
# \hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}<br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
= = = = = = = # mu { a } = mathbb { e } frac { mathbf {1}{ a = a } y }{ p (a | x)}其中 p (a | x) = frac { p (a = a,x = x)}{ p (x = x)}}{ p (x = x)}} # construct hat { p }{ n }(a | x)或 p (a | x)使用任意模型(通常是 Logit模型模型) # 帽子{ mu } ^ { IPWE } _ { a,n } = sum ^ { n } _ { i = 1} frac { y { i }1 _ { a _ { i } = a }{ n hat { p } _ { n }(a _ { i } | x { i })计算每个治疗组的平均值,方差分析和统计 t 检验可以用来判断治疗效果的差异,并确定治疗效果的统计显著性。<br />
<br />
==== 假设 ====<br />
# Consistency: <math>Y = Y^{*}(A)</math><br />
# No unmeasured confounders: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math> <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: <math>P(A=a|X=x)>0 </math> for all <math>a</math> and <math>x</math><br />
<br />
# Consistency: Y = Y^{*}(A)<br />
# No unmeasured confounders: \{Y^{*}(0), Y^{*}(1)\} \perp A|X <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: P(A=a|X=x)>0 for all a and x<br />
<br />
= = = = = = = = = = # 一致性: y = y ^ { <br />
* }(a) # 不存在未测量的混杂因素: { y ^ { <br />
* }(0) ,y ^ { <br />
* }(1)} a/p | x # <br />
* 治疗分配完全基于协数据,与潜在结果无关。# 正性: p (a = a | x = x) > 0表示所有 a 和 x<br />
<br />
==== Limitations ====<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
= = = = 极限 = = = = = 反概率加权估计量(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么 Logit模型模型可能在尾部附近变得不稳定,导致 IPWE 也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref><br />
<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<br />
<br />
另一种估计是增广逆概率加权估计(Augmented Inverse Probability Weighted Estimator,AIPWE) ,它综合了基于回归的估计和逆概率加权估计的性质。因此,这是一个双重稳健的方法,因为它只需要正确指定倾向或结果模型,而不是两者都要求。这种方法增强了 IPWE,减少了变异性,提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件。<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
<math><br />
\begin{align}<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
如果你想要的话,你可以选择<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
Frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q } _ n (x _ i,a) Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
With the following notations:<br />
# <math>1_{A_{i}=a}</math> is an [[indicator function]] if subject i is part of treatment group a (or not).<br />
# Construct regression estimator <math>\hat{Q}_n(x,a)</math> to predict outcome <math>Y</math> based on covariates <math>X</math> and treatment <math>A</math>, for some subject i. For example, using [[ordinary least squares]] regression.<br />
# Construct propensity (probability) estimate <math>\hat{p}_n(A_i|X_i)</math>. For example, using [[logistic regression]].<br />
# Combine in AIPWE to obtain <math>\hat{\mu}^{AIPWE}_{a,n}</math><br />
<br />
With the following notations:<br />
# 1_{A_{i}=a} is an indicator function if subject i is part of treatment group a (or not).<br />
# Construct regression estimator \hat{Q}_n(x,a) to predict outcome Y based on covariates X and treatment A, for some subject i. For example, using ordinary least squares regression.<br />
# Construct propensity (probability) estimate \hat{p}_n(A_i|X_i). For example, using logistic regression.<br />
# Combine in AIPWE to obtain \hat{\mu}^{AIPWE}_{a,n}<br />
<br />
用下面的符号: # 1{ a { i } = a }是一个指示函数,如果主体 i 是治疗组 a 的一部分(或不是)。# 基于协变量 x 和处理 a 构造回归估计量{ q } _ n (x,a)来预测结果 y。例如,使用一般最小平方法回归。# 构造倾向(概率)估计{ p } _ n (a _ i | x _ i)。例如,使用 Logit模型。# 在 AIPWE 中组合以获得 hat { mu } ^ { AIPWE } _ { a,n }<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in <ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>).<br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: \frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: \frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. link for the paper).<br />
<br />
公式的后期重新排列有助于揭示基本思想: 我们的估计是基于使用该模型的平均预测结果(即。: frac {1}{ n } sum { i = 1} ^ n Biggl (hat { q } _ n (x _ i,a) Biggr)).然而,如果模型是偏倚的,那么模型的残差将不会(在完整的治疗组 a)大约0。我们可以通过将模型的平均残差(q)与结果的真实值(y)相加的额外项来纠正这种潜在的偏差。: frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q _ n (x _ i,a) Biggr))).因为我们有 y 的缺失值,所以我们给出权值来膨胀每个剩余值的相对重要性(这些权值基于反向倾向,也就是 a。观察到每个主题的概率)(见 Kang,Joseph DY 和 Joseph l. Schafer 的第10页。去神秘化的双重稳健性: 从不完全数据估计人口平均值的替代策略的比较统计科学22.4(2007) : 523-539. 论文链接)。<br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either <math>\hat{Q}_n(X_i,a)</math> or <math>\hat{p}_{n}(A_{i}|X_{i})</math>, or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref><br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either \hat{Q}_n(X_i,a) or \hat{p}_{n}(A_{i}|X_{i}), or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. link to the paperSeaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. link to the paper<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(hat { q } _ n (xi,a)或 hat { p } _ { n }(a _ { i } | x _ { i }) ,或者两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均数残差很好地估计(并修正)。和 David Haziza。调查抽样中缺失数据的双重稳健推断24.1(2014) : 375-394. link to the paperSeaman,Shaun r. ,and Stijn Vansteelandt.“不完整数据的双重稳健方法介绍”统计科学: 数理统计研究所的评论杂志33.2(2018) : 184. 链接到论文<br />
<br />
The bias of the doubly robust estimators is called a '''second-order bias''', and it depends on the product of the difference <math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math> and the difference <math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>. This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using [[machine learning]] estimators (instead of parametric models).<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref><br />
<br />
The bias of the doubly robust estimators is called a second-order bias, and it depends on the product of the difference \frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})} and the difference \hat{Q}_n(X_i,a) - Q_n(X_i,a). This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using machine learning estimators (instead of parametric models).Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. link to the book - page 179<br />
<br />
双重稳健估计的偏差称为二阶偏差,它取决于差分 frac {1}{ hat { p }{ n }(a _ { i } | x _ { i })}-frac {1}{ p }{ n }(a _ { i } | x _ { i })}和差分{ q } _ n (x _ i,a)-q _ n (x _ i,a)的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差。米格尔 · a · 埃尔南和詹姆斯 · m · 罗宾斯。”因果推理”(2010) : 2. 链接到书-页179<br />
<br />
==See also==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}<br />
<br />
[[Category:Survey methodology]]<br />
[[Category:Epidemiology]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29480逆概率加权2022-03-23T13:03:09Z<p>Wei:</p>
<hr />
<div><br />
<br />
'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref name="refname2" />。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref name="refname3" />。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
<br />
<br />
一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
<br />
<br />
当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref name="refname1" />。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
<br />
== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
<br />
<br />
当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
Suppose observed data are <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math> drawn [[Independent and identically distributed random variables|i.i.d (independent and identically distributed)]] from unknown distribution P, where<br />
* <math>X \in \mathbb{R}^{p}</math> covariates<br />
* <math>A \in \{0, 1\}</math> are the two possible treatments.<br />
* <math>Y \in \mathbb{R}</math> response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, <math>Y^{*}\bigl(a\bigr)</math>, that would be observed if the subject were assigned treatment <math>a</math>. Then compare the mean outcome if all patients in the population were assigned either treatment: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>. We want to estimate <math>\mu_a</math> using observed data <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>.<br />
<br />
Suppose observed data are \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1} drawn i.i.d (independent and identically distributed) from unknown distribution P, where<br />
* X \in \mathbb{R}^{p} covariates<br />
* A \in \{0, 1\} are the two possible treatments.<br />
* Y \in \mathbb{R} response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, Y^{*}\bigl(a\bigr), that would be observed if the subject were assigned treatment a. Then compare the mean outcome if all patients in the population were assigned either treatment: \mu_{a} = \mathbb{E}Y^{*}(a). We want to estimate \mu_a using observed data \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}.<br />
<br />
假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布数据,其中 <br />
* <math>X \in \mathbb{R}^{p}</math> 为协变量; <br />
* <math>A \in \{0, 1\}</math> 是两个可能的处理;<br />
* <math>Y \in \mathbb{R}</math> 为响应量;<br />
* 我们不假设治疗是随机分配的。<br />
<br />
目标是估计潜在结果<math>Y^{*}\bigl(a\bigr)</math>,这个结果可以在给受试者分配治疗 <math>a</math>的情况下观测到。然后比较所有患者在总体中被分配为任一治疗方法的平均结果: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>。我们想用观测数据<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>来估计 <math>\mu_a</math> 。<br />
<br />
=== 估计器公式 ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}<br />
<br />
==== 构建 IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> where <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math><br />
# construct <math>\hat{p}_{n}(a|x)</math> or <math>p(a|x)</math> using any propensity model (often a logistic regression model)<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math><br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
# \mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)} where p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}<br />
# construct \hat{p}_{n}(a|x) or p(a|x) using any propensity model (often a logistic regression model)<br />
# \hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}<br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
= = = = = = = # mu { a } = mathbb { e } frac { mathbf {1}{ a = a } y }{ p (a | x)}其中 p (a | x) = frac { p (a = a,x = x)}{ p (x = x)}}{ p (x = x)}} # construct hat { p }{ n }(a | x)或 p (a | x)使用任意模型(通常是 Logit模型模型) # 帽子{ mu } ^ { IPWE } _ { a,n } = sum ^ { n } _ { i = 1} frac { y { i }1 _ { a _ { i } = a }{ n hat { p } _ { n }(a _ { i } | x { i })计算每个治疗组的平均值,方差分析和统计 t 检验可以用来判断治疗效果的差异,并确定治疗效果的统计显著性。<br />
<br />
==== 假设 ====<br />
# Consistency: <math>Y = Y^{*}(A)</math><br />
# No unmeasured confounders: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math> <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: <math>P(A=a|X=x)>0 </math> for all <math>a</math> and <math>x</math><br />
<br />
# Consistency: Y = Y^{*}(A)<br />
# No unmeasured confounders: \{Y^{*}(0), Y^{*}(1)\} \perp A|X <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: P(A=a|X=x)>0 for all a and x<br />
<br />
= = = = = = = = = = # 一致性: y = y ^ { <br />
* }(a) # 不存在未测量的混杂因素: { y ^ { <br />
* }(0) ,y ^ { <br />
* }(1)} a/p | x # <br />
* 治疗分配完全基于协数据,与潜在结果无关。# 正性: p (a = a | x = x) > 0表示所有 a 和 x<br />
<br />
==== Limitations ====<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
= = = = 极限 = = = = = 反概率加权估计量(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么 Logit模型模型可能在尾部附近变得不稳定,导致 IPWE 也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref><br />
<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<br />
<br />
另一种估计是增广逆概率加权估计(Augmented Inverse Probability Weighted Estimator,AIPWE) ,它综合了基于回归的估计和逆概率加权估计的性质。因此,这是一个双重稳健的方法,因为它只需要正确指定倾向或结果模型,而不是两者都要求。这种方法增强了 IPWE,减少了变异性,提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件。<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
<math><br />
\begin{align}<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
如果你想要的话,你可以选择<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
Frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q } _ n (x _ i,a) Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
With the following notations:<br />
# <math>1_{A_{i}=a}</math> is an [[indicator function]] if subject i is part of treatment group a (or not).<br />
# Construct regression estimator <math>\hat{Q}_n(x,a)</math> to predict outcome <math>Y</math> based on covariates <math>X</math> and treatment <math>A</math>, for some subject i. For example, using [[ordinary least squares]] regression.<br />
# Construct propensity (probability) estimate <math>\hat{p}_n(A_i|X_i)</math>. For example, using [[logistic regression]].<br />
# Combine in AIPWE to obtain <math>\hat{\mu}^{AIPWE}_{a,n}</math><br />
<br />
With the following notations:<br />
# 1_{A_{i}=a} is an indicator function if subject i is part of treatment group a (or not).<br />
# Construct regression estimator \hat{Q}_n(x,a) to predict outcome Y based on covariates X and treatment A, for some subject i. For example, using ordinary least squares regression.<br />
# Construct propensity (probability) estimate \hat{p}_n(A_i|X_i). For example, using logistic regression.<br />
# Combine in AIPWE to obtain \hat{\mu}^{AIPWE}_{a,n}<br />
<br />
用下面的符号: # 1{ a { i } = a }是一个指示函数,如果主体 i 是治疗组 a 的一部分(或不是)。# 基于协变量 x 和处理 a 构造回归估计量{ q } _ n (x,a)来预测结果 y。例如,使用一般最小平方法回归。# 构造倾向(概率)估计{ p } _ n (a _ i | x _ i)。例如,使用 Logit模型。# 在 AIPWE 中组合以获得 hat { mu } ^ { AIPWE } _ { a,n }<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in <ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>).<br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: \frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: \frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. link for the paper).<br />
<br />
公式的后期重新排列有助于揭示基本思想: 我们的估计是基于使用该模型的平均预测结果(即。: frac {1}{ n } sum { i = 1} ^ n Biggl (hat { q } _ n (x _ i,a) Biggr)).然而,如果模型是偏倚的,那么模型的残差将不会(在完整的治疗组 a)大约0。我们可以通过将模型的平均残差(q)与结果的真实值(y)相加的额外项来纠正这种潜在的偏差。: frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q _ n (x _ i,a) Biggr))).因为我们有 y 的缺失值,所以我们给出权值来膨胀每个剩余值的相对重要性(这些权值基于反向倾向,也就是 a。观察到每个主题的概率)(见 Kang,Joseph DY 和 Joseph l. Schafer 的第10页。去神秘化的双重稳健性: 从不完全数据估计人口平均值的替代策略的比较统计科学22.4(2007) : 523-539. 论文链接)。<br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either <math>\hat{Q}_n(X_i,a)</math> or <math>\hat{p}_{n}(A_{i}|X_{i})</math>, or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref><br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either \hat{Q}_n(X_i,a) or \hat{p}_{n}(A_{i}|X_{i}), or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. link to the paperSeaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. link to the paper<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(hat { q } _ n (xi,a)或 hat { p } _ { n }(a _ { i } | x _ { i }) ,或者两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均数残差很好地估计(并修正)。和 David Haziza。调查抽样中缺失数据的双重稳健推断24.1(2014) : 375-394. link to the paperSeaman,Shaun r. ,and Stijn Vansteelandt.“不完整数据的双重稳健方法介绍”统计科学: 数理统计研究所的评论杂志33.2(2018) : 184. 链接到论文<br />
<br />
The bias of the doubly robust estimators is called a '''second-order bias''', and it depends on the product of the difference <math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math> and the difference <math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>. This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using [[machine learning]] estimators (instead of parametric models).<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref><br />
<br />
The bias of the doubly robust estimators is called a second-order bias, and it depends on the product of the difference \frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})} and the difference \hat{Q}_n(X_i,a) - Q_n(X_i,a). This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using machine learning estimators (instead of parametric models).Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. link to the book - page 179<br />
<br />
双重稳健估计的偏差称为二阶偏差,它取决于差分 frac {1}{ hat { p }{ n }(a _ { i } | x _ { i })}-frac {1}{ p }{ n }(a _ { i } | x _ { i })}和差分{ q } _ n (x _ i,a)-q _ n (x _ i,a)的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差。米格尔 · a · 埃尔南和詹姆斯 · m · 罗宾斯。”因果推理”(2010) : 2. 链接到书-页179<br />
<br />
==See also==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}<br />
<br />
[[Category:Survey methodology]]<br />
[[Category:Epidemiology]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29479逆概率加权2022-03-23T12:45:12Z<p>Wei:</p>
<hr />
<div><br />
<br />
'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref name="refname2" />。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref name="refname3" />。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
<br />
<br />
一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
<br />
<br />
当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref name="refname1" />。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
<br />
== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
<br />
<br />
当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。<br />
<br />
Suppose observed data are <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math> drawn [[Independent and identically distributed random variables|i.i.d (independent and identically distributed)]] from unknown distribution P, where<br />
* <math>X \in \mathbb{R}^{p}</math> covariates<br />
* <math>A \in \{0, 1\}</math> are the two possible treatments.<br />
* <math>Y \in \mathbb{R}</math> response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, <math>Y^{*}\bigl(a\bigr)</math>, that would be observed if the subject were assigned treatment <math>a</math>. Then compare the mean outcome if all patients in the population were assigned either treatment: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>. We want to estimate <math>\mu_a</math> using observed data <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>.<br />
<br />
Suppose observed data are \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1} drawn i.i.d (independent and identically distributed) from unknown distribution P, where<br />
* X \in \mathbb{R}^{p} covariates<br />
* A \in \{0, 1\} are the two possible treatments.<br />
* Y \in \mathbb{R} response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, Y^{*}\bigl(a\bigr), that would be observed if the subject were assigned treatment a. Then compare the mean outcome if all patients in the population were assigned either treatment: \mu_{a} = \mathbb{E}Y^{*}(a). We want to estimate \mu_a using observed data \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}.<br />
<br />
假设观测数据是{ bigl (xi,a _ i,y _ i bigr)} ^ { n }{ i = 1}从未知分布 p 中抽取的 i.d (独立同分布) ,其中 <br />
* x 在{0,1}中的数学{ r } ^ { p }协变量 <br />
* a 中是两个可能的处理。我们不假设治疗是随机分配的。目标是估计潜在的结果,y ^ { <br />
* } bigl (a bigr) ,如果给受试者分配治疗 a,可以观察到这个结果。然后比较平均结果,如果所有患者在人口分配任一治疗: mu _ { a } = mathbb { e } y ^ { <br />
* }(a)。我们想用观测数据{ bigl (xi,a _ i,y _ i bigr)} ^ { n }{ i = 1}来估计 mu _ a。<br />
<br />
=== Estimator Formula ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}<br />
<br />
=== Estimator Formula ===<br />
\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}<br />
<br />
==== Constructing the IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> where <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math><br />
# construct <math>\hat{p}_{n}(a|x)</math> or <math>p(a|x)</math> using any propensity model (often a logistic regression model)<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math><br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
# \mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)} where p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}<br />
# construct \hat{p}_{n}(a|x) or p(a|x) using any propensity model (often a logistic regression model)<br />
# \hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}<br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
= = = = = = = # mu { a } = mathbb { e } frac { mathbf {1}{ a = a } y }{ p (a | x)}其中 p (a | x) = frac { p (a = a,x = x)}{ p (x = x)}}{ p (x = x)}} # construct hat { p }{ n }(a | x)或 p (a | x)使用任意模型(通常是 Logit模型模型) # 帽子{ mu } ^ { IPWE } _ { a,n } = sum ^ { n } _ { i = 1} frac { y { i }1 _ { a _ { i } = a }{ n hat { p } _ { n }(a _ { i } | x { i })计算每个治疗组的平均值,方差分析和统计 t 检验可以用来判断治疗效果的差异,并确定治疗效果的统计显著性。<br />
<br />
==== 假设 ====<br />
# Consistency: <math>Y = Y^{*}(A)</math><br />
# No unmeasured confounders: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math> <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: <math>P(A=a|X=x)>0 </math> for all <math>a</math> and <math>x</math><br />
<br />
# Consistency: Y = Y^{*}(A)<br />
# No unmeasured confounders: \{Y^{*}(0), Y^{*}(1)\} \perp A|X <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: P(A=a|X=x)>0 for all a and x<br />
<br />
= = = = = = = = = = # 一致性: y = y ^ { <br />
* }(a) # 不存在未测量的混杂因素: { y ^ { <br />
* }(0) ,y ^ { <br />
* }(1)} a/p | x # <br />
* 治疗分配完全基于协数据,与潜在结果无关。# 正性: p (a = a | x = x) > 0表示所有 a 和 x<br />
<br />
==== Limitations ====<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
= = = = 极限 = = = = = 反概率加权估计量(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么 Logit模型模型可能在尾部附近变得不稳定,导致 IPWE 也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref><br />
<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<br />
<br />
另一种估计是增广逆概率加权估计(Augmented Inverse Probability Weighted Estimator,AIPWE) ,它综合了基于回归的估计和逆概率加权估计的性质。因此,这是一个双重稳健的方法,因为它只需要正确指定倾向或结果模型,而不是两者都要求。这种方法增强了 IPWE,减少了变异性,提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件。<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
<math><br />
\begin{align}<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
如果你想要的话,你可以选择<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
Frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q } _ n (x _ i,a) Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
With the following notations:<br />
# <math>1_{A_{i}=a}</math> is an [[indicator function]] if subject i is part of treatment group a (or not).<br />
# Construct regression estimator <math>\hat{Q}_n(x,a)</math> to predict outcome <math>Y</math> based on covariates <math>X</math> and treatment <math>A</math>, for some subject i. For example, using [[ordinary least squares]] regression.<br />
# Construct propensity (probability) estimate <math>\hat{p}_n(A_i|X_i)</math>. For example, using [[logistic regression]].<br />
# Combine in AIPWE to obtain <math>\hat{\mu}^{AIPWE}_{a,n}</math><br />
<br />
With the following notations:<br />
# 1_{A_{i}=a} is an indicator function if subject i is part of treatment group a (or not).<br />
# Construct regression estimator \hat{Q}_n(x,a) to predict outcome Y based on covariates X and treatment A, for some subject i. For example, using ordinary least squares regression.<br />
# Construct propensity (probability) estimate \hat{p}_n(A_i|X_i). For example, using logistic regression.<br />
# Combine in AIPWE to obtain \hat{\mu}^{AIPWE}_{a,n}<br />
<br />
用下面的符号: # 1{ a { i } = a }是一个指示函数,如果主体 i 是治疗组 a 的一部分(或不是)。# 基于协变量 x 和处理 a 构造回归估计量{ q } _ n (x,a)来预测结果 y。例如,使用一般最小平方法回归。# 构造倾向(概率)估计{ p } _ n (a _ i | x _ i)。例如,使用 Logit模型。# 在 AIPWE 中组合以获得 hat { mu } ^ { AIPWE } _ { a,n }<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in <ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>).<br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: \frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: \frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. link for the paper).<br />
<br />
公式的后期重新排列有助于揭示基本思想: 我们的估计是基于使用该模型的平均预测结果(即。: frac {1}{ n } sum { i = 1} ^ n Biggl (hat { q } _ n (x _ i,a) Biggr)).然而,如果模型是偏倚的,那么模型的残差将不会(在完整的治疗组 a)大约0。我们可以通过将模型的平均残差(q)与结果的真实值(y)相加的额外项来纠正这种潜在的偏差。: frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q _ n (x _ i,a) Biggr))).因为我们有 y 的缺失值,所以我们给出权值来膨胀每个剩余值的相对重要性(这些权值基于反向倾向,也就是 a。观察到每个主题的概率)(见 Kang,Joseph DY 和 Joseph l. Schafer 的第10页。去神秘化的双重稳健性: 从不完全数据估计人口平均值的替代策略的比较统计科学22.4(2007) : 523-539. 论文链接)。<br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either <math>\hat{Q}_n(X_i,a)</math> or <math>\hat{p}_{n}(A_{i}|X_{i})</math>, or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref><br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either \hat{Q}_n(X_i,a) or \hat{p}_{n}(A_{i}|X_{i}), or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. link to the paperSeaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. link to the paper<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(hat { q } _ n (xi,a)或 hat { p } _ { n }(a _ { i } | x _ { i }) ,或者两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均数残差很好地估计(并修正)。和 David Haziza。调查抽样中缺失数据的双重稳健推断24.1(2014) : 375-394. link to the paperSeaman,Shaun r. ,and Stijn Vansteelandt.“不完整数据的双重稳健方法介绍”统计科学: 数理统计研究所的评论杂志33.2(2018) : 184. 链接到论文<br />
<br />
The bias of the doubly robust estimators is called a '''second-order bias''', and it depends on the product of the difference <math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math> and the difference <math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>. This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using [[machine learning]] estimators (instead of parametric models).<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref><br />
<br />
The bias of the doubly robust estimators is called a second-order bias, and it depends on the product of the difference \frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})} and the difference \hat{Q}_n(X_i,a) - Q_n(X_i,a). This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using machine learning estimators (instead of parametric models).Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. link to the book - page 179<br />
<br />
双重稳健估计的偏差称为二阶偏差,它取决于差分 frac {1}{ hat { p }{ n }(a _ { i } | x _ { i })}-frac {1}{ p }{ n }(a _ { i } | x _ { i })}和差分{ q } _ n (x _ i,a)-q _ n (x _ i,a)的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差。米格尔 · a · 埃尔南和詹姆斯 · m · 罗宾斯。”因果推理”(2010) : 2. 链接到书-页179<br />
<br />
==See also==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}<br />
<br />
[[Category:Survey methodology]]<br />
[[Category:Epidemiology]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29383逆概率加权2022-03-21T13:20:08Z<p>Wei:</p>
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<div><br />
<br />
'''逆概率加权'''是一种统计技术,用于计算与收集数据的人群不同的伪总体([[pseudo-population]])的标准化统计数据。在应用中,抽样人群和目标推断人群(目标人群)不一致的研究设计是很常见的<ref name="refname2" />。可能有一些禁止性因素,如成本、时间或道德方面的考虑,使研究人员无法直接从目标人群中抽样<ref name="refname3" />。解决这个问题的方法是使用另一种设计策略,如分层抽样([[stratified sampling]])。如果应用得当,加权可以潜在地提高效率,减少非加权估计的偏差。<br />
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一个非常早期的加权估计器是均值的Horvitz-Thompson估计器([[Horvitz–Thompson estimator]])<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref>。当抽样概率是已知的,抽样人群是从目标人群中抽取的,那么这个概率的倒数被用来加权观测。这种方法已经在不同的框架下被推广到统计学的许多方面。特别是,有加权似然([[likelihood function|weighted likelihoods]])、加权估计方程([[generalized estimating equations|weighted estimating equations]])和加权概率密度([[probability density function|weighted probability densities]]),大多数统计学都是由此而来的。这些应用编纂了其他统计学和估计器的理论,如边际结构模型([[marginal structural models]])、标准化死亡率([[standardized mortality ratio]]),以及用于粗粒度或聚合数据的EM算法([[EM algorithm]])。<br />
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当数据缺失的受试者不能被纳入主要分析时,逆概率加权也被用来解释缺失的数据<ref name="refname1" />。有了对抽样概率的估计,或该因素在另一次测量中被测量的概率,逆概率加权可以用来提高那些由于数据缺失程度大而代表性不足的受试者的权重。<br />
<br />
== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
The inverse probability weighting estimator can be used to demonstrate causality when the researcher cannot conduct a controlled experiment but has observed data to model. Because it is assumed that the treatment is not randomly assigned, the goal is to estimate the counterfactual or potential outcome if all subjects in population were assigned either treatment.<br />
<br />
The inverse probability weighting estimator can be used to demonstrate causality when the researcher cannot conduct a controlled experiment but has observed data to model. Because it is assumed that the treatment is not randomly assigned, the goal is to estimate the counterfactual or potential outcome if all subjects in population were assigned either treatment.<br />
<br />
当研究人员不能进行控制实验,但有观测数据进行模型时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,目标是估计反事实或潜在的结果,如果人口中的所有受试者被分配任何一种治疗。<br />
<br />
Suppose observed data are <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math> drawn [[Independent and identically distributed random variables|i.i.d (independent and identically distributed)]] from unknown distribution P, where<br />
* <math>X \in \mathbb{R}^{p}</math> covariates<br />
* <math>A \in \{0, 1\}</math> are the two possible treatments.<br />
* <math>Y \in \mathbb{R}</math> response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, <math>Y^{*}\bigl(a\bigr)</math>, that would be observed if the subject were assigned treatment <math>a</math>. Then compare the mean outcome if all patients in the population were assigned either treatment: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>. We want to estimate <math>\mu_a</math> using observed data <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>.<br />
<br />
Suppose observed data are \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1} drawn i.i.d (independent and identically distributed) from unknown distribution P, where<br />
* X \in \mathbb{R}^{p} covariates<br />
* A \in \{0, 1\} are the two possible treatments.<br />
* Y \in \mathbb{R} response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, Y^{*}\bigl(a\bigr), that would be observed if the subject were assigned treatment a. Then compare the mean outcome if all patients in the population were assigned either treatment: \mu_{a} = \mathbb{E}Y^{*}(a). We want to estimate \mu_a using observed data \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}.<br />
<br />
假设观测数据是{ bigl (xi,a _ i,y _ i bigr)} ^ { n }{ i = 1}从未知分布 p 中抽取的 i.d (独立同分布) ,其中 <br />
* x 在{0,1}中的数学{ r } ^ { p }协变量 <br />
* a 中是两个可能的处理。我们不假设治疗是随机分配的。目标是估计潜在的结果,y ^ { <br />
* } bigl (a bigr) ,如果给受试者分配治疗 a,可以观察到这个结果。然后比较平均结果,如果所有患者在人口分配任一治疗: mu _ { a } = mathbb { e } y ^ { <br />
* }(a)。我们想用观测数据{ bigl (xi,a _ i,y _ i bigr)} ^ { n }{ i = 1}来估计 mu _ a。<br />
<br />
=== Estimator Formula ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}<br />
<br />
=== Estimator Formula ===<br />
\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}<br />
<br />
==== Constructing the IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> where <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math><br />
# construct <math>\hat{p}_{n}(a|x)</math> or <math>p(a|x)</math> using any propensity model (often a logistic regression model)<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math><br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
# \mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)} where p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}<br />
# construct \hat{p}_{n}(a|x) or p(a|x) using any propensity model (often a logistic regression model)<br />
# \hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}<br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
= = = = = = = # mu { a } = mathbb { e } frac { mathbf {1}{ a = a } y }{ p (a | x)}其中 p (a | x) = frac { p (a = a,x = x)}{ p (x = x)}}{ p (x = x)}} # construct hat { p }{ n }(a | x)或 p (a | x)使用任意模型(通常是 Logit模型模型) # 帽子{ mu } ^ { IPWE } _ { a,n } = sum ^ { n } _ { i = 1} frac { y { i }1 _ { a _ { i } = a }{ n hat { p } _ { n }(a _ { i } | x { i })计算每个治疗组的平均值,方差分析和统计 t 检验可以用来判断治疗效果的差异,并确定治疗效果的统计显著性。<br />
<br />
==== 假设 ====<br />
# Consistency: <math>Y = Y^{*}(A)</math><br />
# No unmeasured confounders: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math> <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: <math>P(A=a|X=x)>0 </math> for all <math>a</math> and <math>x</math><br />
<br />
# Consistency: Y = Y^{*}(A)<br />
# No unmeasured confounders: \{Y^{*}(0), Y^{*}(1)\} \perp A|X <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: P(A=a|X=x)>0 for all a and x<br />
<br />
= = = = = = = = = = # 一致性: y = y ^ { <br />
* }(a) # 不存在未测量的混杂因素: { y ^ { <br />
* }(0) ,y ^ { <br />
* }(1)} a/p | x # <br />
* 治疗分配完全基于协数据,与潜在结果无关。# 正性: p (a = a | x = x) > 0表示所有 a 和 x<br />
<br />
==== Limitations ====<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
= = = = 极限 = = = = = 反概率加权估计量(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么 Logit模型模型可能在尾部附近变得不稳定,导致 IPWE 也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref><br />
<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<br />
<br />
另一种估计是增广逆概率加权估计(Augmented Inverse Probability Weighted Estimator,AIPWE) ,它综合了基于回归的估计和逆概率加权估计的性质。因此,这是一个双重稳健的方法,因为它只需要正确指定倾向或结果模型,而不是两者都要求。这种方法增强了 IPWE,减少了变异性,提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件。<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
<math><br />
\begin{align}<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
如果你想要的话,你可以选择<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
Frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q } _ n (x _ i,a) Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
With the following notations:<br />
# <math>1_{A_{i}=a}</math> is an [[indicator function]] if subject i is part of treatment group a (or not).<br />
# Construct regression estimator <math>\hat{Q}_n(x,a)</math> to predict outcome <math>Y</math> based on covariates <math>X</math> and treatment <math>A</math>, for some subject i. For example, using [[ordinary least squares]] regression.<br />
# Construct propensity (probability) estimate <math>\hat{p}_n(A_i|X_i)</math>. For example, using [[logistic regression]].<br />
# Combine in AIPWE to obtain <math>\hat{\mu}^{AIPWE}_{a,n}</math><br />
<br />
With the following notations:<br />
# 1_{A_{i}=a} is an indicator function if subject i is part of treatment group a (or not).<br />
# Construct regression estimator \hat{Q}_n(x,a) to predict outcome Y based on covariates X and treatment A, for some subject i. For example, using ordinary least squares regression.<br />
# Construct propensity (probability) estimate \hat{p}_n(A_i|X_i). For example, using logistic regression.<br />
# Combine in AIPWE to obtain \hat{\mu}^{AIPWE}_{a,n}<br />
<br />
用下面的符号: # 1{ a { i } = a }是一个指示函数,如果主体 i 是治疗组 a 的一部分(或不是)。# 基于协变量 x 和处理 a 构造回归估计量{ q } _ n (x,a)来预测结果 y。例如,使用一般最小平方法回归。# 构造倾向(概率)估计{ p } _ n (a _ i | x _ i)。例如,使用 Logit模型。# 在 AIPWE 中组合以获得 hat { mu } ^ { AIPWE } _ { a,n }<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in <ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>).<br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: \frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: \frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. link for the paper).<br />
<br />
公式的后期重新排列有助于揭示基本思想: 我们的估计是基于使用该模型的平均预测结果(即。: frac {1}{ n } sum { i = 1} ^ n Biggl (hat { q } _ n (x _ i,a) Biggr)).然而,如果模型是偏倚的,那么模型的残差将不会(在完整的治疗组 a)大约0。我们可以通过将模型的平均残差(q)与结果的真实值(y)相加的额外项来纠正这种潜在的偏差。: frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q _ n (x _ i,a) Biggr))).因为我们有 y 的缺失值,所以我们给出权值来膨胀每个剩余值的相对重要性(这些权值基于反向倾向,也就是 a。观察到每个主题的概率)(见 Kang,Joseph DY 和 Joseph l. Schafer 的第10页。去神秘化的双重稳健性: 从不完全数据估计人口平均值的替代策略的比较统计科学22.4(2007) : 523-539. 论文链接)。<br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either <math>\hat{Q}_n(X_i,a)</math> or <math>\hat{p}_{n}(A_{i}|X_{i})</math>, or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref><br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either \hat{Q}_n(X_i,a) or \hat{p}_{n}(A_{i}|X_{i}), or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. link to the paperSeaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. link to the paper<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(hat { q } _ n (xi,a)或 hat { p } _ { n }(a _ { i } | x _ { i }) ,或者两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均数残差很好地估计(并修正)。和 David Haziza。调查抽样中缺失数据的双重稳健推断24.1(2014) : 375-394. link to the paperSeaman,Shaun r. ,and Stijn Vansteelandt.“不完整数据的双重稳健方法介绍”统计科学: 数理统计研究所的评论杂志33.2(2018) : 184. 链接到论文<br />
<br />
The bias of the doubly robust estimators is called a '''second-order bias''', and it depends on the product of the difference <math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math> and the difference <math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>. This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using [[machine learning]] estimators (instead of parametric models).<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref><br />
<br />
The bias of the doubly robust estimators is called a second-order bias, and it depends on the product of the difference \frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})} and the difference \hat{Q}_n(X_i,a) - Q_n(X_i,a). This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using machine learning estimators (instead of parametric models).Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. link to the book - page 179<br />
<br />
双重稳健估计的偏差称为二阶偏差,它取决于差分 frac {1}{ hat { p }{ n }(a _ { i } | x _ { i })}-frac {1}{ p }{ n }(a _ { i } | x _ { i })}和差分{ q } _ n (x _ i,a)-q _ n (x _ i,a)的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差。米格尔 · a · 埃尔南和詹姆斯 · m · 罗宾斯。”因果推理”(2010) : 2. 链接到书-页179<br />
<br />
==See also==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}<br />
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[[Category:Survey methodology]]<br />
[[Category:Epidemiology]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29329逆概率加权2022-03-20T12:21:34Z<p>Wei:</p>
<hr />
<div>'''Inverse probability weighting''' is a statistical technique for calculating statistics standardized to a [[pseudo-population]] different from that in which the data was collected. Study designs with a disparate sampling population and population of target inference (target population) are common in application.<ref name="refname2" /> There may be prohibitive factors barring researchers from directly sampling from the target population such as cost, time, or ethical concerns.<ref name="refname3" /> A solution to this problem is to use an alternate design strategy, e.g. [[stratified sampling]]. Weighting, when correctly applied, can potentially improve the efficiency and reduce the bias of unweighted estimators.<br />
<br />
Inverse probability weighting is a statistical technique for calculating statistics standardized to a pseudo-population different from that in which the data was collected. Study designs with a disparate sampling population and population of target inference (target population) are common in application. There may be prohibitive factors barring researchers from directly sampling from the target population such as cost, time, or ethical concerns. A solution to this problem is to use an alternate design strategy, e.g. stratified sampling. Weighting, when correctly applied, can potentially improve the efficiency and reduce the bias of unweighted estimators.<br />
<br />
逆概率加权是一种统计技术,用于计算不同于收集数据的伪总体的标准化统计数据。研究设计具有不同的抽样总体和总体目标推断(目标总体)是常见的应用。可能存在一些禁止研究人员直接从目标人群中取样的因素,如成本、时间或伦理问题。解决这个问题的方法是使用替代的设计策略,例如。分层抽样。正确使用加权可以提高效率,减少未加权估计量的偏差。<br />
<br />
One very early weighted estimator is the [[Horvitz–Thompson estimator]] of the mean.<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref> When the [[sampling probability]] is known, from which the sampling population is drawn from the target population, then the inverse of this probability is used to weight the observations. This approach has been generalized to many aspects of statistics under various frameworks. In particular, there are [[likelihood function|weighted likelihoods]], [[generalized estimating equations|weighted estimating equations]], and [[probability density function|weighted probability densities]] from which a majority of statistics are derived. These applications codified the theory of other statistics and estimators such as [[marginal structural models]], the [[standardized mortality ratio]], and the [[EM algorithm]] for coarsened or aggregate data.<br />
<br />
One very early weighted estimator is the Horvitz–Thompson estimator of the mean. When the sampling probability is known, from which the sampling population is drawn from the target population, then the inverse of this probability is used to weight the observations. This approach has been generalized to many aspects of statistics under various frameworks. In particular, there are weighted likelihoods, weighted estimating equations, and weighted probability densities from which a majority of statistics are derived. These applications codified the theory of other statistics and estimators such as marginal structural models, the standardized mortality ratio, and the EM algorithm for coarsened or aggregate data.<br />
<br />
一个非常早期的加权估计是均值的 Horvitz-Thompson 估计。当抽样概率已知时,从目标总体中抽取抽样总体,然后用该概率的倒数来加权观测值。这种方法已经推广到各种框架下的统计的许多方面。特别是,有加权可能性、加权估计方程和加权概率密度,从中得出大多数统计数据。这些应用编纂了其他统计理论和估计器,如边际结构模型,标准死亡率,和 EM 算法的粗化或聚合数据。<br />
<br />
Inverse probability weighting is also used to account for missing data when subjects with missing data cannot be included in the primary analysis.<ref name="refname1"/><br />
With an estimate of the sampling probability, or the probability that the factor would be measured in another measurement, inverse probability weighting can be used to inflate the weight for subjects who are under-represented due to a large degree of [[missing data]].<br />
<br />
Inverse probability weighting is also used to account for missing data when subjects with missing data cannot be included in the primary analysis.<br />
With an estimate of the sampling probability, or the probability that the factor would be measured in another measurement, inverse probability weighting can be used to inflate the weight for subjects who are under-represented due to a large degree of missing data.<br />
<br />
当缺失数据不能包含在初步分析中时,逆概率加权也可用于考虑缺失数据。根据抽样概率的估计,或在另一测量中测量该因素的概率,可以使用逆概率加权来夸大由于大量数据缺失而代表性不足的受试者的权重。<br />
<br />
== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
The inverse probability weighting estimator can be used to demonstrate causality when the researcher cannot conduct a controlled experiment but has observed data to model. Because it is assumed that the treatment is not randomly assigned, the goal is to estimate the counterfactual or potential outcome if all subjects in population were assigned either treatment.<br />
<br />
The inverse probability weighting estimator can be used to demonstrate causality when the researcher cannot conduct a controlled experiment but has observed data to model. Because it is assumed that the treatment is not randomly assigned, the goal is to estimate the counterfactual or potential outcome if all subjects in population were assigned either treatment.<br />
<br />
当研究人员不能进行控制实验,但有观测数据进行模型时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,目标是估计反事实或潜在的结果,如果人口中的所有受试者被分配任何一种治疗。<br />
<br />
Suppose observed data are <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math> drawn [[Independent and identically distributed random variables|i.i.d (independent and identically distributed)]] from unknown distribution P, where<br />
* <math>X \in \mathbb{R}^{p}</math> covariates<br />
* <math>A \in \{0, 1\}</math> are the two possible treatments.<br />
* <math>Y \in \mathbb{R}</math> response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, <math>Y^{*}\bigl(a\bigr)</math>, that would be observed if the subject were assigned treatment <math>a</math>. Then compare the mean outcome if all patients in the population were assigned either treatment: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>. We want to estimate <math>\mu_a</math> using observed data <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>.<br />
<br />
Suppose observed data are \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1} drawn i.i.d (independent and identically distributed) from unknown distribution P, where<br />
* X \in \mathbb{R}^{p} covariates<br />
* A \in \{0, 1\} are the two possible treatments.<br />
* Y \in \mathbb{R} response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, Y^{*}\bigl(a\bigr), that would be observed if the subject were assigned treatment a. Then compare the mean outcome if all patients in the population were assigned either treatment: \mu_{a} = \mathbb{E}Y^{*}(a). We want to estimate \mu_a using observed data \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}.<br />
<br />
假设观测数据是{ bigl (xi,a _ i,y _ i bigr)} ^ { n }{ i = 1}从未知分布 p 中抽取的 i.d (独立同分布) ,其中 <br />
* x 在{0,1}中的数学{ r } ^ { p }协变量 <br />
* a 中是两个可能的处理。我们不假设治疗是随机分配的。目标是估计潜在的结果,y ^ { <br />
* } bigl (a bigr) ,如果给受试者分配治疗 a,可以观察到这个结果。然后比较平均结果,如果所有患者在人口分配任一治疗: mu _ { a } = mathbb { e } y ^ { <br />
* }(a)。我们想用观测数据{ bigl (xi,a _ i,y _ i bigr)} ^ { n }{ i = 1}来估计 mu _ a。<br />
<br />
=== Estimator Formula ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
<br />
\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}<br />
<br />
=== Estimator Formula ===<br />
\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}<br />
<br />
==== Constructing the IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> where <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math><br />
# construct <math>\hat{p}_{n}(a|x)</math> or <math>p(a|x)</math> using any propensity model (often a logistic regression model)<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math><br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
# \mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)} where p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}<br />
# construct \hat{p}_{n}(a|x) or p(a|x) using any propensity model (often a logistic regression model)<br />
# \hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}<br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
= = = = = = = # mu { a } = mathbb { e } frac { mathbf {1}{ a = a } y }{ p (a | x)}其中 p (a | x) = frac { p (a = a,x = x)}{ p (x = x)}}{ p (x = x)}} # construct hat { p }{ n }(a | x)或 p (a | x)使用任意模型(通常是 Logit模型模型) # 帽子{ mu } ^ { IPWE } _ { a,n } = sum ^ { n } _ { i = 1} frac { y { i }1 _ { a _ { i } = a }{ n hat { p } _ { n }(a _ { i } | x { i })计算每个治疗组的平均值,方差分析和统计 t 检验可以用来判断治疗效果的差异,并确定治疗效果的统计显著性。<br />
<br />
==== 假设 ====<br />
# Consistency: <math>Y = Y^{*}(A)</math><br />
# No unmeasured confounders: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math> <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: <math>P(A=a|X=x)>0 </math> for all <math>a</math> and <math>x</math><br />
<br />
# Consistency: Y = Y^{*}(A)<br />
# No unmeasured confounders: \{Y^{*}(0), Y^{*}(1)\} \perp A|X <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: P(A=a|X=x)>0 for all a and x<br />
<br />
= = = = = = = = = = # 一致性: y = y ^ { <br />
* }(a) # 不存在未测量的混杂因素: { y ^ { <br />
* }(0) ,y ^ { <br />
* }(1)} a/p | x # <br />
* 治疗分配完全基于协数据,与潜在结果无关。# 正性: p (a = a | x = x) > 0表示所有 a 和 x<br />
<br />
==== Limitations ====<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
= = = = 极限 = = = = = 反概率加权估计量(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么 Logit模型模型可能在尾部附近变得不稳定,导致 IPWE 也变得不稳定。<br />
<br />
== 增广逆概率加权估计器 ==<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref><br />
<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<br />
<br />
另一种估计是增广逆概率加权估计(Augmented Inverse Probability Weighted Estimator,AIPWE) ,它综合了基于回归的估计和逆概率加权估计的性质。因此,这是一个双重稳健的方法,因为它只需要正确指定倾向或结果模型,而不是两者都要求。这种方法增强了 IPWE,减少了变异性,提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件。<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
<math><br />
\begin{align}<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
如果你想要的话,你可以选择<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
Frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q } _ n (x _ i,a) Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
With the following notations:<br />
# <math>1_{A_{i}=a}</math> is an [[indicator function]] if subject i is part of treatment group a (or not).<br />
# Construct regression estimator <math>\hat{Q}_n(x,a)</math> to predict outcome <math>Y</math> based on covariates <math>X</math> and treatment <math>A</math>, for some subject i. For example, using [[ordinary least squares]] regression.<br />
# Construct propensity (probability) estimate <math>\hat{p}_n(A_i|X_i)</math>. For example, using [[logistic regression]].<br />
# Combine in AIPWE to obtain <math>\hat{\mu}^{AIPWE}_{a,n}</math><br />
<br />
With the following notations:<br />
# 1_{A_{i}=a} is an indicator function if subject i is part of treatment group a (or not).<br />
# Construct regression estimator \hat{Q}_n(x,a) to predict outcome Y based on covariates X and treatment A, for some subject i. For example, using ordinary least squares regression.<br />
# Construct propensity (probability) estimate \hat{p}_n(A_i|X_i). For example, using logistic regression.<br />
# Combine in AIPWE to obtain \hat{\mu}^{AIPWE}_{a,n}<br />
<br />
用下面的符号: # 1{ a { i } = a }是一个指示函数,如果主体 i 是治疗组 a 的一部分(或不是)。# 基于协变量 x 和处理 a 构造回归估计量{ q } _ n (x,a)来预测结果 y。例如,使用一般最小平方法回归。# 构造倾向(概率)估计{ p } _ n (a _ i | x _ i)。例如,使用 Logit模型。# 在 AIPWE 中组合以获得 hat { mu } ^ { AIPWE } _ { a,n }<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
= 解释和“双重稳健性” = <br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in <ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>).<br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: \frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: \frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. link for the paper).<br />
<br />
公式的后期重新排列有助于揭示基本思想: 我们的估计是基于使用该模型的平均预测结果(即。: frac {1}{ n } sum { i = 1} ^ n Biggl (hat { q } _ n (x _ i,a) Biggr)).然而,如果模型是偏倚的,那么模型的残差将不会(在完整的治疗组 a)大约0。我们可以通过将模型的平均残差(q)与结果的真实值(y)相加的额外项来纠正这种潜在的偏差。: frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q _ n (x _ i,a) Biggr))).因为我们有 y 的缺失值,所以我们给出权值来膨胀每个剩余值的相对重要性(这些权值基于反向倾向,也就是 a。观察到每个主题的概率)(见 Kang,Joseph DY 和 Joseph l. Schafer 的第10页。去神秘化的双重稳健性: 从不完全数据估计人口平均值的替代策略的比较统计科学22.4(2007) : 523-539. 论文链接)。<br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either <math>\hat{Q}_n(X_i,a)</math> or <math>\hat{p}_{n}(A_{i}|X_{i})</math>, or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref><br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either \hat{Q}_n(X_i,a) or \hat{p}_{n}(A_{i}|X_{i}), or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. link to the paperSeaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. link to the paper<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(hat { q } _ n (xi,a)或 hat { p } _ { n }(a _ { i } | x _ { i }) ,或者两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均数残差很好地估计(并修正)。和 David Haziza。调查抽样中缺失数据的双重稳健推断24.1(2014) : 375-394. link to the paperSeaman,Shaun r. ,and Stijn Vansteelandt.“不完整数据的双重稳健方法介绍”统计科学: 数理统计研究所的评论杂志33.2(2018) : 184. 链接到论文<br />
<br />
The bias of the doubly robust estimators is called a '''second-order bias''', and it depends on the product of the difference <math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math> and the difference <math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>. This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using [[machine learning]] estimators (instead of parametric models).<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref><br />
<br />
The bias of the doubly robust estimators is called a second-order bias, and it depends on the product of the difference \frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})} and the difference \hat{Q}_n(X_i,a) - Q_n(X_i,a). This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using machine learning estimators (instead of parametric models).Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. link to the book - page 179<br />
<br />
双重稳健估计的偏差称为二阶偏差,它取决于差分 frac {1}{ hat { p }{ n }(a _ { i } | x _ { i })}-frac {1}{ p }{ n }(a _ { i } | x _ { i })}和差分{ q } _ n (x _ i,a)-q _ n (x _ i,a)的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差。米格尔 · a · 埃尔南和詹姆斯 · m · 罗宾斯。”因果推理”(2010) : 2. 链接到书-页179<br />
<br />
==See also==<br />
* 倾向评分匹配([[Propensity score matching]])<br />
<br />
= 参考文献 =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}<br />
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[[Category:Survey methodology]]<br />
[[Category:Epidemiology]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E9%80%86%E6%A6%82%E7%8E%87%E5%8A%A0%E6%9D%83&diff=29290逆概率加权2022-03-20T09:26:41Z<p>Wei:</p>
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<div>'''Inverse probability weighting''' is a statistical technique for calculating statistics standardized to a [[pseudo-population]] different from that in which the data was collected. Study designs with a disparate sampling population and population of target inference (target population) are common in application.<ref name="refname2" /> There may be prohibitive factors barring researchers from directly sampling from the target population such as cost, time, or ethical concerns.<ref name="refname3" /> A solution to this problem is to use an alternate design strategy, e.g. [[stratified sampling]]. Weighting, when correctly applied, can potentially improve the efficiency and reduce the bias of unweighted estimators.<br />
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Inverse probability weighting is a statistical technique for calculating statistics standardized to a pseudo-population different from that in which the data was collected. Study designs with a disparate sampling population and population of target inference (target population) are common in application. There may be prohibitive factors barring researchers from directly sampling from the target population such as cost, time, or ethical concerns. A solution to this problem is to use an alternate design strategy, e.g. stratified sampling. Weighting, when correctly applied, can potentially improve the efficiency and reduce the bias of unweighted estimators.<br />
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逆概率加权是一种统计技术,用于计算不同于收集数据的伪总体的标准化统计数据。研究设计具有不同的抽样总体和总体目标推断(目标总体)是常见的应用。可能存在一些禁止研究人员直接从目标人群中取样的因素,如成本、时间或伦理问题。解决这个问题的方法是使用替代的设计策略,例如。分层抽样。正确使用加权可以提高效率,减少未加权估计量的偏差。<br />
<br />
One very early weighted estimator is the [[Horvitz–Thompson estimator]] of the mean.<ref>{{cite journal | first1 = D. G. |last1 = Horvitz | first2 = D. J. |last2 = Thompson | title = A generalization of sampling without replacement from a finite universe | journal = [[Journal of the American Statistical Association]] | volume = 47 | pages = 663–685 | year = 1952 |issue = 260 | doi=10.1080/01621459.1952.10483446}}</ref> When the [[sampling probability]] is known, from which the sampling population is drawn from the target population, then the inverse of this probability is used to weight the observations. This approach has been generalized to many aspects of statistics under various frameworks. In particular, there are [[likelihood function|weighted likelihoods]], [[generalized estimating equations|weighted estimating equations]], and [[probability density function|weighted probability densities]] from which a majority of statistics are derived. These applications codified the theory of other statistics and estimators such as [[marginal structural models]], the [[standardized mortality ratio]], and the [[EM algorithm]] for coarsened or aggregate data.<br />
<br />
One very early weighted estimator is the Horvitz–Thompson estimator of the mean. When the sampling probability is known, from which the sampling population is drawn from the target population, then the inverse of this probability is used to weight the observations. This approach has been generalized to many aspects of statistics under various frameworks. In particular, there are weighted likelihoods, weighted estimating equations, and weighted probability densities from which a majority of statistics are derived. These applications codified the theory of other statistics and estimators such as marginal structural models, the standardized mortality ratio, and the EM algorithm for coarsened or aggregate data.<br />
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一个非常早期的加权估计是均值的 Horvitz-Thompson 估计。当抽样概率已知时,从目标总体中抽取抽样总体,然后用该概率的倒数来加权观测值。这种方法已经推广到各种框架下的统计的许多方面。特别是,有加权可能性、加权估计方程和加权概率密度,从中得出大多数统计数据。这些应用编纂了其他统计理论和估计器,如边际结构模型,标准死亡率,和 EM 算法的粗化或聚合数据。<br />
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Inverse probability weighting is also used to account for missing data when subjects with missing data cannot be included in the primary analysis.<ref name="refname1"/><br />
With an estimate of the sampling probability, or the probability that the factor would be measured in another measurement, inverse probability weighting can be used to inflate the weight for subjects who are under-represented due to a large degree of [[missing data]].<br />
<br />
Inverse probability weighting is also used to account for missing data when subjects with missing data cannot be included in the primary analysis.<br />
With an estimate of the sampling probability, or the probability that the factor would be measured in another measurement, inverse probability weighting can be used to inflate the weight for subjects who are under-represented due to a large degree of missing data.<br />
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当缺失数据不能包含在初步分析中时,逆概率加权也可用于考虑缺失数据。根据抽样概率的估计,或在另一测量中测量该因素的概率,可以使用逆概率加权来夸大由于大量数据缺失而代表性不足的受试者的权重。<br />
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== 逆概率加权估计量(Inverse Probability Weighted Estimator, IPWE) ==<br />
The inverse probability weighting estimator can be used to demonstrate causality when the researcher cannot conduct a controlled experiment but has observed data to model. Because it is assumed that the treatment is not randomly assigned, the goal is to estimate the counterfactual or potential outcome if all subjects in population were assigned either treatment.<br />
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The inverse probability weighting estimator can be used to demonstrate causality when the researcher cannot conduct a controlled experiment but has observed data to model. Because it is assumed that the treatment is not randomly assigned, the goal is to estimate the counterfactual or potential outcome if all subjects in population were assigned either treatment.<br />
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= = 反概率加权估计量(IPWE) = = 反概率加权估计量可用于证明因果关系,当研究人员不能进行控制实验,但有观测数据进行模型时。因为假设治疗不是随机分配的,目标是估计反事实或潜在的结果,如果人口中的所有受试者被分配任何一种治疗。<br />
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Suppose observed data are <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math> drawn [[Independent and identically distributed random variables|i.i.d (independent and identically distributed)]] from unknown distribution P, where<br />
* <math>X \in \mathbb{R}^{p}</math> covariates<br />
* <math>A \in \{0, 1\}</math> are the two possible treatments.<br />
* <math>Y \in \mathbb{R}</math> response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, <math>Y^{*}\bigl(a\bigr)</math>, that would be observed if the subject were assigned treatment <math>a</math>. Then compare the mean outcome if all patients in the population were assigned either treatment: <math>\mu_{a} = \mathbb{E}Y^{*}(a)</math>. We want to estimate <math>\mu_a</math> using observed data <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>.<br />
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Suppose observed data are \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1} drawn i.i.d (independent and identically distributed) from unknown distribution P, where<br />
* X \in \mathbb{R}^{p} covariates<br />
* A \in \{0, 1\} are the two possible treatments.<br />
* Y \in \mathbb{R} response<br />
* We do not assume treatment is randomly assigned.<br />
The goal is to estimate the potential outcome, Y^{*}\bigl(a\bigr), that would be observed if the subject were assigned treatment a. Then compare the mean outcome if all patients in the population were assigned either treatment: \mu_{a} = \mathbb{E}Y^{*}(a). We want to estimate \mu_a using observed data \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}.<br />
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假设观测数据是{ bigl (xi,a _ i,y _ i bigr)} ^ { n }{ i = 1}从未知分布 p 中抽取的 i.d (独立同分布) ,其中 <br />
* x 在{0,1}中的数学{ r } ^ { p }协变量 <br />
* a 中是两个可能的处理。我们不假设治疗是随机分配的。目标是估计潜在的结果,y ^ { <br />
* } bigl (a bigr) ,如果给受试者分配治疗 a,可以观察到这个结果。然后比较平均结果,如果所有患者在人口分配任一治疗: mu _ { a } = mathbb { e } y ^ { <br />
* }(a)。我们想用观测数据{ bigl (xi,a _ i,y _ i bigr)} ^ { n }{ i = 1}来估计 mu _ a。<br />
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=== Estimator Formula ===<br />
<blockquote><math>\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}</math></blockquote><br />
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\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}<br />
<br />
=== Estimator Formula ===<br />
\hat{\mu}^{IPWE}_{a,n} = \frac{1}{n}\sum^{n}_{i=1}Y_{i} \frac{\mathbf 1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}<br />
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==== Constructing the IPWE ====<br />
# <math>\mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)}</math> where <math>p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}</math><br />
# construct <math>\hat{p}_{n}(a|x)</math> or <math>p(a|x)</math> using any propensity model (often a logistic regression model)<br />
# <math>\hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}</math><br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
# \mu_{a} = \mathbb{E}\frac{\mathbf{1}_{A=a} Y}{p(A|X)} where p(a|x) = \frac{P(A=a,X=x)}{P(X=x)}<br />
# construct \hat{p}_{n}(a|x) or p(a|x) using any propensity model (often a logistic regression model)<br />
# \hat{\mu}^{IPWE}_{a,n} = \sum^{n}_{i=1}\frac{Y_{i} 1_{A_{i}=a}}{n\hat{p}_{n}(A_{i}|X_{i})}<br />
With the mean of each treatment group computed, a statistical t-test or ANOVA test can be used to judge difference between group means and determine statistical significance of treatment effect.<br />
<br />
= = = = = = = # mu { a } = mathbb { e } frac { mathbf {1}{ a = a } y }{ p (a | x)}其中 p (a | x) = frac { p (a = a,x = x)}{ p (x = x)}}{ p (x = x)}} # construct hat { p }{ n }(a | x)或 p (a | x)使用任意模型(通常是 Logit模型模型) # 帽子{ mu } ^ { IPWE } _ { a,n } = sum ^ { n } _ { i = 1} frac { y { i }1 _ { a _ { i } = a }{ n hat { p } _ { n }(a _ { i } | x { i })计算每个治疗组的平均值,方差分析和统计 t 检验可以用来判断治疗效果的差异,并确定治疗效果的统计显著性。<br />
<br />
==== Assumptions ====<br />
# Consistency: <math>Y = Y^{*}(A)</math><br />
# No unmeasured confounders: <math>\{Y^{*}(0), Y^{*}(1)\} \perp A|X</math> <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: <math>P(A=a|X=x)>0 </math> for all <math>a</math> and <math>x</math><br />
<br />
# Consistency: Y = Y^{*}(A)<br />
# No unmeasured confounders: \{Y^{*}(0), Y^{*}(1)\} \perp A|X <br />
#* Treatment assignment is based solely on covariate data and independent of potential outcomes.<br />
# Positivity: P(A=a|X=x)>0 for all a and x<br />
<br />
= = = = = = = = = = # 一致性: y = y ^ { <br />
* }(a) # 不存在未测量的混杂因素: { y ^ { <br />
* }(0) ,y ^ { <br />
* }(1)} a/p | x # <br />
* 治疗分配完全基于协数据,与潜在结果无关。# 正性: p (a = a | x = x) > 0表示所有 a 和 x<br />
<br />
==== Limitations ====<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
The Inverse Probability Weighted Estimator (IPWE) can be unstable if estimated propensities are small. If the probability of either treatment assignment is small, then the logistic regression model can become unstable around the tails causing the IPWE to also be less stable.<br />
<br />
= = = = 极限 = = = = = 反概率加权估计量(IPWE)在估计倾向较小时可能不稳定。如果任一处理分配的概率很小,那么 Logit模型模型可能在尾部附近变得不稳定,导致 IPWE 也变得不稳定。<br />
<br />
== Augmented Inverse Probability Weighted Estimator (AIPWE) ==<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<ref>{{Cite journal|last1=Cao|first1=Weihua|last2=Tsiatis|first2=Anastasios A.|last3=Davidian|first3=Marie|author3-link= Marie Davidian |year=2009|title=Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data|journal=Biometrika|volume=96|issue=3|pages=723–734|doi=10.1093/biomet/asp033|issn=0006-3444|pmc=2798744|pmid=20161511}}</ref><br />
<br />
An alternative estimator is the augmented inverse probability weighted estimator (AIPWE) combines both the properties of the regression based estimator and the inverse probability weighted estimator. It is therefore a 'doubly robust' method in that it only requires either the propensity or outcome model to be correctly specified but not both. This method augments the IPWE to reduce variability and improve estimate efficiency. This model holds the same assumptions as the Inverse Probability Weighted Estimator (IPWE).<br />
<br />
= = 增广逆概率加权估计(AIPWE) = = 另一种估计是增广逆概率加权估计(AIPWE) ,它综合了基于回归的估计和逆概率加权估计的性质。因此,这是一个双重稳健的方法,因为它只需要正确指定倾向或结果模型,而不是两者都要求。这种方法增强了 IPWE,减少了变异性,提高了估计效率。该模型与逆概率加权估计(IPWE)具有相同的假设条件。<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
<math><br />
\begin{align}<br />
<br />
=== Estimator Formula ===<br />
<math><br />
\begin{align}<br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
\hat{\mu}^{AIPWE}_{a,n} <br />
<br />
如果你想要的话,你可以选择<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{Y_{i}1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})} -<br />
\frac{1_{A_{i}=a}-\hat{p}_n(A_i|X_i)}{\hat{p}_n(A_i|X_i)}\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
&=<br />
\frac{1}{n}<br />
\sum_{i=1}^n\Biggl(\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}Y_{i} -<br />
(1-\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})})\hat{Q}_n(X_i,a)\Biggr) \\<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
<br />
&= <br />
\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr) +<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)<br />
<br />
Frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q } _ n (x _ i,a) Biggr)<br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
\end{align}<br />
</math><br />
<br />
With the following notations:<br />
# <math>1_{A_{i}=a}</math> is an [[indicator function]] if subject i is part of treatment group a (or not).<br />
# Construct regression estimator <math>\hat{Q}_n(x,a)</math> to predict outcome <math>Y</math> based on covariates <math>X</math> and treatment <math>A</math>, for some subject i. For example, using [[ordinary least squares]] regression.<br />
# Construct propensity (probability) estimate <math>\hat{p}_n(A_i|X_i)</math>. For example, using [[logistic regression]].<br />
# Combine in AIPWE to obtain <math>\hat{\mu}^{AIPWE}_{a,n}</math><br />
<br />
With the following notations:<br />
# 1_{A_{i}=a} is an indicator function if subject i is part of treatment group a (or not).<br />
# Construct regression estimator \hat{Q}_n(x,a) to predict outcome Y based on covariates X and treatment A, for some subject i. For example, using ordinary least squares regression.<br />
# Construct propensity (probability) estimate \hat{p}_n(A_i|X_i). For example, using logistic regression.<br />
# Combine in AIPWE to obtain \hat{\mu}^{AIPWE}_{a,n}<br />
<br />
用下面的符号: # 1{ a { i } = a }是一个指示函数,如果主体 i 是治疗组 a 的一部分(或不是)。# 基于协变量 x 和处理 a 构造回归估计量{ q } _ n (x,a)来预测结果 y。例如,使用一般最小平方法回归。# 构造倾向(概率)估计{ p } _ n (a _ i | x _ i)。例如,使用 Logit模型。# 在 AIPWE 中组合以获得 hat { mu } ^ { AIPWE } _ { a,n }<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
=== Interpretation and "double robustness" ===<br />
<br />
= = = 解释和“双重稳健性”= = = <br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)</math>). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: <math>\frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)</math>). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in <ref name = "kang2007">Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. [https://projecteuclid.org/journals/statistical-science/volume-22/issue-4/Demystifying-Double-Robustness--A-Comparison-of-Alternative-Strategies-for/10.1214/07-STS227.full link for the paper]</ref>).<br />
<br />
The later rearrangement of the formula helps reveal the underlying idea: our estimator is based on the average predicted outcome using the model (i.e.: \frac{1}{n}\sum_{i=1}^n\Biggl(\hat{Q}_n(X_i,a)\Biggr)). However, if the model is biased, then the residuals of the model will not be (in the full treatment group a) around 0. We can correct this potential bias by adding the extra term of the average residuals of the model (Q) from the true value of the outcome (Y) (i.e.: \frac{1}{n}\sum_{i=1}^n\frac{1_{A_{i}=a}}{\hat{p}_{n}(A_{i}|X_{i})}\Biggl(Y_{i} - \hat{Q}_n(X_i,a)\Biggr)). Because we have missing values of Y, we give weights to inflate the relative importance of each residual (these weights are based on the inverse propensity, a.k.a. probability, of seeing each subject observations) (see page 10 in Kang, Joseph DY, and Joseph L. Schafer. "Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data." Statistical science 22.4 (2007): 523-539. link for the paper).<br />
<br />
公式的后期重新排列有助于揭示基本思想: 我们的估计是基于使用该模型的平均预测结果(即。: frac {1}{ n } sum { i = 1} ^ n Biggl (hat { q } _ n (x _ i,a) Biggr)).然而,如果模型是偏倚的,那么模型的残差将不会(在完整的治疗组 a)大约0。我们可以通过将模型的平均残差(q)与结果的真实值(y)相加的额外项来纠正这种潜在的偏差。: frac {1}{ n } sum { i = 1} ^ n frac {1 _ { a _ { i } = a }{ hat { p }{ n }(a _ { i } | x _ { i })} Biggl (y _ { i }-hat { q _ n (x _ i,a) Biggr))).因为我们有 y 的缺失值,所以我们给出权值来膨胀每个剩余值的相对重要性(这些权值基于反向倾向,也就是 a。观察到每个主题的概率)(见 Kang,Joseph DY 和 Joseph l. Schafer 的第10页。去神秘化的双重稳健性: 从不完全数据估计人口平均值的替代策略的比较统计科学22.4(2007) : 523-539. 论文链接)。<br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either <math>\hat{Q}_n(X_i,a)</math> or <math>\hat{p}_{n}(A_{i}|X_{i})</math>, or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.<ref name = "kang2007"/><ref>Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. [https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1110&context=stat_las_pubs link to the paper]</ref><ref>Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5935236/ link to the paper]</ref><br />
<br />
The "doubly robust" benefit of such an estimator comes from the fact that it's sufficient for one of the two models to be correctly specified, for the estimator to be unbiased (either \hat{Q}_n(X_i,a) or \hat{p}_{n}(A_{i}|X_{i}), or both). This is because if the outcome model is well specified then its residuals will be around 0 (regardless of the weights each residual will get). While if the model is biased, but the weighting model is well specified, then the bias will be well estimated (And corrected for) by the weighted average residuals.Kim, Jae Kwang, and David Haziza. "Doubly robust inference with missing data in survey sampling." Statistica Sinica 24.1 (2014): 375-394. link to the paperSeaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. link to the paper<br />
<br />
这种估计器的“双重稳健”效益来自这样一个事实,即两个模型中的一个已经被正确指定,估计器是无偏的(hat { q } _ n (xi,a)或 hat { p } _ { n }(a _ { i } | x _ { i }) ,或者两者都是)。这是因为如果结果模型被很好地指定,那么它的残差将大约为0(不管每个残差将得到多少权重)。如果模型是有偏差的,但是加权模型是很好地指定的,那么偏差将被加权平均数残差很好地估计(并修正)。和 David Haziza。调查抽样中缺失数据的双重稳健推断24.1(2014) : 375-394. link to the paperSeaman,Shaun r. ,and Stijn Vansteelandt.“不完整数据的双重稳健方法介绍”统计科学: 数理统计研究所的评论杂志33.2(2018) : 184. 链接到论文<br />
<br />
The bias of the doubly robust estimators is called a '''second-order bias''', and it depends on the product of the difference <math>\frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})}</math> and the difference <math>\hat{Q}_n(X_i,a) - Q_n(X_i,a)</math>. This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using [[machine learning]] estimators (instead of parametric models).<ref>Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. [https://cdn1.sph.harvard.edu/wp-content/uploads/sites/1268/2021/03/ciwhatif_hernanrobins_30mar21.pdf link to the book] - page 179</ref><br />
<br />
The bias of the doubly robust estimators is called a second-order bias, and it depends on the product of the difference \frac{1}{\hat{p}_{n}(A_{i}|X_{i})} - \frac{1}{{p}_{n}(A_{i}|X_{i})} and the difference \hat{Q}_n(X_i,a) - Q_n(X_i,a). This property allows us, when having a "large enough" sample size, to lower the overall bias of doubly robust estimators by using machine learning estimators (instead of parametric models).Hernán, Miguel A., and James M. Robins. "Causal inference." (2010): 2. link to the book - page 179<br />
<br />
双重稳健估计的偏差称为二阶偏差,它取决于差分 frac {1}{ hat { p }{ n }(a _ { i } | x _ { i })}-frac {1}{ p }{ n }(a _ { i } | x _ { i })}和差分{ q } _ n (x _ i,a)-q _ n (x _ i,a)的乘积。这个特性使我们在样本容量足够大的情况下,通过使用机器学习估计器(而不是参数模型)来降低双重稳健估计器的总体偏差。米格尔 · a · 埃尔南和詹姆斯 · m · 罗宾斯。”因果推理”(2010) : 2. 链接到书-页179<br />
<br />
==See also==<br />
* [[Propensity score matching]]<br />
<br />
* Propensity score matching<br />
<br />
= = = = = = = <br />
* 倾向评分匹配<br />
<br />
==References==<br />
<br />
==References==<br />
<br />
= = 参考文献 = =<br />
<br />
{{Reflist|refs=<br />
<ref name="refname1"><br />
{{cite journal | last1 = Hernan | first1 = MA | last2 = Robins | first2 = JM | year = 2006 | title = Estimating Causal Effects From Epidemiological Data | citeseerx = 10.1.1.157.9366 | journal = J Epidemiol Community Health | volume = 60 | issue = 7 | pages = 578–596 | doi=10.1136/jech.2004.029496| pmc = 2652882 | pmid=16790829}}<br />
</ref><br />
<ref name="refname2"><br />
{{cite journal | last1 = Robins | first1 = JM | last2 = Rotnitzky | first2 = A | last3 = Zhao | first3 = LP | year = 1994 | title = Estimation of regression coefficients when some regressors are not always observed | journal = [[Journal of the American Statistical Association]] | volume = 89 | issue = 427 | pages = 846–866 | doi=10.1080/01621459.1994.10476818}}<br />
</ref><br />
<ref name="refname3"><br />
{{cite journal | last1 = Breslow | first1 = NE | last2 = Lumley | first2 = T | year = 2009 | pmc = 2768499 | title = Using the Whole Cohort in the Analysis of Case-Cohort Data | journal = Am J Epidemiol | volume = 169 | issue = 11 | pages = 1398–1405 | doi=10.1093/aje/kwp055 | pmid=19357328|display-authors=etal}}<br />
</ref><br />
}}<br />
<br />
[[Category:Survey methodology]]<br />
[[Category:Epidemiology]]<br />
<br />
Category:Survey methodology<br />
Category:Epidemiology<br />
<br />
类别: 社会统计调查流行病学<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Inverse probability weighting]]. Its edit history can be viewed at [[逆概率加权/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=Clark_Glymour&diff=29289Clark Glymour2022-03-20T09:08:35Z<p>Wei:</p>
<hr />
<div>'''克拉克 · 格里默'''(Clark N. Glymour)生于1942年,是卡内基梅隆大学哲学系的校友大学名誉教授。他也是佛罗里达人类和机器认知研究所([[Florida Institute for Human and Machine Cognition]])的高级研究科学家。<ref>{{cite web|url=https://www.cmu.edu/dietrich/philosophy/people/emeritus/glymour.html|title=Clark Glymour|publisher=Carnegie Mellon University|accessdate=December 16, 2019}}</ref><br />
<br />
== 工作经历 ==<br />
<br />
<br />
<br />
格里默是卡内基梅隆大学哲学系的创始人,古根海姆研究员([[Guggenheim Fellowship|Guggenheim Fellow]]),行为科学高级研究中心研究员<ref>{{cite web|url=https://casbs.stanford.edu/news/awards-and-elections-fall-2019|title=Awards and Elections, Fall 2019|publisher=Center for Advanced Study in Behavioral Sciences|accessdate=December 16, 2019}}</ref>,[[Phi Beta Kappa Society|Phi Beta Kappa]]联谊会讲师<ref>{{cite web|url=https://www.pbk.org/Awards/Romanell/PastWinners|title=Romanell-Phi Beta Kappa Professorship Past Winners|publisher=Phi Beta Kappa|accessdate=December 16, 2019}}</ref>,美国科学促进会(AAAS)统计部门研究员<ref>{{cite web|url=https://www.amacad.org/person/clark-glymour|title=Clark Glymour|publisher=American Academy of Arts and Sciences|accessdate=December 16, 2019}}</ref>。格里默和他的合作者创造了贝叶斯网络的因果解释<ref>P. Spirtes, C. Glymour, R. Scheines, Causation, Prediction and Search, Springer Lecture Notes in Statistics, 1993.</ref>。他的研究兴趣领域包括: 认识论([[epistemology]])<ref>Epistemology: 5 Questions Edited by Vincent F. Hendricks and Duncan Pritchard, September 2008, [[wikipedia:ISBN_(identifier)|ISBN]] [[wikipedia:Special:BookSources/87-92130-07-0|87-92130-07-0]]. </ref>(尤其是 Android 认识论([[Android epistemology]]))、机器学习([[machine learning]],)、自动推理([[automated reasoning]])、判断心理学([[psychology]] of judgment)和数学心理学([[mathematical psychology]])<ref>{{cite web|url=https://www.ihmc.us/groups/clark-glymour/|title=Clark Glymour|accessdate=December 16, 2019}}</ref>。格里默对科学哲学的主要贡献之一是在贝叶斯概率([[Bayesian probability]])领域,特别是在他对贝叶斯“旧证据问题”的分析中<ref>{{cite web|url=http://plato.stanford.edu/entries/epistemology-bayesian/|title=Bayesian Epistemology|date=July 12, 2001}}</ref><ref>Glymour, C.; Theory and evidence (1981), pp. 63-93.</ref>。格里默与彼得 · 斯皮尔茨(Peter Spirtes)和理查德 · 谢恩斯(Richard Scheines)合作,还开发了一种自动因果推理算法,以软件形式实现,命名为[[TETRAD]]<ref>[http://www.phil.cmu.edu/projects/tetrad/publications.html Publications] TETRAD. Retrieved December 16, 2019.</ref>。采用多元统计数据作为输入,TETRAD 从所有可能的因果关系模型中快速搜索,并根据这些变量之间的条件依赖关系输出最合理的因果模型。该算法基于统计学、图论、科学哲学和人工智能的原理<ref>Glymour, Clark; Scheines, Richard; Spirtes, Peter; Kelly, Kevin. "TETRAD: Discovering Causal Structure" Multivariate Behavioral Research 23.2 (1988). 10 July 2010. doi:[https://doi.org/10.1207%2Fs15327906mbr2302_13 10.1207/s15327906mbr2302_13]. [[wikipedia:PMID_(identifier)|PMID]] [https://pubmed.ncbi.nlm.nih.gov/26764954 26764954].</ref>。<br />
<br />
<br />
格里默获得了化学([[chemistry]])和哲学([[philosophy]])的本科学位。他研究生工作专注于化学物理学([[chemical physics]]),并于1969年获得印第安纳大学( [[Indiana University (Bloomington)|Indiana University]])历史与科学哲学博士学位。<br />
<br />
==发表的成果==<br />
===书籍===<br />
*''Theory and Evidence'' (Princeton, 1980)<br />
*''Examining Holistic Medicine'' (with D. Stalker), Prometheus, 1985<br />
*''Foundations of Space-Time Theories'' (with J. Earman), University of Minnesota Press, 1986<br />
*''Discovering Causal Structure'' (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*''Causation, Prediction and Search'' (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*''Thinking Things Through'', MIT Press, 1994<br />
*''Android Epistemology'' (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*''The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology'', MIT Press, 2001<br />
*''Galileo in Pittsburgh'' Harvard University Press, 2010.<br />
<br />
*Theory and Evidence (Princeton, 1980)<br />
*Examining Holistic Medicine (with D. Stalker), Prometheus, 1985<br />
*Foundations of Space-Time Theories (with J. Earman), University of Minnesota Press, 1986<br />
*Discovering Causal Structure (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*Causation, Prediction and Search (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*Thinking Things Through, MIT Press, 1994<br />
*Android Epistemology (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology, MIT Press, 2001<br />
*Galileo in Pittsburgh Harvard University Press, 2010.<br />
<br />
===期刊论文===<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", ''Open Philosophy'', 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", ''[[Philosophy of Science (journal)|Philosophy of Science]]'', 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", ''[[Journal of Philosophy]]'', 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. ''Physical Theory and Its Interpretation: Essays in Honor of [[Jeffrey Bub]]'', Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", ''[[Mind (journal)|Mind]]'', 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", ''UAI Proceedings'', 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", ''[[Genomics]]'', Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", ''[[Statistical Applications in Genetics and Molecular Biology]]'', Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", ''Behavioral and Brain Sciences'', in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", ''Philosophy of Science'', Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", ''[[Encyclopedia of Social Science]]'', in press<br />
*"We believe in freedom of the will so that we can learn", ''[[Behavioral and Brain Sciences]]'', Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", ''[[Daedalus (journal)|Daedelus]]'', Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, ''Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence'', August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", ''Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics'', (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", ''[[Erkenntnis]]'', Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", ''[[British Journal for Philosophy of Science]]'', Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", ''[[Journal of Econometrics]]'', Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", ''[[Trends in Cognitive Sciences]]'', Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", ''[[Psychological Review]], Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. ''[[Philosophical Essays on Freud]]'', Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", Open Philosophy, 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", Philosophy of Science, 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", Journal of Philosophy, 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. Physical Theory and Its Interpretation: Essays in Honor of Jeffrey Bub, Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", Mind, 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", UAI Proceedings, 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", Genomics, Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", Statistical Applications in Genetics and Molecular Biology, Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", Behavioral and Brain Sciences, in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", Philosophy of Science, Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", Encyclopedia of Social Science, in press<br />
*"We believe in freedom of the will so that we can learn", Behavioral and Brain Sciences, Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", Daedelus, Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence, August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics, (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", Erkenntnis, Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", British Journal for Philosophy of Science, Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", Journal of Econometrics, Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", Trends in Cognitive Sciences, Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", Psychological Review, Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. Philosophical Essays on Freud, Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
* <br />
<br />
==参考文献==<br />
{{Reflist}}<br />
<br />
== 外部链接 ==<br />
*IHMC 网站:[https://www.ihmc.us/groups/clark-glymour/ IHMC website]<br />
*卡内基梅隆大学哲学系主页:[https://web.archive.org/web/20100601161806/http://www.hss.cmu.edu/philosophy/faculty-glymour.php Carnegie Mellon Department of Philosophy faculty page]<br />
*TETRAD项目:[http://www.phil.cmu.edu/projects/tetrad/publications.html TETRAD Project]</div>Weihttps://wiki.swarma.org/index.php?title=Clark_Glymour&diff=29288Clark Glymour2022-03-20T09:01:08Z<p>Wei:</p>
<hr />
<div>'''克拉克 · 格莱莫尔'''(Clark N. Glymour)生于1942年,是卡内基梅隆大学哲学系的校友大学名誉教授。他也是佛罗里达人类和机器认知研究所([[Florida Institute for Human and Machine Cognition]])的高级研究科学家。<ref>{{cite web|url=https://www.cmu.edu/dietrich/philosophy/people/emeritus/glymour.html|title=Clark Glymour|publisher=Carnegie Mellon University|accessdate=December 16, 2019}}</ref><br />
<br />
== 工作经历 ==<br />
<br />
<br />
格莱默是卡内基梅隆大学哲学系的创始人,古根海姆研究员([[Guggenheim Fellowship|Guggenheim Fellow]]),行为科学高级研究中心研究员<ref>{{cite web|url=https://casbs.stanford.edu/news/awards-and-elections-fall-2019|title=Awards and Elections, Fall 2019|publisher=Center for Advanced Study in Behavioral Sciences|accessdate=December 16, 2019}}</ref>,[[Phi Beta Kappa Society|Phi Beta Kappa]]联谊会讲师<ref>{{cite web|url=https://www.pbk.org/Awards/Romanell/PastWinners|title=Romanell-Phi Beta Kappa Professorship Past Winners|publisher=Phi Beta Kappa|accessdate=December 16, 2019}}</ref>,美国科学促进会(AAAS)统计部门研究员<ref>{{cite web|url=https://www.amacad.org/person/clark-glymour|title=Clark Glymour|publisher=American Academy of Arts and Sciences|accessdate=December 16, 2019}}</ref>。格莱默和他的合作者创造了贝叶斯网络的因果解释<ref>P. Spirtes, C. Glymour, R. Scheines, Causation, Prediction and Search, Springer Lecture Notes in Statistics, 1993.</ref>。他的研究兴趣领域包括: 认识论([[epistemology]])<ref>Epistemology: 5 Questions Edited by Vincent F. Hendricks and Duncan Pritchard, September 2008, [[wikipedia:ISBN_(identifier)|ISBN]] [[wikipedia:Special:BookSources/87-92130-07-0|87-92130-07-0]]. </ref>(尤其是 Android 认识论([[Android epistemology]]))、机器学习([[machine learning]],)、自动推理([[automated reasoning]])、判断心理学([[psychology]] of judgment)和数学心理学([[mathematical psychology]])。<ref>{{cite web|url=https://www.ihmc.us/groups/clark-glymour/|title=Clark Glymour|accessdate=December 16, 2019}}</ref>格莱莫尔对科学哲学的主要贡献之一是在贝叶斯概率([[Bayesian probability]])领域,特别是在他对贝叶斯“旧证据问题”的分析中<ref>{{cite web|url=http://plato.stanford.edu/entries/epistemology-bayesian/|title=Bayesian Epistemology|date=July 12, 2001}}</ref><ref>Glymour, C.; Theory and evidence (1981), pp. 63-93.</ref>。格莱默与彼得 · 斯皮尔茨(Peter Spirtes)和理查德 · 谢恩斯(Richard Scheines)合作,还开发了一种自动因果推理算法,以软件形式实现,命名为[[TETRAD]]<ref>[http://www.phil.cmu.edu/projects/tetrad/publications.html Publications] TETRAD. Retrieved December 16, 2019.</ref>。采用多元统计数据作为输入,TETRAD 从所有可能的因果关系模型中快速搜索,并根据这些变量之间的条件依赖关系输出最合理的因果模型。该算法基于统计学、图论、科学哲学和人工智能的原理<ref>Glymour, Clark; Scheines, Richard; Spirtes, Peter; Kelly, Kevin. "TETRAD: Discovering Causal Structure" Multivariate Behavioral Research 23.2 (1988). 10 July 2010. doi:[https://doi.org/10.1207%2Fs15327906mbr2302_13 10.1207/s15327906mbr2302_13]. [[wikipedia:PMID_(identifier)|PMID]] [https://pubmed.ncbi.nlm.nih.gov/26764954 26764954].</ref>。<br />
<br />
<br />
格莱默获得了化学([[chemistry]])和哲学([[philosophy]])的本科学位。他研究生工作专注于化学物理学([[chemical physics]]),并于1969年获得印第安纳大学( [[Indiana University (Bloomington)|Indiana University]])历史与科学哲学博士学位。<br />
<br />
==发表的成果==<br />
===书籍===<br />
*''Theory and Evidence'' (Princeton, 1980)<br />
*''Examining Holistic Medicine'' (with D. Stalker), Prometheus, 1985<br />
*''Foundations of Space-Time Theories'' (with J. Earman), University of Minnesota Press, 1986<br />
*''Discovering Causal Structure'' (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*''Causation, Prediction and Search'' (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*''Thinking Things Through'', MIT Press, 1994<br />
*''Android Epistemology'' (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*''The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology'', MIT Press, 2001<br />
*''Galileo in Pittsburgh'' Harvard University Press, 2010.<br />
<br />
*Theory and Evidence (Princeton, 1980)<br />
*Examining Holistic Medicine (with D. Stalker), Prometheus, 1985<br />
*Foundations of Space-Time Theories (with J. Earman), University of Minnesota Press, 1986<br />
*Discovering Causal Structure (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*Causation, Prediction and Search (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*Thinking Things Through, MIT Press, 1994<br />
*Android Epistemology (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology, MIT Press, 2001<br />
*Galileo in Pittsburgh Harvard University Press, 2010.<br />
<br />
===期刊论文===<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", ''Open Philosophy'', 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", ''[[Philosophy of Science (journal)|Philosophy of Science]]'', 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", ''[[Journal of Philosophy]]'', 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. ''Physical Theory and Its Interpretation: Essays in Honor of [[Jeffrey Bub]]'', Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", ''[[Mind (journal)|Mind]]'', 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", ''UAI Proceedings'', 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", ''[[Genomics]]'', Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", ''[[Statistical Applications in Genetics and Molecular Biology]]'', Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", ''Behavioral and Brain Sciences'', in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", ''Philosophy of Science'', Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", ''[[Encyclopedia of Social Science]]'', in press<br />
*"We believe in freedom of the will so that we can learn", ''[[Behavioral and Brain Sciences]]'', Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", ''[[Daedalus (journal)|Daedelus]]'', Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, ''Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence'', August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", ''Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics'', (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", ''[[Erkenntnis]]'', Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", ''[[British Journal for Philosophy of Science]]'', Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", ''[[Journal of Econometrics]]'', Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", ''[[Trends in Cognitive Sciences]]'', Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", ''[[Psychological Review]], Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. ''[[Philosophical Essays on Freud]]'', Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", Open Philosophy, 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", Philosophy of Science, 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", Journal of Philosophy, 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. Physical Theory and Its Interpretation: Essays in Honor of Jeffrey Bub, Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", Mind, 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", UAI Proceedings, 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", Genomics, Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", Statistical Applications in Genetics and Molecular Biology, Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", Behavioral and Brain Sciences, in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", Philosophy of Science, Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", Encyclopedia of Social Science, in press<br />
*"We believe in freedom of the will so that we can learn", Behavioral and Brain Sciences, Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", Daedelus, Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence, August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics, (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", Erkenntnis, Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", British Journal for Philosophy of Science, Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", Journal of Econometrics, Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", Trends in Cognitive Sciences, Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", Psychological Review, Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. Philosophical Essays on Freud, Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
* <br />
<br />
==参考文献==<br />
{{Reflist}}<br />
<br />
== 外部链接 ==<br />
*IHMC 网站:[https://www.ihmc.us/groups/clark-glymour/ IHMC website]<br />
*卡内基梅隆大学哲学系主页:[https://web.archive.org/web/20100601161806/http://www.hss.cmu.edu/philosophy/faculty-glymour.php Carnegie Mellon Department of Philosophy faculty page]<br />
*TETRAD项目:[http://www.phil.cmu.edu/projects/tetrad/publications.html TETRAD Project]</div>Weihttps://wiki.swarma.org/index.php?title=Clark_Glymour&diff=29287Clark Glymour2022-03-20T09:00:13Z<p>Wei:</p>
<hr />
<div>'''克拉克 · 格莱莫尔'''(Clark N. Glymour)生于1942年,是卡内基梅隆大学哲学系的校友大学名誉教授。他也是佛罗里达人类和机器认知研究所([[Florida Institute for Human and Machine Cognition]])的高级研究科学家。<ref>{{cite web|url=https://www.cmu.edu/dietrich/philosophy/people/emeritus/glymour.html|title=Clark Glymour|publisher=Carnegie Mellon University|accessdate=December 16, 2019}}</ref><br />
<br />
== 工作经历 ==<br />
<br />
<br />
格莱默是卡内基梅隆大学哲学系的创始人,古根海姆研究员([[Guggenheim Fellowship|Guggenheim Fellow]]),行为科学高级研究中心研究员<ref>{{cite web|url=https://casbs.stanford.edu/news/awards-and-elections-fall-2019|title=Awards and Elections, Fall 2019|publisher=Center for Advanced Study in Behavioral Sciences|accessdate=December 16, 2019}}</ref>,[[Phi Beta Kappa Society|Phi Beta Kappa]]联谊会讲师<ref>{{cite web|url=https://www.pbk.org/Awards/Romanell/PastWinners|title=Romanell-Phi Beta Kappa Professorship Past Winners|publisher=Phi Beta Kappa|accessdate=December 16, 2019}}</ref>,美国科学促进会(AAAS)统计部门研究员<ref>{{cite web|url=https://www.amacad.org/person/clark-glymour|title=Clark Glymour|publisher=American Academy of Arts and Sciences|accessdate=December 16, 2019}}</ref>。格莱默和他的合作者创造了贝叶斯网络的因果解释<ref>P. Spirtes, C. Glymour, R. Scheines, Causation, Prediction and Search, Springer Lecture Notes in Statistics, 1993.</ref>。他的研究兴趣领域包括: 认识论([[epistemology]])<ref>Epistemology: 5 Questions Edited by Vincent F. Hendricks and Duncan Pritchard, September 2008, [[wikipedia:ISBN_(identifier)|ISBN]] [[wikipedia:Special:BookSources/87-92130-07-0|87-92130-07-0]]. </ref>(尤其是 Android 认识论([[Android epistemology]]))、机器学习([[machine learning]],)、自动推理([[automated reasoning]])、判断心理学([[psychology]] of judgment)和数学心理学([[mathematical psychology]])。<ref>{{cite web|url=https://www.ihmc.us/groups/clark-glymour/|title=Clark Glymour|accessdate=December 16, 2019}}</ref>格莱莫尔对科学哲学的主要贡献之一是在贝叶斯概率([[Bayesian probability]])领域,特别是在他对贝叶斯“旧证据问题”的分析中<ref>{{cite web|url=http://plato.stanford.edu/entries/epistemology-bayesian/|title=Bayesian Epistemology|date=July 12, 2001}}</ref><ref>Glymour, C.; Theory and evidence (1981), pp. 63-93.</ref>。格莱默与彼得 · 斯皮尔茨(Peter Spirtes)和理查德 · 谢恩斯(Richard Scheines)合作,还开发了一种自动因果推理算法,以软件形式实现,命名为[[TETRAD]]<ref>[http://www.phil.cmu.edu/projects/tetrad/publications.html Publications] TETRAD. Retrieved December 16, 2019.</ref>。采用多元统计数据作为输入,TETRAD 从所有可能的因果关系模型中快速搜索,并根据这些变量之间的条件依赖关系输出最合理的因果模型。该算法基于统计学、图论、科学哲学和人工智能的原理<ref>Glymour, Clark; Scheines, Richard; Spirtes, Peter; Kelly, Kevin. "TETRAD: Discovering Causal Structure" Multivariate Behavioral Research 23.2 (1988). 10 July 2010. doi:[https://doi.org/10.1207%2Fs15327906mbr2302_13 10.1207/s15327906mbr2302_13]. [[wikipedia:PMID_(identifier)|PMID]] [https://pubmed.ncbi.nlm.nih.gov/26764954 26764954].</ref>。<br />
<br />
<br />
格莱默获得了化学([[chemistry]])和哲学([[philosophy]])的本科学位。他研究生工作专注于化学物理学([[chemical physics]]),并于1969年获得印第安纳大学( [[Indiana University (Bloomington)|Indiana University]])历史与科学哲学博士学位。<br />
<br />
==研究成果(Publications)==<br />
===书籍===<br />
*''Theory and Evidence'' (Princeton, 1980)<br />
*''Examining Holistic Medicine'' (with D. Stalker), Prometheus, 1985<br />
*''Foundations of Space-Time Theories'' (with J. Earman), University of Minnesota Press, 1986<br />
*''Discovering Causal Structure'' (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*''Causation, Prediction and Search'' (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*''Thinking Things Through'', MIT Press, 1994<br />
*''Android Epistemology'' (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*''The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology'', MIT Press, 2001<br />
*''Galileo in Pittsburgh'' Harvard University Press, 2010.<br />
<br />
*Theory and Evidence (Princeton, 1980)<br />
*Examining Holistic Medicine (with D. Stalker), Prometheus, 1985<br />
*Foundations of Space-Time Theories (with J. Earman), University of Minnesota Press, 1986<br />
*Discovering Causal Structure (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*Causation, Prediction and Search (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*Thinking Things Through, MIT Press, 1994<br />
*Android Epistemology (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology, MIT Press, 2001<br />
*Galileo in Pittsburgh Harvard University Press, 2010.<br />
<br />
===期刊论文===<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", ''Open Philosophy'', 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", ''[[Philosophy of Science (journal)|Philosophy of Science]]'', 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", ''[[Journal of Philosophy]]'', 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. ''Physical Theory and Its Interpretation: Essays in Honor of [[Jeffrey Bub]]'', Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", ''[[Mind (journal)|Mind]]'', 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", ''UAI Proceedings'', 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", ''[[Genomics]]'', Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", ''[[Statistical Applications in Genetics and Molecular Biology]]'', Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", ''Behavioral and Brain Sciences'', in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", ''Philosophy of Science'', Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", ''[[Encyclopedia of Social Science]]'', in press<br />
*"We believe in freedom of the will so that we can learn", ''[[Behavioral and Brain Sciences]]'', Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", ''[[Daedalus (journal)|Daedelus]]'', Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, ''Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence'', August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", ''Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics'', (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", ''[[Erkenntnis]]'', Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", ''[[British Journal for Philosophy of Science]]'', Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", ''[[Journal of Econometrics]]'', Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", ''[[Trends in Cognitive Sciences]]'', Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", ''[[Psychological Review]], Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. ''[[Philosophical Essays on Freud]]'', Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", Open Philosophy, 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", Philosophy of Science, 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", Journal of Philosophy, 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. Physical Theory and Its Interpretation: Essays in Honor of Jeffrey Bub, Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", Mind, 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", UAI Proceedings, 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", Genomics, Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", Statistical Applications in Genetics and Molecular Biology, Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", Behavioral and Brain Sciences, in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", Philosophy of Science, Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", Encyclopedia of Social Science, in press<br />
*"We believe in freedom of the will so that we can learn", Behavioral and Brain Sciences, Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", Daedelus, Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence, August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics, (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", Erkenntnis, Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", British Journal for Philosophy of Science, Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", Journal of Econometrics, Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", Trends in Cognitive Sciences, Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", Psychological Review, Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. Philosophical Essays on Freud, Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
* <br />
<br />
==参考文献==<br />
{{Reflist}}<br />
<br />
== 外部链接 ==<br />
*IHMC 网站:[https://www.ihmc.us/groups/clark-glymour/ IHMC website]<br />
*卡内基梅隆大学哲学系主页:[https://web.archive.org/web/20100601161806/http://www.hss.cmu.edu/philosophy/faculty-glymour.php Carnegie Mellon Department of Philosophy faculty page]<br />
*TETRAD项目:[http://www.phil.cmu.edu/projects/tetrad/publications.html TETRAD Project]</div>Weihttps://wiki.swarma.org/index.php?title=Clark_Glymour&diff=29286Clark Glymour2022-03-20T08:57:13Z<p>Wei:</p>
<hr />
<div>'''克拉克 · 格莱莫尔'''(Clark N. Glymour)生于1942年,是卡内基梅隆大学哲学系的校友大学名誉教授。他也是佛罗里达人类和机器认知研究所([[Florida Institute for Human and Machine Cognition]])的高级研究科学家。<ref>{{cite web|url=https://www.cmu.edu/dietrich/philosophy/people/emeritus/glymour.html|title=Clark Glymour|publisher=Carnegie Mellon University|accessdate=December 16, 2019}}</ref><br />
<br />
==工作经历==<br />
<br />
<br />
格莱默是卡内基梅隆大学哲学系的创始人,古根海姆研究员([[Guggenheim Fellowship|Guggenheim Fellow]]),行为科学高级研究中心研究员<ref>{{cite web|url=https://casbs.stanford.edu/news/awards-and-elections-fall-2019|title=Awards and Elections, Fall 2019|publisher=Center for Advanced Study in Behavioral Sciences|accessdate=December 16, 2019}}</ref>,[[Phi Beta Kappa Society|Phi Beta Kappa]]联谊会讲师<ref>{{cite web|url=https://www.pbk.org/Awards/Romanell/PastWinners|title=Romanell-Phi Beta Kappa Professorship Past Winners|publisher=Phi Beta Kappa|accessdate=December 16, 2019}}</ref>,美国科学促进会(AAAS)统计部门研究员<ref>{{cite web|url=https://www.amacad.org/person/clark-glymour|title=Clark Glymour|publisher=American Academy of Arts and Sciences|accessdate=December 16, 2019}}</ref>。格莱默和他的合作者创造了贝叶斯网络的因果解释<ref>P. Spirtes, C. Glymour, R. Scheines, Causation, Prediction and Search, Springer Lecture Notes in Statistics, 1993.</ref>。他的研究兴趣领域包括: 认识论([[epistemology]])<ref>Epistemology: 5 Questions Edited by Vincent F. Hendricks and Duncan Pritchard, September 2008, [[wikipedia:ISBN_(identifier)|ISBN]] [[wikipedia:Special:BookSources/87-92130-07-0|87-92130-07-0]]. </ref>(尤其是 Android 认识论([[Android epistemology]]))、机器学习([[machine learning]],)、自动推理([[automated reasoning]])、判断心理学([[psychology]] of judgment)和数学心理学([[mathematical psychology]])。<ref>{{cite web|url=https://www.ihmc.us/groups/clark-glymour/|title=Clark Glymour|accessdate=December 16, 2019}}</ref>格莱莫尔对科学哲学的主要贡献之一是在贝叶斯概率([[Bayesian probability]])领域,特别是在他对贝叶斯“旧证据问题”的分析中<ref>{{cite web|url=http://plato.stanford.edu/entries/epistemology-bayesian/|title=Bayesian Epistemology|date=July 12, 2001}}</ref><ref>Glymour, C.; Theory and evidence (1981), pp. 63-93.</ref>。格莱默与彼得 · 斯皮尔茨(Peter Spirtes)和理查德 · 谢恩斯(Richard Scheines)合作,还开发了一种自动因果推理算法,以软件形式实现,命名为[[TETRAD]]<ref>[http://www.phil.cmu.edu/projects/tetrad/publications.html Publications] TETRAD. Retrieved December 16, 2019.</ref>。采用多元统计数据作为输入,TETRAD 从所有可能的因果关系模型中快速搜索,并根据这些变量之间的条件依赖关系输出最合理的因果模型。该算法基于统计学、图论、科学哲学和人工智能的原理<ref>Glymour, Clark; Scheines, Richard; Spirtes, Peter; Kelly, Kevin. "TETRAD: Discovering Causal Structure" Multivariate Behavioral Research 23.2 (1988). 10 July 2010. doi:[https://doi.org/10.1207%2Fs15327906mbr2302_13 10.1207/s15327906mbr2302_13]. [[wikipedia:PMID_(identifier)|PMID]] [https://pubmed.ncbi.nlm.nih.gov/26764954 26764954].</ref>。<br />
<br />
<br />
格莱默获得了化学([[chemistry]])和哲学([[philosophy]])的本科学位。他研究生工作专注于化学物理学([[chemical physics]]),并于1969年获得印第安纳大学( [[Indiana University (Bloomington)|Indiana University]])历史与科学哲学博士学位。<br />
<br />
==研究成果(Publications)==<br />
===书籍===<br />
*''Theory and Evidence'' (Princeton, 1980)<br />
*''Examining Holistic Medicine'' (with D. Stalker), Prometheus, 1985<br />
*''Foundations of Space-Time Theories'' (with J. Earman), University of Minnesota Press, 1986<br />
*''Discovering Causal Structure'' (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*''Causation, Prediction and Search'' (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*''Thinking Things Through'', MIT Press, 1994<br />
*''Android Epistemology'' (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*''The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology'', MIT Press, 2001<br />
*''Galileo in Pittsburgh'' Harvard University Press, 2010.<br />
<br />
*Theory and Evidence (Princeton, 1980)<br />
*Examining Holistic Medicine (with D. Stalker), Prometheus, 1985<br />
*Foundations of Space-Time Theories (with J. Earman), University of Minnesota Press, 1986<br />
*Discovering Causal Structure (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*Causation, Prediction and Search (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*Thinking Things Through, MIT Press, 1994<br />
*Android Epistemology (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology, MIT Press, 2001<br />
*Galileo in Pittsburgh Harvard University Press, 2010.<br />
<br />
===期刊论文===<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", ''Open Philosophy'', 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", ''[[Philosophy of Science (journal)|Philosophy of Science]]'', 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", ''[[Journal of Philosophy]]'', 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. ''Physical Theory and Its Interpretation: Essays in Honor of [[Jeffrey Bub]]'', Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", ''[[Mind (journal)|Mind]]'', 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", ''UAI Proceedings'', 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", ''[[Genomics]]'', Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", ''[[Statistical Applications in Genetics and Molecular Biology]]'', Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", ''Behavioral and Brain Sciences'', in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", ''Philosophy of Science'', Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", ''[[Encyclopedia of Social Science]]'', in press<br />
*"We believe in freedom of the will so that we can learn", ''[[Behavioral and Brain Sciences]]'', Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", ''[[Daedalus (journal)|Daedelus]]'', Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, ''Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence'', August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", ''Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics'', (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", ''[[Erkenntnis]]'', Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", ''[[British Journal for Philosophy of Science]]'', Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", ''[[Journal of Econometrics]]'', Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", ''[[Trends in Cognitive Sciences]]'', Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", ''[[Psychological Review]], Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. ''[[Philosophical Essays on Freud]]'', Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", Open Philosophy, 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", Philosophy of Science, 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", Journal of Philosophy, 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. Physical Theory and Its Interpretation: Essays in Honor of Jeffrey Bub, Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", Mind, 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", UAI Proceedings, 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", Genomics, Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", Statistical Applications in Genetics and Molecular Biology, Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", Behavioral and Brain Sciences, in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", Philosophy of Science, Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", Encyclopedia of Social Science, in press<br />
*"We believe in freedom of the will so that we can learn", Behavioral and Brain Sciences, Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", Daedelus, Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence, August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics, (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", Erkenntnis, Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", British Journal for Philosophy of Science, Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", Journal of Econometrics, Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", Trends in Cognitive Sciences, Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", Psychological Review, Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. Philosophical Essays on Freud, Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
* <br />
<br />
==参考文献==<br />
{{Reflist}}<br />
<br />
==外部链接==<br />
*IHMC 网站:[https://www.ihmc.us/groups/clark-glymour/ IHMC website]<br />
*卡内基梅隆大学哲学系主页:[https://web.archive.org/web/20100601161806/http://www.hss.cmu.edu/philosophy/faculty-glymour.php Carnegie Mellon Department of Philosophy faculty page]<br />
*TETRAD项目:[http://www.phil.cmu.edu/projects/tetrad/publications.html TETRAD Project]<br />
<br />
{{DEFAULTSORT:Glymour, Clark}}<br />
[[Category:1942 births]]<br />
[[Category:Living people]]<br />
[[Category:American logicians]]<br />
[[Category:Philosophers of science]]<br />
[[Category:Indiana University alumni]]<br />
[[Category:Florida Institute for Human and Machine Cognition people]]<br />
[[Category:20th-century American philosophers]]<br />
[[Category:Carnegie Mellon University faculty]]<br />
[[Category:Place of birth missing (living people)]]<br />
[[Category:Fellows of the American Academy of Arts and Sciences]]</div>Weihttps://wiki.swarma.org/index.php?title=Clark_Glymour&diff=29285Clark Glymour2022-03-20T08:53:40Z<p>Wei:</p>
<hr />
<div>'''克拉克 · 格莱莫尔'''(Clark N. Glymour)生于1942年,是卡内基梅隆大学哲学系的校友大学名誉教授。他也是佛罗里达人类和机器认知研究所([[Florida Institute for Human and Machine Cognition]])的高级研究科学家。<ref>{{cite web|url=https://www.cmu.edu/dietrich/philosophy/people/emeritus/glymour.html|title=Clark Glymour|publisher=Carnegie Mellon University|accessdate=December 16, 2019}}</ref><br />
<br />
==工作经历==<br />
<br />
<br />
格莱默是卡内基梅隆大学哲学系的创始人,古根海姆研究员([[Guggenheim Fellowship|Guggenheim Fellow]]),行为科学高级研究中心研究员<ref>{{cite web|url=https://casbs.stanford.edu/news/awards-and-elections-fall-2019|title=Awards and Elections, Fall 2019|publisher=Center for Advanced Study in Behavioral Sciences|accessdate=December 16, 2019}}</ref>,[[Phi Beta Kappa Society|Phi Beta Kappa]]联谊会讲师<ref>{{cite web|url=https://www.pbk.org/Awards/Romanell/PastWinners|title=Romanell-Phi Beta Kappa Professorship Past Winners|publisher=Phi Beta Kappa|accessdate=December 16, 2019}}</ref>,美国科学促进会(AAAS)统计部门研究员<ref>{{cite web|url=https://www.amacad.org/person/clark-glymour|title=Clark Glymour|publisher=American Academy of Arts and Sciences|accessdate=December 16, 2019}}</ref>。格莱默和他的合作者创造了贝叶斯网络的因果解释<ref>P. Spirtes, C. Glymour, R. Scheines, Causation, Prediction and Search, Springer Lecture Notes in Statistics, 1993.</ref>。他的研究兴趣领域包括: 认识论([[epistemology]])<ref>Epistemology: 5 Questions Edited by Vincent F. Hendricks and Duncan Pritchard, September 2008, [[wikipedia:ISBN_(identifier)|ISBN]] [[wikipedia:Special:BookSources/87-92130-07-0|87-92130-07-0]]. </ref>(尤其是 Android 认识论([[Android epistemology]]))、机器学习([[machine learning]],)、自动推理([[automated reasoning]])、判断心理学([[psychology]] of judgment)和数学心理学([[mathematical psychology]])。<ref>{{cite web|url=https://www.ihmc.us/groups/clark-glymour/|title=Clark Glymour|accessdate=December 16, 2019}}</ref>格莱莫尔对科学哲学的主要贡献之一是在贝叶斯概率([[Bayesian probability]])领域,特别是在他对贝叶斯“旧证据问题”的分析中<ref>{{cite web|url=http://plato.stanford.edu/entries/epistemology-bayesian/|title=Bayesian Epistemology|date=July 12, 2001}}</ref><ref>Glymour, C.; Theory and evidence (1981), pp. 63-93.</ref>。格莱默与彼得 · 斯皮尔茨(Peter Spirtes)和理查德 · 谢恩斯(Richard Scheines)合作,还开发了一种自动因果推理算法,以软件形式实现,命名为[[TETRAD]]<ref>[http://www.phil.cmu.edu/projects/tetrad/publications.html Publications] TETRAD. Retrieved December 16, 2019.</ref>。采用多元统计数据作为输入,TETRAD 从所有可能的因果关系模型中快速搜索,并根据这些变量之间的条件依赖关系输出最合理的因果模型。该算法基于统计学、图论、科学哲学和人工智能的原理<ref>Glymour, Clark; Scheines, Richard; Spirtes, Peter; Kelly, Kevin. "TETRAD: Discovering Causal Structure" Multivariate Behavioral Research 23.2 (1988). 10 July 2010. doi:[https://doi.org/10.1207%2Fs15327906mbr2302_13 10.1207/s15327906mbr2302_13]. [[wikipedia:PMID_(identifier)|PMID]] [https://pubmed.ncbi.nlm.nih.gov/26764954 26764954].</ref>。<br />
<br />
<br />
格莱默获得了化学([[chemistry]])和哲学([[philosophy]])的本科学位。他研究生工作专注于化学物理学([[chemical physics]]),并于1969年获得印第安纳大学( [[Indiana University (Bloomington)|Indiana University]])历史与科学哲学博士学位。<br />
<br />
==研究成果(Publications)==<br />
===书籍===<br />
*''Theory and Evidence'' (Princeton, 1980)<br />
*''Examining Holistic Medicine'' (with D. Stalker), Prometheus, 1985<br />
*''Foundations of Space-Time Theories'' (with J. Earman), University of Minnesota Press, 1986<br />
*''Discovering Causal Structure'' (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*''Causation, Prediction and Search'' (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*''Thinking Things Through'', MIT Press, 1994<br />
*''Android Epistemology'' (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*''The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology'', MIT Press, 2001<br />
*''Galileo in Pittsburgh'' Harvard University Press, 2010.<br />
<br />
*Theory and Evidence (Princeton, 1980)<br />
*Examining Holistic Medicine (with D. Stalker), Prometheus, 1985<br />
*Foundations of Space-Time Theories (with J. Earman), University of Minnesota Press, 1986<br />
*Discovering Causal Structure (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*Causation, Prediction and Search (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*Thinking Things Through, MIT Press, 1994<br />
*Android Epistemology (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology, MIT Press, 2001<br />
*Galileo in Pittsburgh Harvard University Press, 2010.<br />
<br />
===期刊论文===<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", ''Open Philosophy'', 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", ''[[Philosophy of Science (journal)|Philosophy of Science]]'', 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", ''[[Journal of Philosophy]]'', 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. ''Physical Theory and Its Interpretation: Essays in Honor of [[Jeffrey Bub]]'', Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", ''[[Mind (journal)|Mind]]'', 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", ''UAI Proceedings'', 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", ''[[Genomics]]'', Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", ''[[Statistical Applications in Genetics and Molecular Biology]]'', Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", ''Behavioral and Brain Sciences'', in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", ''Philosophy of Science'', Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", ''[[Encyclopedia of Social Science]]'', in press<br />
*"We believe in freedom of the will so that we can learn", ''[[Behavioral and Brain Sciences]]'', Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", ''[[Daedalus (journal)|Daedelus]]'', Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, ''Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence'', August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", ''Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics'', (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", ''[[Erkenntnis]]'', Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", ''[[British Journal for Philosophy of Science]]'', Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", ''[[Journal of Econometrics]]'', Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", ''[[Trends in Cognitive Sciences]]'', Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", ''[[Psychological Review]], Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. ''[[Philosophical Essays on Freud]]'', Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", Open Philosophy, 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", Philosophy of Science, 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", Journal of Philosophy, 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. Physical Theory and Its Interpretation: Essays in Honor of Jeffrey Bub, Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", Mind, 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", UAI Proceedings, 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", Genomics, Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", Statistical Applications in Genetics and Molecular Biology, Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", Behavioral and Brain Sciences, in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", Philosophy of Science, Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", Encyclopedia of Social Science, in press<br />
*"We believe in freedom of the will so that we can learn", Behavioral and Brain Sciences, Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", Daedelus, Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence, August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics, (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", Erkenntnis, Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", British Journal for Philosophy of Science, Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", Journal of Econometrics, Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", Trends in Cognitive Sciences, Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", Psychological Review, Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. Philosophical Essays on Freud, Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
* <br />
<br />
==参考文献==<br />
{{Reflist}}<br />
<br />
==<nowiki>= = 外部链接 =</nowiki>==<br />
*IHMC 网站:[https://www.ihmc.us/groups/clark-glymour/ IHMC website]<br />
*卡内基梅隆大学哲学系主页:[https://web.archive.org/web/20100601161806/http://www.hss.cmu.edu/philosophy/faculty-glymour.php Carnegie Mellon Department of Philosophy faculty page]<br />
*TETRAD项目:[http://www.phil.cmu.edu/projects/tetrad/publications.html TETRAD Project]<br />
<br />
{{Authority control}}<br />
<br />
{{DEFAULTSORT:Glymour, Clark}}<br />
[[Category:1942 births]]<br />
[[Category:Living people]]<br />
[[Category:American logicians]]<br />
[[Category:Philosophers of science]]<br />
[[Category:Indiana University alumni]]<br />
[[Category:Florida Institute for Human and Machine Cognition people]]<br />
[[Category:20th-century American philosophers]]<br />
[[Category:Carnegie Mellon University faculty]]<br />
[[Category:Place of birth missing (living people)]]<br />
[[Category:Fellows of the American Academy of Arts and Sciences]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=Clark_Glymour&diff=29284Clark Glymour2022-03-20T08:51:52Z<p>Wei:</p>
<hr />
<div>'''克拉克 · 格莱莫尔'''(Clark N. Glymour)生于1942年,是卡内基梅隆大学哲学系的校友大学名誉教授。他也是佛罗里达人类和机器认知研究所([[Florida Institute for Human and Machine Cognition]])的高级研究科学家。<ref>{{cite web|url=https://www.cmu.edu/dietrich/philosophy/people/emeritus/glymour.html|title=Clark Glymour|publisher=Carnegie Mellon University|accessdate=December 16, 2019}}</ref><br />
<br />
==工作经历==<br />
<br />
<br />
格莱默是卡内基梅隆大学哲学系的创始人,古根海姆研究员([[Guggenheim Fellowship|Guggenheim Fellow]]),行为科学高级研究中心研究员<ref>{{cite web|url=https://casbs.stanford.edu/news/awards-and-elections-fall-2019|title=Awards and Elections, Fall 2019|publisher=Center for Advanced Study in Behavioral Sciences|accessdate=December 16, 2019}}</ref>,[[Phi Beta Kappa Society|Phi Beta Kappa]]联谊会讲师<ref>{{cite web|url=https://www.pbk.org/Awards/Romanell/PastWinners|title=Romanell-Phi Beta Kappa Professorship Past Winners|publisher=Phi Beta Kappa|accessdate=December 16, 2019}}</ref>,美国科学促进会(AAAS)统计部门研究员<ref>{{cite web|url=https://www.amacad.org/person/clark-glymour|title=Clark Glymour|publisher=American Academy of Arts and Sciences|accessdate=December 16, 2019}}</ref>。格莱默和他的合作者创造了贝叶斯网络的因果解释<ref>P. Spirtes, C. Glymour, R. Scheines, Causation, Prediction and Search, Springer Lecture Notes in Statistics, 1993.</ref>。他的研究兴趣领域包括: 认识论([[epistemology]])<ref>Epistemology: 5 Questions Edited by Vincent F. Hendricks and Duncan Pritchard, September 2008, {{ISBN|87-92130-07-0}}.</ref>(尤其是 Android 认识论([[Android epistemology]]))、机器学习([[machine learning]],)、自动推理([[automated reasoning]])、判断心理学([[psychology]] of judgment)和数学心理学([[mathematical psychology]])。<ref>{{cite web|url=https://www.ihmc.us/groups/clark-glymour/|title=Clark Glymour|accessdate=December 16, 2019}}</ref>格莱莫尔对科学哲学的主要贡献之一是在贝叶斯概率([[Bayesian probability]])领域,特别是在他对贝叶斯“旧证据问题”的分析中<ref>{{cite web|url=http://plato.stanford.edu/entries/epistemology-bayesian/|title=Bayesian Epistemology|date=July 12, 2001}}</ref><ref>Glymour, C.; Theory and evidence (1981), pp. 63-93.</ref>。格莱默与彼得 · 斯皮尔茨(Peter Spirtes)和理查德 · 谢恩斯(Richard Scheines)合作,还开发了一种自动因果推理算法,以软件形式实现,命名为[[TETRAD]]<ref>[http://www.phil.cmu.edu/projects/tetrad/publications.html Publications] TETRAD. Retrieved December 16, 2019.</ref>。采用多元统计数据作为输入,TETRAD 从所有可能的因果关系模型中快速搜索,并根据这些变量之间的条件依赖关系输出最合理的因果模型。该算法基于统计学、图论、科学哲学和人工智能的原理<ref>Glymour, Clark; Scheines, Richard; Spirtes, Peter; Kelly, Kevin. "TETRAD: Discovering Causal Structure" Multivariate Behavioral Research 23.2 (1988). 10 July 2010. doi:[https://doi.org/10.1207%2Fs15327906mbr2302_13 10.1207/s15327906mbr2302_13]. [[wikipedia:PMID_(identifier)|PMID]] [https://pubmed.ncbi.nlm.nih.gov/26764954 26764954].</ref>。<br />
<br />
<br />
格莱默获得了化学([[chemistry]])和哲学([[philosophy]])的本科学位。他研究生工作专注于化学物理学([[chemical physics]]),并于1969年获得印第安纳大学( [[Indiana University (Bloomington)|Indiana University]])历史与科学哲学博士学位。<br />
<br />
==研究成果(Publications)==<br />
===书籍===<br />
*''Theory and Evidence'' (Princeton, 1980)<br />
*''Examining Holistic Medicine'' (with D. Stalker), Prometheus, 1985<br />
*''Foundations of Space-Time Theories'' (with J. Earman), University of Minnesota Press, 1986<br />
*''Discovering Causal Structure'' (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*''Causation, Prediction and Search'' (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*''Thinking Things Through'', MIT Press, 1994<br />
*''Android Epistemology'' (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*''The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology'', MIT Press, 2001<br />
*''Galileo in Pittsburgh'' Harvard University Press, 2010.<br />
<br />
*Theory and Evidence (Princeton, 1980)<br />
*Examining Holistic Medicine (with D. Stalker), Prometheus, 1985<br />
*Foundations of Space-Time Theories (with J. Earman), University of Minnesota Press, 1986<br />
*Discovering Causal Structure (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*Causation, Prediction and Search (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*Thinking Things Through, MIT Press, 1994<br />
*Android Epistemology (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology, MIT Press, 2001<br />
*Galileo in Pittsburgh Harvard University Press, 2010.<br />
<br />
===期刊论文===<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", ''Open Philosophy'', 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", ''[[Philosophy of Science (journal)|Philosophy of Science]]'', 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", ''[[Journal of Philosophy]]'', 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. ''Physical Theory and Its Interpretation: Essays in Honor of [[Jeffrey Bub]]'', Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", ''[[Mind (journal)|Mind]]'', 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", ''UAI Proceedings'', 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", ''[[Genomics]]'', Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", ''[[Statistical Applications in Genetics and Molecular Biology]]'', Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", ''Behavioral and Brain Sciences'', in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", ''Philosophy of Science'', Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", ''[[Encyclopedia of Social Science]]'', in press<br />
*"We believe in freedom of the will so that we can learn", ''[[Behavioral and Brain Sciences]]'', Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", ''[[Daedalus (journal)|Daedelus]]'', Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, ''Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence'', August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", ''Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics'', (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", ''[[Erkenntnis]]'', Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", ''[[British Journal for Philosophy of Science]]'', Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", ''[[Journal of Econometrics]]'', Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", ''[[Trends in Cognitive Sciences]]'', Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", ''[[Psychological Review]], Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. ''[[Philosophical Essays on Freud]]'', Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", Open Philosophy, 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", Philosophy of Science, 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", Journal of Philosophy, 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. Physical Theory and Its Interpretation: Essays in Honor of Jeffrey Bub, Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", Mind, 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", UAI Proceedings, 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", Genomics, Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", Statistical Applications in Genetics and Molecular Biology, Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", Behavioral and Brain Sciences, in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", Philosophy of Science, Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", Encyclopedia of Social Science, in press<br />
*"We believe in freedom of the will so that we can learn", Behavioral and Brain Sciences, Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", Daedelus, Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence, August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics, (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", Erkenntnis, Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", British Journal for Philosophy of Science, Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", Journal of Econometrics, Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", Trends in Cognitive Sciences, Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", Psychological Review, Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. Philosophical Essays on Freud, Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
* <br />
<br />
==参考文献==<br />
{{Reflist}}<br />
<br />
==<nowiki>= = 外部链接 =</nowiki>==<br />
*IHMC 网站:[https://www.ihmc.us/groups/clark-glymour/ IHMC website]<br />
*卡内基梅隆大学哲学系主页:[https://web.archive.org/web/20100601161806/http://www.hss.cmu.edu/philosophy/faculty-glymour.php Carnegie Mellon Department of Philosophy faculty page]<br />
*TETRAD项目:[http://www.phil.cmu.edu/projects/tetrad/publications.html TETRAD Project]<br />
<br />
{{Authority control}}<br />
<br />
{{DEFAULTSORT:Glymour, Clark}}<br />
[[Category:1942 births]]<br />
[[Category:Living people]]<br />
[[Category:American logicians]]<br />
[[Category:Philosophers of science]]<br />
[[Category:Indiana University alumni]]<br />
[[Category:Florida Institute for Human and Machine Cognition people]]<br />
[[Category:20th-century American philosophers]]<br />
[[Category:Carnegie Mellon University faculty]]<br />
[[Category:Place of birth missing (living people)]]<br />
[[Category:Fellows of the American Academy of Arts and Sciences]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=Clark_Glymour&diff=29283Clark Glymour2022-03-20T08:51:06Z<p>Wei:</p>
<hr />
<div>'''克拉克 · 格莱莫尔'''(Clark N. Glymour)生于1942年,是卡内基梅隆大学哲学系的校友大学名誉教授。他也是佛罗里达人类和机器认知研究所([[Florida Institute for Human and Machine Cognition]])的高级研究科学家。<ref>{{cite web|url=https://www.cmu.edu/dietrich/philosophy/people/emeritus/glymour.html|title=Clark Glymour|publisher=Carnegie Mellon University|accessdate=December 16, 2019}}</ref><br />
<br />
==工作经历==<br />
<br />
<br />
格莱默是卡内基梅隆大学哲学系的创始人,古根海姆研究员([[Guggenheim Fellowship|Guggenheim Fellow]]),行为科学高级研究中心研究员<ref>{{cite web|url=https://casbs.stanford.edu/news/awards-and-elections-fall-2019|title=Awards and Elections, Fall 2019|publisher=Center for Advanced Study in Behavioral Sciences|accessdate=December 16, 2019}}</ref>,[[Phi Beta Kappa Society|Phi Beta Kappa]]联谊会讲师<ref>{{cite web|url=https://www.pbk.org/Awards/Romanell/PastWinners|title=Romanell-Phi Beta Kappa Professorship Past Winners|publisher=Phi Beta Kappa|accessdate=December 16, 2019}}</ref>,美国科学促进会(AAAS)统计部门研究员<ref>{{cite web|url=https://www.amacad.org/person/clark-glymour|title=Clark Glymour|publisher=American Academy of Arts and Sciences|accessdate=December 16, 2019}}</ref>。格莱默和他的合作者创造了贝叶斯网络的因果解释<ref>P. Spirtes, C. Glymour, R. Scheines, Causation, Prediction and Search, Springer Lecture Notes in Statistics, 1993.</ref>。他的研究兴趣领域包括: 认识论([[epistemology]])<ref>Epistemology: 5 Questions Edited by Vincent F. Hendricks and Duncan Pritchard, September 2008, {{ISBN|87-92130-07-0}}.</ref>(尤其是 Android 认识论([[Android epistemology]]))、机器学习([[machine learning]],)、自动推理([[automated reasoning]])、判断心理学([[psychology]] of judgment)和数学心理学([[mathematical psychology]])。<ref>{{cite web|url=https://www.ihmc.us/groups/clark-glymour/|title=Clark Glymour|accessdate=December 16, 2019}}</ref>格莱莫尔对科学哲学的主要贡献之一是在贝叶斯概率([[Bayesian probability]])领域,特别是在他对贝叶斯“旧证据问题”的分析中<ref>{{cite web|url=http://plato.stanford.edu/entries/epistemology-bayesian/|title=Bayesian Epistemology|date=July 12, 2001}}</ref><ref>Glymour, C.; Theory and evidence (1981), pp. 63-93.</ref>。格莱默与彼得 · 斯皮尔茨(Peter Spirtes)和理查德 · 谢恩斯(Richard Scheines)合作,还开发了一种自动因果推理算法,以软件形式实现,命名为[[TETRAD]]<ref>[http://www.phil.cmu.edu/projects/tetrad/publications.html Publications] TETRAD. Retrieved December 16, 2019.</ref>。采用多元统计数据作为输入,TETRAD 从所有可能的因果关系模型中快速搜索,并根据这些变量之间的条件依赖关系输出最合理的因果模型。该算法基于统计学、图论、科学哲学和人工智能的原理<ref>Glymour, Clark; Scheines, Richard; Spirtes, Peter; Kelly, Kevin. "TETRAD: Discovering Causal Structure" Multivariate Behavioral Research 23.2 (1988). 10 July 2010. doi:[https://doi.org/10.1207%2Fs15327906mbr2302_13 10.1207/s15327906mbr2302_13]. [[wikipedia:PMID_(identifier)|PMID]] [https://pubmed.ncbi.nlm.nih.gov/26764954 26764954].</ref>。<br />
<br />
<br />
格莱默获得了化学([[chemistry]])和哲学([[philosophy]])的本科学位。他研究生工作专注于化学物理学([[chemical physics]]),并于1969年获得印第安纳大学( [[Indiana University (Bloomington)|Indiana University]])历史与科学哲学博士学位。<br />
<br />
==研究成果(Publications)==<br />
===书籍===<br />
*''Theory and Evidence'' (Princeton, 1980)<br />
*''Examining Holistic Medicine'' (with D. Stalker), Prometheus, 1985<br />
*''Foundations of Space-Time Theories'' (with J. Earman), University of Minnesota Press, 1986<br />
*''Discovering Causal Structure'' (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*''Causation, Prediction and Search'' (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*''Thinking Things Through'', MIT Press, 1994<br />
*''Android Epistemology'' (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*''The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology'', MIT Press, 2001<br />
*''Galileo in Pittsburgh'' Harvard University Press, 2010.<br />
<br />
*Theory and Evidence (Princeton, 1980)<br />
*Examining Holistic Medicine (with D. Stalker), Prometheus, 1985<br />
*Foundations of Space-Time Theories (with J. Earman), University of Minnesota Press, 1986<br />
*Discovering Causal Structure (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*Causation, Prediction and Search (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*Thinking Things Through, MIT Press, 1994<br />
*Android Epistemology (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology, MIT Press, 2001<br />
*Galileo in Pittsburgh Harvard University Press, 2010.<br />
<br />
= = = = = = = = = = = 理论与证据(普林斯顿,1980) <br />
* 检验整体医学(与 d. Stalker 合著) ,普罗米修斯,1985 <br />
* 时空理论基础(与 j. Earman 合著) ,明尼苏达大学出版社,1986 <br />
* 发现因果结构(r. Scheines,p. Spirtes 和 K.Kelly 合著)学术出版社,1987 <br />
* 因果关系,预测和搜索(p. Spirtes 和 r. Scheines 合著) ,Springer,1993,第二版麻省理工学院出版社,2001 <br />
* ,1994 <br />
* 安卓认识论(与 k · 福特和 p · 海耶斯合著)麻省理工学院/AAAI 出版社,1996 <br />
* 心灵的箭头: 贝叶斯网和心理学中的图形因果模型,麻省理工学院出版社,2001 <br />
* 伽利略,匹兹堡哈佛大学出版社,2010。<br />
<br />
===期刊论文===<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", ''Open Philosophy'', 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", ''[[Philosophy of Science (journal)|Philosophy of Science]]'', 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", ''[[Journal of Philosophy]]'', 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. ''Physical Theory and Its Interpretation: Essays in Honor of [[Jeffrey Bub]]'', Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", ''[[Mind (journal)|Mind]]'', 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", ''UAI Proceedings'', 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", ''[[Genomics]]'', Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", ''[[Statistical Applications in Genetics and Molecular Biology]]'', Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", ''Behavioral and Brain Sciences'', in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", ''Philosophy of Science'', Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", ''[[Encyclopedia of Social Science]]'', in press<br />
*"We believe in freedom of the will so that we can learn", ''[[Behavioral and Brain Sciences]]'', Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", ''[[Daedalus (journal)|Daedelus]]'', Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, ''Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence'', August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", ''Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics'', (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", ''[[Erkenntnis]]'', Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", ''[[British Journal for Philosophy of Science]]'', Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", ''[[Journal of Econometrics]]'', Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", ''[[Trends in Cognitive Sciences]]'', Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", ''[[Psychological Review]], Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. ''[[Philosophical Essays on Freud]]'', Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", Open Philosophy, 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", Philosophy of Science, 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", Journal of Philosophy, 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. Physical Theory and Its Interpretation: Essays in Honor of Jeffrey Bub, Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", Mind, 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", UAI Proceedings, 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", Genomics, Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", Statistical Applications in Genetics and Molecular Biology, Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", Behavioral and Brain Sciences, in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", Philosophy of Science, Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", Encyclopedia of Social Science, in press<br />
*"We believe in freedom of the will so that we can learn", Behavioral and Brain Sciences, Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", Daedelus, Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence, August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics, (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", Erkenntnis, Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", British Journal for Philosophy of Science, Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", Journal of Econometrics, Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", Trends in Cognitive Sciences, Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", Psychological Review, Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. Philosophical Essays on Freud, Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
* <br />
<br />
==参考文献==<br />
{{Reflist}}<br />
<br />
==<nowiki>= = 外部链接 =</nowiki>==<br />
*IHMC 网站:[https://www.ihmc.us/groups/clark-glymour/ IHMC website]<br />
*卡内基梅隆大学哲学系主页:[https://web.archive.org/web/20100601161806/http://www.hss.cmu.edu/philosophy/faculty-glymour.php Carnegie Mellon Department of Philosophy faculty page]<br />
*TETRAD项目:[http://www.phil.cmu.edu/projects/tetrad/publications.html TETRAD Project]<br />
<br />
{{Authority control}}<br />
<br />
{{DEFAULTSORT:Glymour, Clark}}<br />
[[Category:1942 births]]<br />
[[Category:Living people]]<br />
[[Category:American logicians]]<br />
[[Category:Philosophers of science]]<br />
[[Category:Indiana University alumni]]<br />
[[Category:Florida Institute for Human and Machine Cognition people]]<br />
[[Category:20th-century American philosophers]]<br />
[[Category:Carnegie Mellon University faculty]]<br />
[[Category:Place of birth missing (living people)]]<br />
[[Category:Fellows of the American Academy of Arts and Sciences]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=Clark_Glymour&diff=29280Clark Glymour2022-03-20T08:28:46Z<p>Wei:</p>
<hr />
<div>'''克拉克 · 格莱莫尔'''(Clark N. Glymour)生于1942年,是卡内基梅隆大学哲学系的校友大学名誉教授。他也是佛罗里达人类和机器认知研究所([[Florida Institute for Human and Machine Cognition]])的高级研究科学家。<ref>{{cite web|url=https://www.cmu.edu/dietrich/philosophy/people/emeritus/glymour.html|title=Clark Glymour|publisher=Carnegie Mellon University|accessdate=December 16, 2019}}</ref><br />
<br />
==工作经历==<br />
Glymour is the founder of the Philosophy Department at Carnegie Mellon University, a [[Guggenheim Fellowship|Guggenheim Fellow]], a Fellow of the Center for Advanced Study in Behavioral Sciences,<ref>{{cite web|url=https://casbs.stanford.edu/news/awards-and-elections-fall-2019|title=Awards and Elections, Fall 2019|publisher=Center for Advanced Study in Behavioral Sciences|accessdate=December 16, 2019}}</ref> a [[Phi Beta Kappa Society|Phi Beta Kappa]] lecturer,<ref>{{cite web|url=https://www.pbk.org/Awards/Romanell/PastWinners|title=Romanell-Phi Beta Kappa Professorship Past Winners|publisher=Phi Beta Kappa|accessdate=December 16, 2019}}</ref> and is a Fellow of the statistics section of the AAAS.<ref>{{cite web|url=https://www.amacad.org/person/clark-glymour|title=Clark Glymour|publisher=American Academy of Arts and Sciences|accessdate=December 16, 2019}}</ref> Glymour and his collaborators created the causal interpretation of Bayes nets.<ref>P. Spirtes, C. Glymour, R. Scheines, Causation, Prediction and Search, Springer Lecture Notes in Statistics, 1993.</ref> His areas of interest include [[epistemology]]<ref>Epistemology: 5 Questions Edited by Vincent F. Hendricks and Duncan Pritchard, September 2008, {{ISBN|87-92130-07-0}}.</ref> (particularly [[Android epistemology]]), [[machine learning]], [[automated reasoning]], [[psychology]] of judgment, and [[mathematical psychology]].<ref>{{cite web|url=https://www.ihmc.us/groups/clark-glymour/|title=Clark Glymour|accessdate=December 16, 2019}}</ref> One of Glymour's main contributions to the philosophy of science is in the area of [[Bayesian probability]], particularly in his analysis of the Bayesian "problem of old evidence".<ref>{{cite web|url=http://plato.stanford.edu/entries/epistemology-bayesian/|title=Bayesian Epistemology|date=July 12, 2001}}</ref><ref>Glymour, C.; Theory and evidence (1981), pp. 63-93.</ref> Glymour, in collaboration with Peter Spirtes and Richard Scheines, also developed an automated causal inference algorithm implemented as software named [[TETRAD]].<ref>[http://www.phil.cmu.edu/projects/tetrad/publications.html Publications] TETRAD. Retrieved December 16, 2019.</ref> Using multivariate statistical data as input, TETRAD rapidly searches from among all possible causal relationship models and returns the most plausible causal models based on conditional dependence relationships between those variables. The algorithm is based on principles from statistics, graph theory, philosophy of science, and artificial intelligence.<ref>Glymour, Clark; Scheines, Richard; Spirtes, Peter; Kelly, Kevin. "TETRAD: Discovering Causal Structure" Multivariate Behavioral Research 23.2 (1988). 10 July 2010. {{DOI|10.1207/s15327906mbr2302_13}}. {{PMID|26764954}}.</ref><br />
<br />
Glymour is the founder of the Philosophy Department at Carnegie Mellon University, a Guggenheim Fellow, a Fellow of the Center for Advanced Study in Behavioral Sciences, a Phi Beta Kappa lecturer, and is a Fellow of the statistics section of the AAAS. Glymour and his collaborators created the causal interpretation of Bayes nets.P. Spirtes, C. Glymour, R. Scheines, Causation, Prediction and Search, Springer Lecture Notes in Statistics, 1993. His areas of interest include epistemologyEpistemology: 5 Questions Edited by Vincent F. Hendricks and Duncan Pritchard, September 2008, . (particularly Android epistemology), machine learning, automated reasoning, psychology of judgment, and mathematical psychology. One of Glymour's main contributions to the philosophy of science is in the area of Bayesian probability, particularly in his analysis of the Bayesian "problem of old evidence".Glymour, C.; Theory and evidence (1981), pp. 63-93. Glymour, in collaboration with Peter Spirtes and Richard Scheines, also developed an automated causal inference algorithm implemented as software named TETRAD.Publications TETRAD. Retrieved December 16, 2019. Using multivariate statistical data as input, TETRAD rapidly searches from among all possible causal relationship models and returns the most plausible causal models based on conditional dependence relationships between those variables. The algorithm is based on principles from statistics, graph theory, philosophy of science, and artificial intelligence.Glymour, Clark; Scheines, Richard; Spirtes, Peter; Kelly, Kevin. "TETRAD: Discovering Causal Structure" Multivariate Behavioral Research 23.2 (1988). 10 July 2010. . .<br />
<br />
格莱默是卡内基梅隆大学哲学系的创始人,古根海姆研究员,行为科学高级研究中心研究员,斐陶斐学会讲师,美国科学促进会统计部门研究员。和他的合作者创造了贝叶斯网络的因果解释。斯皮尔特斯,c. 格莱莫尔,r. 舍因斯,因果关系,预测和搜索,斯普林格统计讲义,1993。他的兴趣领域包括: 由 Vincent f. Hendricks 和 Duncan Pritchard 编辑的《认识论/认识论: 5个问题》 ,2008年9月,。(尤其是 Android 认识论)、机器学习、自动推理、判断心理学和数学心理学。格莱莫尔对科学哲学的主要贡献之一是在贝叶斯概率领域,特别是在他对贝叶斯“旧证据问题”的分析中。理论与证据(1981) ,页。63-93.格莱莫尔与彼得 · 斯皮尔茨和理查德 · 谢恩斯合作,还开发了一种自动因果推理算法,称为 TETRAD.Publications TETRAD。16,2019.利用多元统计数据作为输入,TETRAD 从所有可能的因果关系模型中快速搜索,并根据这些变量之间的条件依赖关系返回最合理的因果模型。该算法基于统计学、图论、科学哲学和人工智能的原理。格莱莫尔,克拉克; 舍因斯,理查德; Spirtes,彼得; 凯利,凯文。“四合一: 发现因果结构”多元行为研究23.2(1988)。二零一零年七月十日。.<br />
<br />
Glymour earned undergraduate degrees in [[chemistry]] and [[philosophy]]. He did graduate work in [[chemical physics]] and obtained a Ph.D in History and Philosophy of Science from [[Indiana University (Bloomington)|Indiana University]] in 1969.<br />
<br />
Glymour earned undergraduate degrees in chemistry and philosophy. He did graduate work in chemical physics and obtained a Ph.D in History and Philosophy of Science from Indiana University in 1969.<br />
<br />
获得了化学和哲学的本科学位。他毕业于化学物理学,并于1969年获得印第安纳大学历史与科学哲学博士学位。<br />
<br />
==研究成果(Publications)==<br />
===书籍===<br />
*''Theory and Evidence'' (Princeton, 1980)<br />
*''Examining Holistic Medicine'' (with D. Stalker), Prometheus, 1985<br />
*''Foundations of Space-Time Theories'' (with J. Earman), University of Minnesota Press, 1986<br />
*''Discovering Causal Structure'' (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*''Causation, Prediction and Search'' (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*''Thinking Things Through'', MIT Press, 1994<br />
*''Android Epistemology'' (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*''The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology'', MIT Press, 2001<br />
*''Galileo in Pittsburgh'' Harvard University Press, 2010.<br />
<br />
*Theory and Evidence (Princeton, 1980)<br />
*Examining Holistic Medicine (with D. Stalker), Prometheus, 1985<br />
*Foundations of Space-Time Theories (with J. Earman), University of Minnesota Press, 1986<br />
*Discovering Causal Structure (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*Causation, Prediction and Search (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*Thinking Things Through, MIT Press, 1994<br />
*Android Epistemology (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology, MIT Press, 2001<br />
*Galileo in Pittsburgh Harvard University Press, 2010.<br />
<br />
= = = = = = = = = = = 理论与证据(普林斯顿,1980) <br />
* 检验整体医学(与 d. Stalker 合著) ,普罗米修斯,1985 <br />
* 时空理论基础(与 j. Earman 合著) ,明尼苏达大学出版社,1986 <br />
* 发现因果结构(r. Scheines,p. Spirtes 和 K.Kelly 合著)学术出版社,1987 <br />
* 因果关系,预测和搜索(p. Spirtes 和 r. Scheines 合著) ,Springer,1993,第二版麻省理工学院出版社,2001 <br />
* ,1994 <br />
* 安卓认识论(与 k · 福特和 p · 海耶斯合著)麻省理工学院/AAAI 出版社,1996 <br />
* 心灵的箭头: 贝叶斯网和心理学中的图形因果模型,麻省理工学院出版社,2001 <br />
* 伽利略,匹兹堡哈佛大学出版社,2010。<br />
<br />
===期刊论文===<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", ''Open Philosophy'', 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", ''[[Philosophy of Science (journal)|Philosophy of Science]]'', 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", ''[[Journal of Philosophy]]'', 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. ''Physical Theory and Its Interpretation: Essays in Honor of [[Jeffrey Bub]]'', Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", ''[[Mind (journal)|Mind]]'', 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", ''UAI Proceedings'', 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", ''[[Genomics]]'', Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", ''[[Statistical Applications in Genetics and Molecular Biology]]'', Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", ''Behavioral and Brain Sciences'', in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", ''Philosophy of Science'', Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", ''[[Encyclopedia of Social Science]]'', in press<br />
*"We believe in freedom of the will so that we can learn", ''[[Behavioral and Brain Sciences]]'', Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", ''[[Daedalus (journal)|Daedelus]]'', Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, ''Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence'', August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", ''Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics'', (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", ''[[Erkenntnis]]'', Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", ''[[British Journal for Philosophy of Science]]'', Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", ''[[Journal of Econometrics]]'', Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", ''[[Trends in Cognitive Sciences]]'', Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", ''[[Psychological Review]], Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. ''[[Philosophical Essays on Freud]]'', Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", Open Philosophy, 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", Philosophy of Science, 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", Journal of Philosophy, 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. Physical Theory and Its Interpretation: Essays in Honor of Jeffrey Bub, Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", Mind, 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", UAI Proceedings, 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", Genomics, Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", Statistical Applications in Genetics and Molecular Biology, Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", Behavioral and Brain Sciences, in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", Philosophy of Science, Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", Encyclopedia of Social Science, in press<br />
*"We believe in freedom of the will so that we can learn", Behavioral and Brain Sciences, Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", Daedelus, Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence, August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics, (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", Erkenntnis, Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", British Journal for Philosophy of Science, Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", Journal of Econometrics, Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", Trends in Cognitive Sciences, Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", Psychological Review, Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. Philosophical Essays on Freud, Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
* <br />
<br />
==参考文献==<br />
{{Reflist}}<br />
<br />
==<nowiki>= = 外部链接 =</nowiki>==<br />
*IHMC 网站:[https://www.ihmc.us/groups/clark-glymour/ IHMC website]<br />
*卡内基梅隆大学哲学系主页:[https://web.archive.org/web/20100601161806/http://www.hss.cmu.edu/philosophy/faculty-glymour.php Carnegie Mellon Department of Philosophy faculty page]<br />
*TETRAD项目:[http://www.phil.cmu.edu/projects/tetrad/publications.html TETRAD Project]<br />
<br />
{{Authority control}}<br />
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{{DEFAULTSORT:Glymour, Clark}}<br />
[[Category:1942 births]]<br />
[[Category:Living people]]<br />
[[Category:American logicians]]<br />
[[Category:Philosophers of science]]<br />
[[Category:Indiana University alumni]]<br />
[[Category:Florida Institute for Human and Machine Cognition people]]<br />
[[Category:20th-century American philosophers]]<br />
[[Category:Carnegie Mellon University faculty]]<br />
[[Category:Place of birth missing (living people)]]<br />
[[Category:Fellows of the American Academy of Arts and Sciences]]<br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=Clark_Glymour&diff=29278Clark Glymour2022-03-20T08:22:29Z<p>Wei:</p>
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<div>{{Infobox academic<br />
|image =<br />
|caption =<br />
|birth_date = 1942<br />
|birth_place =<br />
|death_date =<br />
|death_place =<br />
|alma_mater = [[Indiana University (Bloomington)|Indiana University]] ({{midsize|Ph.D., 1969}})<br />
|workplaces = [[Carnegie Mellon University]]<br />
}}<br />
<br />
'''克拉克 · 格莱莫尔'''(Clark N. Glymour)生于1942年,是卡内基梅隆大学哲学系的校友大学名誉教授。他也是佛罗里达人类和机器认知研究所([[Florida Institute for Human and Machine Cognition]])的高级研究科学家。<ref>{{cite web|url=https://www.cmu.edu/dietrich/philosophy/people/emeritus/glymour.html|title=Clark Glymour|publisher=Carnegie Mellon University|accessdate=December 16, 2019}}</ref><br />
<br />
==Work==<br />
Glymour is the founder of the Philosophy Department at Carnegie Mellon University, a [[Guggenheim Fellowship|Guggenheim Fellow]], a Fellow of the Center for Advanced Study in Behavioral Sciences,<ref>{{cite web|url=https://casbs.stanford.edu/news/awards-and-elections-fall-2019|title=Awards and Elections, Fall 2019|publisher=Center for Advanced Study in Behavioral Sciences|accessdate=December 16, 2019}}</ref> a [[Phi Beta Kappa Society|Phi Beta Kappa]] lecturer,<ref>{{cite web|url=https://www.pbk.org/Awards/Romanell/PastWinners|title=Romanell-Phi Beta Kappa Professorship Past Winners|publisher=Phi Beta Kappa|accessdate=December 16, 2019}}</ref> and is a Fellow of the statistics section of the AAAS.<ref>{{cite web|url=https://www.amacad.org/person/clark-glymour|title=Clark Glymour|publisher=American Academy of Arts and Sciences|accessdate=December 16, 2019}}</ref> Glymour and his collaborators created the causal interpretation of Bayes nets.<ref>P. Spirtes, C. Glymour, R. Scheines, Causation, Prediction and Search, Springer Lecture Notes in Statistics, 1993.</ref> His areas of interest include [[epistemology]]<ref>Epistemology: 5 Questions Edited by Vincent F. Hendricks and Duncan Pritchard, September 2008, {{ISBN|87-92130-07-0}}.</ref> (particularly [[Android epistemology]]), [[machine learning]], [[automated reasoning]], [[psychology]] of judgment, and [[mathematical psychology]].<ref>{{cite web|url=https://www.ihmc.us/groups/clark-glymour/|title=Clark Glymour|accessdate=December 16, 2019}}</ref> One of Glymour's main contributions to the philosophy of science is in the area of [[Bayesian probability]], particularly in his analysis of the Bayesian "problem of old evidence".<ref>{{cite web|url=http://plato.stanford.edu/entries/epistemology-bayesian/|title=Bayesian Epistemology|date=July 12, 2001}}</ref><ref>Glymour, C.; Theory and evidence (1981), pp. 63-93.</ref> Glymour, in collaboration with Peter Spirtes and Richard Scheines, also developed an automated causal inference algorithm implemented as software named [[TETRAD]].<ref>[http://www.phil.cmu.edu/projects/tetrad/publications.html Publications] TETRAD. Retrieved December 16, 2019.</ref> Using multivariate statistical data as input, TETRAD rapidly searches from among all possible causal relationship models and returns the most plausible causal models based on conditional dependence relationships between those variables. The algorithm is based on principles from statistics, graph theory, philosophy of science, and artificial intelligence.<ref>Glymour, Clark; Scheines, Richard; Spirtes, Peter; Kelly, Kevin. "TETRAD: Discovering Causal Structure" Multivariate Behavioral Research 23.2 (1988). 10 July 2010. {{DOI|10.1207/s15327906mbr2302_13}}. {{PMID|26764954}}.</ref><br />
<br />
Glymour is the founder of the Philosophy Department at Carnegie Mellon University, a Guggenheim Fellow, a Fellow of the Center for Advanced Study in Behavioral Sciences, a Phi Beta Kappa lecturer, and is a Fellow of the statistics section of the AAAS. Glymour and his collaborators created the causal interpretation of Bayes nets.P. Spirtes, C. Glymour, R. Scheines, Causation, Prediction and Search, Springer Lecture Notes in Statistics, 1993. His areas of interest include epistemologyEpistemology: 5 Questions Edited by Vincent F. Hendricks and Duncan Pritchard, September 2008, . (particularly Android epistemology), machine learning, automated reasoning, psychology of judgment, and mathematical psychology. One of Glymour's main contributions to the philosophy of science is in the area of Bayesian probability, particularly in his analysis of the Bayesian "problem of old evidence".Glymour, C.; Theory and evidence (1981), pp. 63-93. Glymour, in collaboration with Peter Spirtes and Richard Scheines, also developed an automated causal inference algorithm implemented as software named TETRAD.Publications TETRAD. Retrieved December 16, 2019. Using multivariate statistical data as input, TETRAD rapidly searches from among all possible causal relationship models and returns the most plausible causal models based on conditional dependence relationships between those variables. The algorithm is based on principles from statistics, graph theory, philosophy of science, and artificial intelligence.Glymour, Clark; Scheines, Richard; Spirtes, Peter; Kelly, Kevin. "TETRAD: Discovering Causal Structure" Multivariate Behavioral Research 23.2 (1988). 10 July 2010. . .<br />
<br />
格莱默是卡内基梅隆大学哲学系的创始人,古根海姆研究员,行为科学高级研究中心研究员,斐陶斐学会讲师,美国科学促进会统计部门研究员。和他的合作者创造了贝叶斯网络的因果解释。斯皮尔特斯,c. 格莱莫尔,r. 舍因斯,因果关系,预测和搜索,斯普林格统计讲义,1993。他的兴趣领域包括: 由 Vincent f. Hendricks 和 Duncan Pritchard 编辑的《认识论/认识论: 5个问题》 ,2008年9月,。(尤其是 Android 认识论)、机器学习、自动推理、判断心理学和数学心理学。格莱莫尔对科学哲学的主要贡献之一是在贝叶斯概率领域,特别是在他对贝叶斯“旧证据问题”的分析中。理论与证据(1981) ,页。63-93.格莱莫尔与彼得 · 斯皮尔茨和理查德 · 谢恩斯合作,还开发了一种自动因果推理算法,称为 TETRAD.Publications TETRAD。16,2019.利用多元统计数据作为输入,TETRAD 从所有可能的因果关系模型中快速搜索,并根据这些变量之间的条件依赖关系返回最合理的因果模型。该算法基于统计学、图论、科学哲学和人工智能的原理。格莱莫尔,克拉克; 舍因斯,理查德; Spirtes,彼得; 凯利,凯文。“四合一: 发现因果结构”多元行为研究23.2(1988)。二零一零年七月十日。.<br />
<br />
Glymour earned undergraduate degrees in [[chemistry]] and [[philosophy]]. He did graduate work in [[chemical physics]] and obtained a Ph.D in History and Philosophy of Science from [[Indiana University (Bloomington)|Indiana University]] in 1969.<br />
<br />
Glymour earned undergraduate degrees in chemistry and philosophy. He did graduate work in chemical physics and obtained a Ph.D in History and Philosophy of Science from Indiana University in 1969.<br />
<br />
获得了化学和哲学的本科学位。他毕业于化学物理学,并于1969年获得印第安纳大学历史与科学哲学博士学位。<br />
<br />
==Publications==<br />
===Books===<br />
*''Theory and Evidence'' (Princeton, 1980)<br />
*''Examining Holistic Medicine'' (with D. Stalker), Prometheus, 1985<br />
*''Foundations of Space-Time Theories'' (with J. Earman), University of Minnesota Press, 1986<br />
*''Discovering Causal Structure'' (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*''Causation, Prediction and Search'' (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*''Thinking Things Through'', MIT Press, 1994<br />
*''Android Epistemology'' (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*''The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology'', MIT Press, 2001<br />
*''Galileo in Pittsburgh'' Harvard University Press, 2010.<br />
<br />
*Theory and Evidence (Princeton, 1980)<br />
*Examining Holistic Medicine (with D. Stalker), Prometheus, 1985<br />
*Foundations of Space-Time Theories (with J. Earman), University of Minnesota Press, 1986<br />
*Discovering Causal Structure (with R. Scheines, P. Spirtes and K.Kelly) Academic Press, 1987<br />
*Causation, Prediction and Search (with P.Spirtes and R. Scheines), Springer, 1993, 2nd Edition MIT Press, 2001<br />
*Thinking Things Through, MIT Press, 1994<br />
*Android Epistemology (with K. Ford and P. Hayes) MIT/AAAI Press, 1996<br />
*The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology, MIT Press, 2001<br />
*Galileo in Pittsburgh Harvard University Press, 2010.<br />
<br />
= = = = = = = = = = = 理论与证据(普林斯顿,1980) <br />
* 检验整体医学(与 d. Stalker 合著) ,普罗米修斯,1985 <br />
* 时空理论基础(与 j. Earman 合著) ,明尼苏达大学出版社,1986 <br />
* 发现因果结构(r. Scheines,p. Spirtes 和 K.Kelly 合著)学术出版社,1987 <br />
* 因果关系,预测和搜索(p. Spirtes 和 r. Scheines 合著) ,Springer,1993,第二版麻省理工学院出版社,2001 <br />
* ,1994 <br />
* 安卓认识论(与 k · 福特和 p · 海耶斯合著)麻省理工学院/AAAI 出版社,1996 <br />
* 心灵的箭头: 贝叶斯网和心理学中的图形因果模型,麻省理工学院出版社,2001 <br />
* 伽利略,匹兹堡哈佛大学出版社,2010。<br />
<br />
===Journal articles===<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", ''Open Philosophy'', 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", ''[[Philosophy of Science (journal)|Philosophy of Science]]'', 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", ''[[Journal of Philosophy]]'', 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. ''Physical Theory and Its Interpretation: Essays in Honor of [[Jeffrey Bub]]'', Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", ''[[Mind (journal)|Mind]]'', 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", ''UAI Proceedings'', 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", ''[[Genomics]]'', Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", ''[[Statistical Applications in Genetics and Molecular Biology]]'', Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", ''Behavioral and Brain Sciences'', in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", ''Philosophy of Science'', Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", ''[[Encyclopedia of Social Science]]'', in press<br />
*"We believe in freedom of the will so that we can learn", ''[[Behavioral and Brain Sciences]]'', Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", ''[[Daedalus (journal)|Daedelus]]'', Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, ''Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence'', August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", ''Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics'', (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", ''[[Erkenntnis]]'', Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", ''[[British Journal for Philosophy of Science]]'', Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", ''[[Journal of Econometrics]]'', Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", ''[[Trends in Cognitive Sciences]]'', Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", ''[[Psychological Review]], Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. ''[[Philosophical Essays on Freud]]'', Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
*"The Evaluation of Discovery: Models, Simulation and Search through “Big Data”", Open Philosophy, 2019. Available on-line (Open Access): https://doi.org/10.1515/opphil-2019-0005 <br />
* "When is a Brain Like the Planet?", Philosophy of Science, 2008.<br />
*(with David Danks) "Reasons as Causes in Bayesian Epistemology", Journal of Philosophy, 2008.<br />
*"Markov Properties and Quantum Experiments", in W. Demopoulos and I. Pitowsky, eds. Physical Theory and Its Interpretation: Essays in Honor of Jeffrey Bub, Springer 2006.<br />
*(with Chu, T. and David Danks) "Data Driven Methods for Granger Causality and Contemporaneous Causality with Non-Linear Corrections: Climate Teleconnection Mechanisms", 2004.<br />
*"Review of Phil Dowe and Paul Nordhoff: Cause and Chance: Causation in an Indeterministic World", Mind, 2005.<br />
*(with Eberhardt, Frederick, and Richard Scheines). "N-1 Experiments Suffice to Determine the Causal Relations Among N Variables", 2004.<br />
*(with F. Eberhardt and R. Scheines), "Log2(N) Experiments are Sufficient, and in the Worst Case Necessary, for Identifying Causal Structure", UAI Proceedings, 2005<br />
*(with Handley, Daniel, Nicoleta Serban, David Peters, Robert O'Doherty, Melvin Field, Larry Wasserman, Peter Spirtes, and Richard Scheines), "Evidence of systematic expressed sequence tag IMAGE clone cross-hybridization on cDNA microarrays", Genomics, Vol. 83, Issue 6 (June, 2004), 1169-1175.<br />
*(with Handley, Daniel, Nicoleta Serban, and David G. Peters). "Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors", Statistical Applications in Genetics and Molecular Biology, Vol. 3, Issue 1 (October 6, 2004), Article 25.<br />
*"Comment on D. Lerner", "The Illusion of Conscious Will", Behavioral and Brain Sciences, in press.<br />
*"Review of Joseph E. Early, Sr. (Ed.): Chemical Explanation: Characteristics, Development, Autonomy", Philosophy of Science, Vol. 71, No. 3 (July, 2004), 415-418.<br />
*(with Spirtes, and Peter Glymour). "Causal Inference", Encyclopedia of Social Science, in press<br />
*"We believe in freedom of the will so that we can learn", Behavioral and Brain Sciences, Vol. 27, No. 5 (2004), 661-662.<br />
*"The Automation of Discovery", Daedelus, Vol. Winter (2004), 69-77.<br />
*(with Serban, Nicoleta, Larry Wasserman, David Peters, Peter Spirtes, Robert O'Doherty, Dan Handley, and Richard Scheines). "Analysis of microarray data for treated fat cells", (2003).<br />
*(with Danks, David, and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", (2003).<br />
*(with Silva, Ricardo, Richard Scheines, and Peter Spirtes). "Learning Measurement Models for Unobserved Variables", UAI '03, Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence, August 7–10, 2003, Acapulco, Mexico (2003), 543-550.<br />
*(with Danks, David and Peter Spirtes). "The Computational and Experimental Complexity of Gene Perturbations for Regulatory Network Search", Proceedings of IJCAI-2003 Workshop on Learning Graphical Models for Computational Genomics, (2003), 22-31.<br />
*(with Frank Wimberly, Thomas Heiman, and Joseph Ramsey). "Experiments on the Accuracy of Algorithms for Inferring the Structure of Genetic Regulatory Networks from Microarray Expression Levels", International Joint Conference on Artificial Intelligence Workshop, 2003<br />
*"A Semantics and Methodology for Ceteris Paribus Hypotheses", Erkenntnis, Vol. 57 (2002), 395-405.<br />
*"Review of James Woodward, Making Things Happen: A Theory of Causal Explanation", British Journal for Philosophy of Science, Vol. 55 (2004), 779-790.<br />
*(with Fienberg, Stephen, and Richard Scheines). "Expert statistical testimony and epidemiological evidence: the toxic effects of lead exposure on children", Journal of Econometrics, Vol 113 (2003), 33-48.<br />
*"Learning, prediction and causal Bayes Nets", Trends in Cognitive Sciences, Vol. 7, No. 1 (2003), 43-47.<br />
*(with Alison Gopnik, David M. Sobel, Laura E. Schulz, Tamar Kushnir, and David Danks). "A theory of causal learning in children: Causal maps and Bayes nets", Psychological Review, Vol. 111, No. 1 (2004).<br />
*"Freud, Kepler, and the clinical evidence", in R. Wollheim and J. Hopkins, eds. Philosophical Essays on Freud, Cambridge University Press 1982.<br />
*and many others dating back to 1970.<br />
<br />
= = = 期刊文章 = = = =”发现的评估: 模型,模拟和通过”大数据”的搜索”,开放哲学,2019年。可用的在线(开放存取) : https://doi.org/10.1515/opphil-2019-0005 <br />
* “什么时候大脑像地球?科学哲学》 ,2008年。<br />
* (与大卫 · 丹克斯合著)《贝叶斯认识论中的原因》 ,《哲学杂志》 ,2008年。<br />
* 《马尔可夫性质与量子实验》 ,w. Demopoulos and i. Pitowsky,eds。物理学理论及其解释: 纪念杰弗里 · 巴布的文章,斯普林格2006年。<br />
* (与 Chu,t. 和 David Danks 合著)“数据驱动的格兰杰因果关系和同时期的因果关系与非线性校正: 气候遥相关机制”,2004年。<br />
* 《回顾 Phil Dowe 和 Paul Nordhoff: 原因和机会: 不确定世界中的因果关系》 ,Mind,2005年。<br />
* (与埃伯哈特、弗雷德里克和理查德 · 谢因斯)。“ n-1实验足以确定 n 个变量之间的因果关系”,2004年。<br />
* (与 f. Eberhardt 和 r. Scheines 合作) ,“ Log2(n)实验是充分的,在最坏的情况下是必要的,以确定因果结构”,UAI Proceedings,2005 <br />
* ,(与 Handley,Daniel,Nicoleta Serban,David Peters,Robert o’doherty,Melvin Field,Larry Wasserman,Peter Spirtes,和 Richard Scheines 合作) ,“ cDNA 微阵列上系统性的表达序列标签图像克隆交叉杂交的证据”,Vol。83,Issue 6(June,2004) ,1169-1175.<br />
* (与 Handley、 Daniel、 Nicoleta Serban 和 David g. Peters 合作)。“关于由于交叉杂交和序列错误引起的斑点 cDNA 微阵列的不可靠数据的关注”,遗传学和分子生物学统计应用,卷。第三期第一期(二○○四年十月六日)第二十五条。<br />
* 《对 d. Lerner 的评论》 ,《有意识的错觉》 ,《行为与脑科学》 ,出版社。<br />
*”约瑟夫 · e · 厄利先生评论”。(教育署。《化学解释: 特征、发展、自主》 ,载《科学哲学》第卷。71,No.3(2004年7月) ,415-418。<br />
* (与 Spirtes 和 Peter Glymour 合作)。“因果推理”,社会科学百科全书,出版 <br />
* “我们相信意志的自由,所以我们可以学习”,行为和脑科学,卷。27,No.5 (2004), 661-662.<br />
* 《发现的自动化》 ,代达罗斯,第一卷。冬季(2004) ,69-77。<br />
* (与 Serban、 Nicoleta、 Larry Wasserman、 David Peters、 Peter Spirtes、 Robert o’doherty、 Dan Handley 和 Richard Scheines 合作)。“处理过的脂肪细胞的微阵列数据分析”,(2003)。<br />
* (与丹克斯、大卫和彼得 · 斯皮尔特斯合作)。“调控网络搜索的基因扰动的计算和实验复杂性”,(2003)。<br />
* (与席尔瓦、里卡多、理查德•谢因斯和彼得•斯皮尔特斯)。“未观测变量的学习测量模型”,UAI’03,第19届人工智能不确定性会议论文集,2003年8月7-10,Acapulco (2003) ,543-550。<br />
* (与丹克斯、大卫和彼得 · 斯皮尔特斯合作)。“调控网络搜索的基因扰动的计算和实验复杂性”,ijcai-2003计算基因组学习图形模型研讨会论文集,(2003) ,22-31。<br />
* (与弗兰克 · 温伯利、托马斯 · 海曼和约瑟夫 · 拉姆齐)。“从微阵列表达水平推断基因调控网络结构的算法准确性实验”,人工智能研讨会国际联席会议,2003年 <br />
* “ Ceteris Paribus 的语义学和方法学”,Erkenntnis,Vol。57 (2002), 395-405.<br />
* 《詹姆斯 · 伍德沃德评论,使事情发生: 因果解释理论》 ,《英国科学哲学杂志》 ,第一卷。55 (2004), 779-790.<br />
* (与芬伯格、斯蒂芬和理查德 · 谢恩斯)。“专家统计证据和流行病学证据: 铅暴露对儿童的毒性影响”,《计量经济学杂志》 ,2003年第113卷,33-48页。<br />
*”学习、预测和因果贝叶斯网络”,《认知科学趋势》 ,第一卷。7,No.1 (2003), 43-47.<br />
* (与艾莉森•高普尼克、大卫•索贝尔、劳拉• e •舒尔茨、塔玛•库什尼尔和大卫•丹克斯)。“儿童因果学习理论: 因果地图和贝叶斯网”,《心理学评论》 ,第卷。111,No.1 (2004).<br />
* 《弗洛伊德、开普勒与临床证据》 ,载于 r. Wollheim 和 j. Hopkins 出版社编辑。弗洛伊德哲学论文集,剑桥大学出版社,1982。<br />
* 还有许多可以追溯到1970年的作品。<br />
<br />
==References==<br />
{{Reflist}}<br />
<br />
==External links==<br />
*[https://www.ihmc.us/groups/clark-glymour/ IHMC website]<br />
*[https://web.archive.org/web/20100601161806/http://www.hss.cmu.edu/philosophy/faculty-glymour.php Carnegie Mellon Department of Philosophy faculty page]<br />
*[http://www.phil.cmu.edu/projects/tetrad/publications.html TETRAD Project]<br />
<br />
*IHMC website<br />
*Carnegie Mellon Department of Philosophy faculty page<br />
*TETRAD Project<br />
<br />
= = = 外部链接 = = <br />
* IHMC 网站 <br />
* 卡内基梅隆大学哲学系主页 <br />
* 四维项目<br />
<br />
{{Authority control}}<br />
<br />
{{DEFAULTSORT:Glymour, Clark}}<br />
[[Category:1942 births]]<br />
[[Category:Living people]]<br />
[[Category:American logicians]]<br />
[[Category:Philosophers of science]]<br />
[[Category:Indiana University alumni]]<br />
[[Category:Florida Institute for Human and Machine Cognition people]]<br />
[[Category:20th-century American philosophers]]<br />
[[Category:Carnegie Mellon University faculty]]<br />
[[Category:Place of birth missing (living people)]]<br />
[[Category:Fellows of the American Academy of Arts and Sciences]]<br />
<br />
<br />
Category:1942 births<br />
Category:Living people<br />
Category:American logicians<br />
Category:Philosophers of science<br />
Category:Indiana University alumni<br />
Category:Florida Institute for Human and Machine Cognition people<br />
Category:20th-century American philosophers<br />
Category:Carnegie Mellon University faculty<br />
Category:Place of birth missing (living people)<br />
Category:Fellows of the American Academy of Arts and Sciences<br />
<br />
类别: 1942年出生类别: 活人类别: 美国逻辑学家类别: 科学哲学家类别: 印第安纳大学校友类别: 佛罗里达人类与机器认知类别: 20世纪美国哲学家类别: 卡内基梅隆大学教员类别: 出生地缺失(活人)类别: 美国艺术与科学院院士<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Clark Glymour]]. Its edit history can be viewed at [[Clark Glymour/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22799反事实2021-06-01T12:09:11Z<p>Wei:/* 严格的条件 */</p>
<hr />
<div><br />
'''<font color="#ff8000"> 反事实条件句 Counterfactual conditionals</font>'''(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的<font color="#ff8000"> 条件句 conditional sentence</font>。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
<br />
反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是显而易见的事实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
<br />
<br />
==概述==<br />
<br />
<br />
===案例 ===<br />
<br />
<br />
指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
<br />
# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
# '''一般过去时的反事实''':如果现在正在下雨,那么Sally应该在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
<br />
这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
<br />
英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
<br />
# '''过去完成时的反事实''':如果昨天下了雨,那么Sally当时应该会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
<br />
另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
<br />
# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
<br />
过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
<br />
# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
<br />
===术语===<br />
<br />
“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的前件条件是假的或不可能的。<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
<br />
# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
<br />
这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
<br />
''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
<br />
最近有研究提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为''O-Marked''条件语,反映了它们的''o''普通标记。<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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<br />
一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
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==逻辑和语义==<br />
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===经典问题===<br />
<br />
====反事实的问题====<br />
<br />
根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
<br />
# 如果那块黄油被加热到150度,它就会融化。<br />
# 如果那块黄油被加热到150度,它就不会融化。<br />
<br />
更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
<br />
====上下文依赖和含糊不清====<br />
<br />
反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
<br />
# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
<br />
====非单调性====<br />
<br />
反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
<br />
# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
<br />
对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
<br />
* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
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===考虑可能存在的世界===<br />
<br />
反事实的最常见的逻辑解释是'''<font color="#ff8000"> 可能世界语义 Possible World Semantics</font>'''。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
<br />
大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,学术上有多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
<br />
====严格的条件====<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
<br />
* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
<br />
与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活跃"的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
<br />
严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
<br />
这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
<br />
Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
<br />
# 如果Natalia明天离开,她会准时到达。<br />
# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
<br />
Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
<br />
====可变严格条件====<br />
<br />
在可变严格方法中,条件''A'' > ''B''的语义是由一些函数给出的,一方面是A为真、B为真的世界,另一方面是A为真、B为假的世界的相对接近程度。<br />
<br />
在刘易斯的论述中,A > C 是(a)空洞的真实,只有在没有A为真的世界时(例如,如果A在逻辑上或形而上学上是不可能的);(b)非空洞的真实,只有在A为真的世界中,一些C为真的世界比任何C不为真的世界更接近实际世界;或者(c)虚假,在其他世界里。尽管在刘易斯的《反事实》中,他对“接近性(closeness)”的意思并不清晰,但在后来的著作中,刘易斯明确表示,他并不打算将“接近性”的尺度简单地作为我们对整体相似性的普通概念。<br />
<br />
例子:<br />
:如果他在早餐时吃多一点,他在上午11点就不会饿。<br />
<br />
根据刘易斯的说法,这个陈述的真理在于:在他早餐吃得更多的可能世界中,至少有一个他在上午11点不饿的世界比任何他早餐吃得更多但在上午11点仍然饿的世界更接近我们的世界。<br />
<br />
过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
<br />
Stalnaker的论述与Lewis的论述最明显的不同在于,他接受了“极限(limit)”和“唯一性假设(uniqueness assumptions)”。唯一性假设的论点是:对于任何前件A,在A为真的可能世界中,有一个最接近实际世界的单一(唯一)世界。极限假设的论点是,对于一个给定的前件A,如果存在一个A为真的可能世界链,每个世界都比它的前一个世界更接近实际世界,那么这个链就有一个极限:一个A为真的可能世界比这个链中的所有世界更接近实际世界。(唯一性假设包含了极限假设,但极限假设并不包含唯一性假设)。根据Stalnaker的观点,当且仅当在最接近A为真的世界中,C为真时,A>C才是非空洞的真。因此,上面的例子是真的,只是在他吃了更多早餐的唯一最接近的世界中,他在上午11点不觉得饿。虽然有争议,但Lewis拒绝了极限假设(因此也拒绝了唯一性假设),因为它排除了这样一种可能性,即可能存在着越来越接近实际世界的世界,而没有极限。例如,可能会有一系列无限的世界,每个世界的咖啡杯都在其实际位置的左边小几分之一英寸,但其中没有一个是唯一最接近的。(参见Lewis 1973: 20)。<br />
<br />
Stalnaker接受唯一性假设的一个结果是,如果排除中间律是真的,那么公式(A>C)∨(A>¬C)的所有实例都是真的。排他性中间律的论题是:对于所有命题p,p∨¬p都是真的。如果唯一性假设为真,那么对于每一个前件A,都有一个唯一最接近的世界,其中A为真。如果排除中间法则是真的,任何结果C在A为真的那个世界里要么是真,要么是假。所以对于每一个反事实A>C,要么A>C,要么A>¬C为真。这就是所谓的条件排除中间法(CEM)。例子:<br />
<br />
:(1) 如果公平的硬币被抛出,它将会正面朝上。<br />
:(2) 如果公平的硬币被抛出,它将会反面朝上(即不是正面朝上)。<br />
<br />
根据Stalnaker的分析,存在一个最接近的世界,在这个世界里,(1)和(2)中提到的公平的硬币被抛出,硬币要么正面朝上,要么反面朝上。因此,要么(1)是真,(2)是假,要么(1)是假,(2)是真。然而,根据Lewis的分析,(1)和(2)都是假的,因为公平的硬币正面朝上的世界并不比反面朝上的世界更接近或更远离。对Lewis来说,“如果硬币被抛出,它将正面朝上或反面朝上”是真的,但这并不意味着“如果硬币被抛出,它将落在正面”,或“如果硬币被抛出,它就会反面朝上”。<br />
<br />
=== 其他考虑===<br />
<br />
====因果模型====<br />
<br />
<font color="#ff8000">因果模型框架 Causal Models Framework</font>从<font color="#ff8000">结构方程(structural equations)Structural Equation Model</font>系统的角度分析反事实。在一个方程系统中,每个变量都被分配了一个值,这个值是系统中其他变量的显式函数。给定这样一个模型,“如果X是X,Y就会是Y(''Y'' would be ''y'' had ''X'' been ''x'')”这个句子 (形式上为 ''X = x'' > ''Y = y'' )被定义为断言。如果我们用一个常数''X = x''取代当前决定 ''X''的方程,并求解变量''Y''的方程组,得到的解将是''Y = y''。这个定义已被证明与可能世界语义学的公理兼容,并构成自然科学和社会科学中因果推理的基础。因为这些领域的每个结构方程都对应于一个熟悉的因果机制,这个因果机制可以被研究者进行有意义地推理。这种方法是由Judea Pearl(2000)提出的,作为编码关于因果关系的细粒度直觉的手段,这些直觉在其他提议的系统中难以捕捉。<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
<br />
====信念修正====<br />
<br />
在信念修正框架中,反事实是用 ''Ramsey检验''的形式化实现来处理的。在这些系统中,当且仅当在当前的知识体系添加 ''A''后得到的结果是B时,反事实''A'' > ''B''成立。这个条件将反事实条件与信念修正联系起来,因为对''A'' > ''B''的评价可以通过首先用''A''修正当前的知识,然后检查''B''在什么结果中是否为真。当''A''与当前的信念一致时,修正是很容易的,但在其他情况下可能会很难。每一个用于信念修正的语义都可以用于评价条件语句。反过来说,每一种评价条件语句的方法都可以被看作是一种执行修正的方法。<br />
<br />
====Ginsberg====<br />
<br />
Ginsberg(1986)提出了一种条件句的语义,它假定当前的信念形成了一组命题公式,考虑这些公式中与''A''一致的最大集合,并在每个集合中加入''A''。其理由是,这些最大集合中的每一个都代表了一种可能的信念状态,在这种状态下,''A''为真,且与原始状态尽可能相似。因此,当且仅当''B''在所有这些集合中都为真时,条件陈述句''A'' > ''B''才成立。<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref></div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22798反事实2021-06-01T12:08:45Z<p>Wei:/* 案例 */</p>
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'''<font color="#ff8000"> 反事实条件句 Counterfactual conditionals</font>'''(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的<font color="#ff8000"> 条件句 conditional sentence</font>。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是显而易见的事实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==概述==<br />
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===案例 ===<br />
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指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
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# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
# '''一般过去时的反事实''':如果现在正在下雨,那么Sally应该在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
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英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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# '''过去完成时的反事实''':如果昨天下了雨,那么Sally当时应该会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
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另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
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过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
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===术语===<br />
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“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的前件条件是假的或不可能的。<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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最近有研究提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为''O-Marked''条件语,反映了它们的''o''普通标记。<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
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==逻辑和语义==<br />
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===经典问题===<br />
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====反事实的问题====<br />
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根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
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# 如果那块黄油被加热到150度,它就会融化。<br />
# 如果那块黄油被加热到150度,它就不会融化。<br />
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更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
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====上下文依赖和含糊不清====<br />
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反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
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# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
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====非单调性====<br />
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反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
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对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
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* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
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===考虑可能存在的世界===<br />
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反事实的最常见的逻辑解释是'''<font color="#ff8000"> 可能世界语义 Possible World Semantics</font>'''。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
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大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,学术上有多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
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====严格的条件====<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
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* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
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与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活跃"的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
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严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
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这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
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Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
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# 如果Natalia明天离开,她会准时到达。<br />
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# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
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Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
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====可变严格条件====<br />
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在可变严格方法中,条件''A'' > ''B''的语义是由一些函数给出的,一方面是A为真、B为真的世界,另一方面是A为真、B为假的世界的相对接近程度。<br />
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在刘易斯的论述中,A > C 是(a)空洞的真实,只有在没有A为真的世界时(例如,如果A在逻辑上或形而上学上是不可能的);(b)非空洞的真实,只有在A为真的世界中,一些C为真的世界比任何C不为真的世界更接近实际世界;或者(c)虚假,在其他世界里。尽管在刘易斯的《反事实》中,他对“接近性(closeness)”的意思并不清晰,但在后来的著作中,刘易斯明确表示,他并不打算将“接近性”的尺度简单地作为我们对整体相似性的普通概念。<br />
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例子:<br />
:如果他在早餐时吃多一点,他在上午11点就不会饿。<br />
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根据刘易斯的说法,这个陈述的真理在于:在他早餐吃得更多的可能世界中,至少有一个他在上午11点不饿的世界比任何他早餐吃得更多但在上午11点仍然饿的世界更接近我们的世界。<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker的论述与Lewis的论述最明显的不同在于,他接受了“极限(limit)”和“唯一性假设(uniqueness assumptions)”。唯一性假设的论点是:对于任何前件A,在A为真的可能世界中,有一个最接近实际世界的单一(唯一)世界。极限假设的论点是,对于一个给定的前件A,如果存在一个A为真的可能世界链,每个世界都比它的前一个世界更接近实际世界,那么这个链就有一个极限:一个A为真的可能世界比这个链中的所有世界更接近实际世界。(唯一性假设包含了极限假设,但极限假设并不包含唯一性假设)。根据Stalnaker的观点,当且仅当在最接近A为真的世界中,C为真时,A>C才是非空洞的真。因此,上面的例子是真的,只是在他吃了更多早餐的唯一最接近的世界中,他在上午11点不觉得饿。虽然有争议,但Lewis拒绝了极限假设(因此也拒绝了唯一性假设),因为它排除了这样一种可能性,即可能存在着越来越接近实际世界的世界,而没有极限。例如,可能会有一系列无限的世界,每个世界的咖啡杯都在其实际位置的左边小几分之一英寸,但其中没有一个是唯一最接近的。(参见Lewis 1973: 20)。<br />
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Stalnaker接受唯一性假设的一个结果是,如果排除中间律是真的,那么公式(A>C)∨(A>¬C)的所有实例都是真的。排他性中间律的论题是:对于所有命题p,p∨¬p都是真的。如果唯一性假设为真,那么对于每一个前件A,都有一个唯一最接近的世界,其中A为真。如果排除中间法则是真的,任何结果C在A为真的那个世界里要么是真,要么是假。所以对于每一个反事实A>C,要么A>C,要么A>¬C为真。这就是所谓的条件排除中间法(CEM)。例子:<br />
<br />
:(1) 如果公平的硬币被抛出,它将会正面朝上。<br />
:(2) 如果公平的硬币被抛出,它将会反面朝上(即不是正面朝上)。<br />
<br />
根据Stalnaker的分析,存在一个最接近的世界,在这个世界里,(1)和(2)中提到的公平的硬币被抛出,硬币要么正面朝上,要么反面朝上。因此,要么(1)是真,(2)是假,要么(1)是假,(2)是真。然而,根据Lewis的分析,(1)和(2)都是假的,因为公平的硬币正面朝上的世界并不比反面朝上的世界更接近或更远离。对Lewis来说,“如果硬币被抛出,它将正面朝上或反面朝上”是真的,但这并不意味着“如果硬币被抛出,它将落在正面”,或“如果硬币被抛出,它就会反面朝上”。<br />
<br />
=== 其他考虑===<br />
<br />
====因果模型====<br />
<br />
<font color="#ff8000">因果模型框架 Causal Models Framework</font>从<font color="#ff8000">结构方程(structural equations)Structural Equation Model</font>系统的角度分析反事实。在一个方程系统中,每个变量都被分配了一个值,这个值是系统中其他变量的显式函数。给定这样一个模型,“如果X是X,Y就会是Y(''Y'' would be ''y'' had ''X'' been ''x'')”这个句子 (形式上为 ''X = x'' > ''Y = y'' )被定义为断言。如果我们用一个常数''X = x''取代当前决定 ''X''的方程,并求解变量''Y''的方程组,得到的解将是''Y = y''。这个定义已被证明与可能世界语义学的公理兼容,并构成自然科学和社会科学中因果推理的基础。因为这些领域的每个结构方程都对应于一个熟悉的因果机制,这个因果机制可以被研究者进行有意义地推理。这种方法是由Judea Pearl(2000)提出的,作为编码关于因果关系的细粒度直觉的手段,这些直觉在其他提议的系统中难以捕捉。<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
<br />
====信念修正====<br />
<br />
在信念修正框架中,反事实是用 ''Ramsey检验''的形式化实现来处理的。在这些系统中,当且仅当在当前的知识体系添加 ''A''后得到的结果是B时,反事实''A'' > ''B''成立。这个条件将反事实条件与信念修正联系起来,因为对''A'' > ''B''的评价可以通过首先用''A''修正当前的知识,然后检查''B''在什么结果中是否为真。当''A''与当前的信念一致时,修正是很容易的,但在其他情况下可能会很难。每一个用于信念修正的语义都可以用于评价条件语句。反过来说,每一种评价条件语句的方法都可以被看作是一种执行修正的方法。<br />
<br />
====Ginsberg====<br />
<br />
Ginsberg(1986)提出了一种条件句的语义,它假定当前的信念形成了一组命题公式,考虑这些公式中与''A''一致的最大集合,并在每个集合中加入''A''。其理由是,这些最大集合中的每一个都代表了一种可能的信念状态,在这种状态下,''A''为真,且与原始状态尽可能相似。因此,当且仅当''B''在所有这些集合中都为真时,条件陈述句''A'' > ''B''才成立。<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref></div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22797反事实2021-06-01T12:07:13Z<p>Wei:/* 案例 */</p>
<hr />
<div><br />
'''<font color="#ff8000"> 反事实条件句 Counterfactual conditionals</font>'''(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的<font color="#ff8000"> 条件句 conditional sentence</font>。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
<br />
反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是显而易见的事实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
<br />
<br />
==概述==<br />
<br />
<br />
===案例 ===<br />
<br />
<br />
指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
<br />
# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
# '''一般过去时的反事实''':如果现在正在下雨,那么Sally应该在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
<br />
这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
<br />
英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
<br />
# '''过去完成时的反事实''':如果昨天下了雨,那么Sally当时应该会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
<br />
另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
<br />
# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
<br />
过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
<br />
<br />
# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
<br />
===术语===<br />
<br />
“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的前件条件是假的或不可能的。<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
<br />
# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
<br />
这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
<br />
''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
<br />
最近有研究提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为''O-Marked''条件语,反映了它们的''o''普通标记。<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
<br />
<br />
一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
<br />
==逻辑和语义==<br />
<br />
===经典问题===<br />
<br />
====反事实的问题====<br />
<br />
根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
<br />
# 如果那块黄油被加热到150度,它就会融化。<br />
# 如果那块黄油被加热到150度,它就不会融化。<br />
<br />
更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
<br />
====上下文依赖和含糊不清====<br />
<br />
反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
<br />
# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
<br />
====非单调性====<br />
<br />
反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
<br />
# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
<br />
对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
<br />
* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
<br />
===考虑可能存在的世界===<br />
<br />
反事实的最常见的逻辑解释是'''<font color="#ff8000"> 可能世界语义 Possible World Semantics</font>'''。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
<br />
大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,学术上有多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
<br />
====严格的条件====<br />
<br />
严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
<br />
* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
<br />
与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活跃"的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
<br />
严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
<br />
这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
<br />
Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
<br />
# 如果Natalia明天离开,她会准时到达。<br />
<br />
# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
<br />
Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
<br />
====可变严格条件====<br />
<br />
在可变严格方法中,条件''A'' > ''B''的语义是由一些函数给出的,一方面是A为真、B为真的世界,另一方面是A为真、B为假的世界的相对接近程度。<br />
<br />
在刘易斯的论述中,A > C 是(a)空洞的真实,只有在没有A为真的世界时(例如,如果A在逻辑上或形而上学上是不可能的);(b)非空洞的真实,只有在A为真的世界中,一些C为真的世界比任何C不为真的世界更接近实际世界;或者(c)虚假,在其他世界里。尽管在刘易斯的《反事实》中,他对“接近性(closeness)”的意思并不清晰,但在后来的著作中,刘易斯明确表示,他并不打算将“接近性”的尺度简单地作为我们对整体相似性的普通概念。<br />
<br />
例子:<br />
:如果他在早餐时吃多一点,他在上午11点就不会饿。<br />
<br />
根据刘易斯的说法,这个陈述的真理在于:在他早餐吃得更多的可能世界中,至少有一个他在上午11点不饿的世界比任何他早餐吃得更多但在上午11点仍然饿的世界更接近我们的世界。<br />
<br />
过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
<br />
Stalnaker的论述与Lewis的论述最明显的不同在于,他接受了“极限(limit)”和“唯一性假设(uniqueness assumptions)”。唯一性假设的论点是:对于任何前件A,在A为真的可能世界中,有一个最接近实际世界的单一(唯一)世界。极限假设的论点是,对于一个给定的前件A,如果存在一个A为真的可能世界链,每个世界都比它的前一个世界更接近实际世界,那么这个链就有一个极限:一个A为真的可能世界比这个链中的所有世界更接近实际世界。(唯一性假设包含了极限假设,但极限假设并不包含唯一性假设)。根据Stalnaker的观点,当且仅当在最接近A为真的世界中,C为真时,A>C才是非空洞的真。因此,上面的例子是真的,只是在他吃了更多早餐的唯一最接近的世界中,他在上午11点不觉得饿。虽然有争议,但Lewis拒绝了极限假设(因此也拒绝了唯一性假设),因为它排除了这样一种可能性,即可能存在着越来越接近实际世界的世界,而没有极限。例如,可能会有一系列无限的世界,每个世界的咖啡杯都在其实际位置的左边小几分之一英寸,但其中没有一个是唯一最接近的。(参见Lewis 1973: 20)。<br />
<br />
Stalnaker接受唯一性假设的一个结果是,如果排除中间律是真的,那么公式(A>C)∨(A>¬C)的所有实例都是真的。排他性中间律的论题是:对于所有命题p,p∨¬p都是真的。如果唯一性假设为真,那么对于每一个前件A,都有一个唯一最接近的世界,其中A为真。如果排除中间法则是真的,任何结果C在A为真的那个世界里要么是真,要么是假。所以对于每一个反事实A>C,要么A>C,要么A>¬C为真。这就是所谓的条件排除中间法(CEM)。例子:<br />
<br />
:(1) 如果公平的硬币被抛出,它将会正面朝上。<br />
:(2) 如果公平的硬币被抛出,它将会反面朝上(即不是正面朝上)。<br />
<br />
根据Stalnaker的分析,存在一个最接近的世界,在这个世界里,(1)和(2)中提到的公平的硬币被抛出,硬币要么正面朝上,要么反面朝上。因此,要么(1)是真,(2)是假,要么(1)是假,(2)是真。然而,根据Lewis的分析,(1)和(2)都是假的,因为公平的硬币正面朝上的世界并不比反面朝上的世界更接近或更远离。对Lewis来说,“如果硬币被抛出,它将正面朝上或反面朝上”是真的,但这并不意味着“如果硬币被抛出,它将落在正面”,或“如果硬币被抛出,它就会反面朝上”。<br />
<br />
=== 其他考虑===<br />
<br />
====因果模型====<br />
<br />
<font color="#ff8000">因果模型框架 Causal Models Framework</font>从<font color="#ff8000">结构方程(structural equations)Structural Equation Model</font>系统的角度分析反事实。在一个方程系统中,每个变量都被分配了一个值,这个值是系统中其他变量的显式函数。给定这样一个模型,“如果X是X,Y就会是Y(''Y'' would be ''y'' had ''X'' been ''x'')”这个句子 (形式上为 ''X = x'' > ''Y = y'' )被定义为断言。如果我们用一个常数''X = x''取代当前决定 ''X''的方程,并求解变量''Y''的方程组,得到的解将是''Y = y''。这个定义已被证明与可能世界语义学的公理兼容,并构成自然科学和社会科学中因果推理的基础。因为这些领域的每个结构方程都对应于一个熟悉的因果机制,这个因果机制可以被研究者进行有意义地推理。这种方法是由Judea Pearl(2000)提出的,作为编码关于因果关系的细粒度直觉的手段,这些直觉在其他提议的系统中难以捕捉。<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
<br />
====信念修正====<br />
<br />
在信念修正框架中,反事实是用 ''Ramsey检验''的形式化实现来处理的。在这些系统中,当且仅当在当前的知识体系添加 ''A''后得到的结果是B时,反事实''A'' > ''B''成立。这个条件将反事实条件与信念修正联系起来,因为对''A'' > ''B''的评价可以通过首先用''A''修正当前的知识,然后检查''B''在什么结果中是否为真。当''A''与当前的信念一致时,修正是很容易的,但在其他情况下可能会很难。每一个用于信念修正的语义都可以用于评价条件语句。反过来说,每一种评价条件语句的方法都可以被看作是一种执行修正的方法。<br />
<br />
====Ginsberg====<br />
<br />
Ginsberg(1986)提出了一种条件句的语义,它假定当前的信念形成了一组命题公式,考虑这些公式中与''A''一致的最大集合,并在每个集合中加入''A''。其理由是,这些最大集合中的每一个都代表了一种可能的信念状态,在这种状态下,''A''为真,且与原始状态尽可能相似。因此,当且仅当''B''在所有这些集合中都为真时,条件陈述句''A'' > ''B''才成立。<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref></div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22796反事实2021-06-01T12:05:38Z<p>Wei:/* 其他考虑 */</p>
<hr />
<div><br />
'''<font color="#ff8000"> 反事实条件句 Counterfactual conditionals</font>'''(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的<font color="#ff8000"> 条件句 conditional sentence</font>。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
<br />
反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是显而易见的事实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
<br />
<br />
==概述==<br />
<br />
<br />
===案例 ===<br />
<br />
<br />
指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
<br />
# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
<br />
# '''一般过去时的反事实''':如果现在正在下雨,那么Sally应该在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
<br />
这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
<br />
英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
<br />
# '''过去完成时的反事实''':如果昨天下了雨,那么Sally当时应该会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
<br />
另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
<br />
# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
<br />
过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
<br />
<br />
# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
<br />
# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
<br />
===术语===<br />
<br />
“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的前件条件是假的或不可能的。<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
<br />
# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
<br />
这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
<br />
''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
<br />
最近有研究提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为''O-Marked''条件语,反映了它们的''o''普通标记。<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
<br />
<br />
一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
<br />
==逻辑和语义==<br />
<br />
===经典问题===<br />
<br />
====反事实的问题====<br />
<br />
根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
<br />
# 如果那块黄油被加热到150度,它就会融化。<br />
# 如果那块黄油被加热到150度,它就不会融化。<br />
<br />
更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
<br />
====上下文依赖和含糊不清====<br />
<br />
反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
<br />
# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
<br />
====非单调性====<br />
<br />
反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
<br />
# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
<br />
对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
<br />
* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
<br />
===考虑可能存在的世界===<br />
<br />
反事实的最常见的逻辑解释是'''<font color="#ff8000"> 可能世界语义 Possible World Semantics</font>'''。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
<br />
大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,学术上有多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
<br />
====严格的条件====<br />
<br />
严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
<br />
* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
<br />
与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活跃"的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
<br />
严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
<br />
这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
<br />
Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
<br />
# 如果Natalia明天离开,她会准时到达。<br />
<br />
# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
<br />
Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
<br />
====可变严格条件====<br />
<br />
在可变严格方法中,条件''A'' > ''B''的语义是由一些函数给出的,一方面是A为真、B为真的世界,另一方面是A为真、B为假的世界的相对接近程度。<br />
<br />
在刘易斯的论述中,A > C 是(a)空洞的真实,只有在没有A为真的世界时(例如,如果A在逻辑上或形而上学上是不可能的);(b)非空洞的真实,只有在A为真的世界中,一些C为真的世界比任何C不为真的世界更接近实际世界;或者(c)虚假,在其他世界里。尽管在刘易斯的《反事实》中,他对“接近性(closeness)”的意思并不清晰,但在后来的著作中,刘易斯明确表示,他并不打算将“接近性”的尺度简单地作为我们对整体相似性的普通概念。<br />
<br />
例子:<br />
:如果他在早餐时吃多一点,他在上午11点就不会饿。<br />
<br />
根据刘易斯的说法,这个陈述的真理在于:在他早餐吃得更多的可能世界中,至少有一个他在上午11点不饿的世界比任何他早餐吃得更多但在上午11点仍然饿的世界更接近我们的世界。<br />
<br />
过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
<br />
Stalnaker的论述与Lewis的论述最明显的不同在于,他接受了“极限(limit)”和“唯一性假设(uniqueness assumptions)”。唯一性假设的论点是:对于任何前件A,在A为真的可能世界中,有一个最接近实际世界的单一(唯一)世界。极限假设的论点是,对于一个给定的前件A,如果存在一个A为真的可能世界链,每个世界都比它的前一个世界更接近实际世界,那么这个链就有一个极限:一个A为真的可能世界比这个链中的所有世界更接近实际世界。(唯一性假设包含了极限假设,但极限假设并不包含唯一性假设)。根据Stalnaker的观点,当且仅当在最接近A为真的世界中,C为真时,A>C才是非空洞的真。因此,上面的例子是真的,只是在他吃了更多早餐的唯一最接近的世界中,他在上午11点不觉得饿。虽然有争议,但Lewis拒绝了极限假设(因此也拒绝了唯一性假设),因为它排除了这样一种可能性,即可能存在着越来越接近实际世界的世界,而没有极限。例如,可能会有一系列无限的世界,每个世界的咖啡杯都在其实际位置的左边小几分之一英寸,但其中没有一个是唯一最接近的。(参见Lewis 1973: 20)。<br />
<br />
Stalnaker接受唯一性假设的一个结果是,如果排除中间律是真的,那么公式(A>C)∨(A>¬C)的所有实例都是真的。排他性中间律的论题是:对于所有命题p,p∨¬p都是真的。如果唯一性假设为真,那么对于每一个前件A,都有一个唯一最接近的世界,其中A为真。如果排除中间法则是真的,任何结果C在A为真的那个世界里要么是真,要么是假。所以对于每一个反事实A>C,要么A>C,要么A>¬C为真。这就是所谓的条件排除中间法(CEM)。例子:<br />
<br />
:(1) 如果公平的硬币被抛出,它将会正面朝上。<br />
:(2) 如果公平的硬币被抛出,它将会反面朝上(即不是正面朝上)。<br />
<br />
根据Stalnaker的分析,存在一个最接近的世界,在这个世界里,(1)和(2)中提到的公平的硬币被抛出,硬币要么正面朝上,要么反面朝上。因此,要么(1)是真,(2)是假,要么(1)是假,(2)是真。然而,根据Lewis的分析,(1)和(2)都是假的,因为公平的硬币正面朝上的世界并不比反面朝上的世界更接近或更远离。对Lewis来说,“如果硬币被抛出,它将正面朝上或反面朝上”是真的,但这并不意味着“如果硬币被抛出,它将落在正面”,或“如果硬币被抛出,它就会反面朝上”。<br />
<br />
=== 其他考虑===<br />
<br />
====因果模型====<br />
<br />
<font color="#ff8000">因果模型框架 Causal Models Framework</font>从<font color="#ff8000">结构方程(structural equations)Structural Equation Model</font>系统的角度分析反事实。在一个方程系统中,每个变量都被分配了一个值,这个值是系统中其他变量的显式函数。给定这样一个模型,“如果X是X,Y就会是Y(''Y'' would be ''y'' had ''X'' been ''x'')”这个句子 (形式上为 ''X = x'' > ''Y = y'' )被定义为断言。如果我们用一个常数''X = x''取代当前决定 ''X''的方程,并求解变量''Y''的方程组,得到的解将是''Y = y''。这个定义已被证明与可能世界语义学的公理兼容,并构成自然科学和社会科学中因果推理的基础。因为这些领域的每个结构方程都对应于一个熟悉的因果机制,这个因果机制可以被研究者进行有意义地推理。这种方法是由Judea Pearl(2000)提出的,作为编码关于因果关系的细粒度直觉的手段,这些直觉在其他提议的系统中难以捕捉。<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
<br />
====信念修正====<br />
<br />
在信念修正框架中,反事实是用 ''Ramsey检验''的形式化实现来处理的。在这些系统中,当且仅当在当前的知识体系添加 ''A''后得到的结果是B时,反事实''A'' > ''B''成立。这个条件将反事实条件与信念修正联系起来,因为对''A'' > ''B''的评价可以通过首先用''A''修正当前的知识,然后检查''B''在什么结果中是否为真。当''A''与当前的信念一致时,修正是很容易的,但在其他情况下可能会很难。每一个用于信念修正的语义都可以用于评价条件语句。反过来说,每一种评价条件语句的方法都可以被看作是一种执行修正的方法。<br />
<br />
====Ginsberg====<br />
<br />
Ginsberg(1986)提出了一种条件句的语义,它假定当前的信念形成了一组命题公式,考虑这些公式中与''A''一致的最大集合,并在每个集合中加入''A''。其理由是,这些最大集合中的每一个都代表了一种可能的信念状态,在这种状态下,''A''为真,且与原始状态尽可能相似。因此,当且仅当''B''在所有这些集合中都为真时,条件陈述句''A'' > ''B''才成立。<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref></div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22795反事实2021-06-01T12:05:04Z<p>Wei:/* 术语 */</p>
<hr />
<div><br />
'''<font color="#ff8000"> 反事实条件句 Counterfactual conditionals</font>'''(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的<font color="#ff8000"> 条件句 conditional sentence</font>。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
<br />
反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是显而易见的事实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
<br />
<br />
==概述==<br />
<br />
<br />
===案例 ===<br />
<br />
<br />
指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
<br />
# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
<br />
# '''一般过去时的反事实''':如果现在正在下雨,那么Sally应该在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
<br />
这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
<br />
英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
<br />
# '''过去完成时的反事实''':如果昨天下了雨,那么Sally当时应该会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
<br />
另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
<br />
# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
<br />
过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
<br />
<br />
# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
<br />
# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
<br />
===术语===<br />
<br />
“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的前件条件是假的或不可能的。<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
<br />
# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
<br />
这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
<br />
''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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最近有研究提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为''O-Marked''条件语,反映了它们的''o''普通标记。<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
<br />
<br />
一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
<br />
==逻辑和语义==<br />
<br />
===经典问题===<br />
<br />
====反事实的问题====<br />
<br />
根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
<br />
# 如果那块黄油被加热到150度,它就会融化。<br />
# 如果那块黄油被加热到150度,它就不会融化。<br />
<br />
更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
<br />
====上下文依赖和含糊不清====<br />
<br />
反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
<br />
# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
<br />
====非单调性====<br />
<br />
反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
<br />
# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
<br />
对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
<br />
* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
<br />
===考虑可能存在的世界===<br />
<br />
反事实的最常见的逻辑解释是'''<font color="#ff8000"> 可能世界语义 Possible World Semantics</font>'''。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
<br />
大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,学术上有多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
<br />
====严格的条件====<br />
<br />
严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
<br />
* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
<br />
与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活跃"的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
<br />
严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
<br />
这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
<br />
Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
<br />
# 如果Natalia明天离开,她会准时到达。<br />
<br />
# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
<br />
Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
<br />
====可变严格条件====<br />
<br />
在可变严格方法中,条件''A'' > ''B''的语义是由一些函数给出的,一方面是A为真、B为真的世界,另一方面是A为真、B为假的世界的相对接近程度。<br />
<br />
在刘易斯的论述中,A > C 是(a)空洞的真实,只有在没有A为真的世界时(例如,如果A在逻辑上或形而上学上是不可能的);(b)非空洞的真实,只有在A为真的世界中,一些C为真的世界比任何C不为真的世界更接近实际世界;或者(c)虚假,在其他世界里。尽管在刘易斯的《反事实》中,他对“接近性(closeness)”的意思并不清晰,但在后来的著作中,刘易斯明确表示,他并不打算将“接近性”的尺度简单地作为我们对整体相似性的普通概念。<br />
<br />
例子:<br />
:如果他在早餐时吃多一点,他在上午11点就不会饿。<br />
<br />
根据刘易斯的说法,这个陈述的真理在于:在他早餐吃得更多的可能世界中,至少有一个他在上午11点不饿的世界比任何他早餐吃得更多但在上午11点仍然饿的世界更接近我们的世界。<br />
<br />
过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
<br />
Stalnaker的论述与Lewis的论述最明显的不同在于,他接受了“极限(limit)”和“唯一性假设(uniqueness assumptions)”。唯一性假设的论点是:对于任何前件A,在A为真的可能世界中,有一个最接近实际世界的单一(唯一)世界。极限假设的论点是,对于一个给定的前件A,如果存在一个A为真的可能世界链,每个世界都比它的前一个世界更接近实际世界,那么这个链就有一个极限:一个A为真的可能世界比这个链中的所有世界更接近实际世界。(唯一性假设包含了极限假设,但极限假设并不包含唯一性假设)。根据Stalnaker的观点,当且仅当在最接近A为真的世界中,C为真时,A>C才是非空洞的真。因此,上面的例子是真的,只是在他吃了更多早餐的唯一最接近的世界中,他在上午11点不觉得饿。虽然有争议,但Lewis拒绝了极限假设(因此也拒绝了唯一性假设),因为它排除了这样一种可能性,即可能存在着越来越接近实际世界的世界,而没有极限。例如,可能会有一系列无限的世界,每个世界的咖啡杯都在其实际位置的左边小几分之一英寸,但其中没有一个是唯一最接近的。(参见Lewis 1973: 20)。<br />
<br />
Stalnaker接受唯一性假设的一个结果是,如果排除中间律是真的,那么公式(A>C)∨(A>¬C)的所有实例都是真的。排他性中间律的论题是:对于所有命题p,p∨¬p都是真的。如果唯一性假设为真,那么对于每一个前件A,都有一个唯一最接近的世界,其中A为真。如果排除中间法则是真的,任何结果C在A为真的那个世界里要么是真,要么是假。所以对于每一个反事实A>C,要么A>C,要么A>¬C为真。这就是所谓的条件排除中间法(CEM)。例子:<br />
<br />
:(1) 如果公平的硬币被抛出,它将会正面朝上。<br />
:(2) 如果公平的硬币被抛出,它将会反面朝上(即不是正面朝上)。<br />
<br />
根据Stalnaker的分析,存在一个最接近的世界,在这个世界里,(1)和(2)中提到的公平的硬币被抛出,硬币要么正面朝上,要么反面朝上。因此,要么(1)是真,(2)是假,要么(1)是假,(2)是真。然而,根据Lewis的分析,(1)和(2)都是假的,因为公平的硬币正面朝上的世界并不比反面朝上的世界更接近或更远离。对Lewis来说,“如果硬币被抛出,它将正面朝上或反面朝上”是真的,但这并不意味着“如果硬币被抛出,它将落在正面”,或“如果硬币被抛出,它就会反面朝上”。<br />
<br />
=== 其他考虑===<br />
<br />
====因果模型====<br />
<br />
<font color="#ff8000">因果模型框架 Causal Models Framework</font>从<font color="#ff8000">结构方程(structural equations)Structural Equation Model</font>系统的角度分析反事实。在一个方程系统中,每个变量都被分配了一个值,这个值是系统中其他变量的显式函数。给定这样一个模型,“如果X是X,Y就会是Y(''Y'' would be ''y'' had ''X'' been ''x'')”这个句子 (形式上为 ''X = x'' > ''Y = y'' )被定义为断言。如果我们用一个常数''X = x''取代当前决定 ''X''的方程,并求解变量''Y''的方程组,得到的解将是''Y = y''。这个定义已被证明与可能世界语义学的公理兼容,并构成自然科学和社会科学中因果推理的基础。因为这些领域的每个结构方程都对应于一个熟悉的因果机制,这个因果机制可以被研究者进行有意义地推理。这种方法是由Judea Pearl(2000)提出的,作为编码关于因果关系的细粒度直觉的手段,这些直觉在其他提议的系统中难以捕捉。<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
<br />
====信念修正====<br />
<br />
在信念修正框架中,反事实是用 ''Ramsey检验''的形式化实现来处理的。在这些系统中,当且仅当在当前的知识体系添加 ''A''后得到的结果是B时,反事实''A'' > ''B''成立。这个条件将反事实条件与信念修正联系起来,因为对''A'' > ''B''的评价可以通过首先用''A''修正当前的知识,然后检查''B''在什么结果中是否为真。当''A''与当前的信念一致时,修正是很容易的,但在其他情况下可能会很难。每一个用于信念修正的语义都可以用于评价条件语句。反过来说,每一种评价条件语句的方法都可以被看作是一种执行修正的方法。<br />
<br />
<br />
====Ginsberg====<br />
<br />
Ginsberg(1986)提出了一种条件句的语义,它假定当前的信念形成了一组命题公式,考虑这些公式中与''A''一致的最大集合,并在每个集合中加入''A''。其理由是,这些最大集合中的每一个都代表了一种可能的信念状态,在这种状态下,''A''为真,且与原始状态尽可能相似。因此,当且仅当''B''在所有这些集合中都为真时,条件陈述句''A'' > ''B''才成立。<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref></div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22794反事实2021-06-01T12:03:20Z<p>Wei:/* 因果模型 */</p>
<hr />
<div><br />
'''<font color="#ff8000"> 反事实条件句 Counterfactual conditionals</font>'''(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的<font color="#ff8000"> 条件句 conditional sentence</font>。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是显而易见的事实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==概述==<br />
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===案例 ===<br />
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指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
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# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
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# '''一般过去时的反事实''':如果现在正在下雨,那么Sally应该在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
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英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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# '''过去完成时的反事实''':如果昨天下了雨,那么Sally当时应该会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
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另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
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过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
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# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
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===术语===<br />
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“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的前件条件是假的或不可能的。<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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最近有研究提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为''O-Marked''条件语,反映了它们的''o''普通标记。<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
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==逻辑和语义==<br />
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===经典问题===<br />
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====反事实的问题====<br />
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根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
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# 如果那块黄油被加热到150度,它就会融化。<br />
# 如果那块黄油被加热到150度,它就不会融化。<br />
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更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
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====上下文依赖和含糊不清====<br />
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反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
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# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
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====非单调性====<br />
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反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
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对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
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* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
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===考虑可能存在的世界===<br />
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反事实的最常见的逻辑解释是'''<font color="#ff8000"> 可能世界语义 Possible World Semantics</font>'''。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
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大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,学术上有多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
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====严格的条件====<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
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* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
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与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活跃"的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
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严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
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这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
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Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
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# 如果Natalia明天离开,她会准时到达。<br />
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# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
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Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
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====可变严格条件====<br />
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在可变严格方法中,条件''A'' > ''B''的语义是由一些函数给出的,一方面是A为真、B为真的世界,另一方面是A为真、B为假的世界的相对接近程度。<br />
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在刘易斯的论述中,A > C 是(a)空洞的真实,只有在没有A为真的世界时(例如,如果A在逻辑上或形而上学上是不可能的);(b)非空洞的真实,只有在A为真的世界中,一些C为真的世界比任何C不为真的世界更接近实际世界;或者(c)虚假,在其他世界里。尽管在刘易斯的《反事实》中,他对“接近性(closeness)”的意思并不清晰,但在后来的著作中,刘易斯明确表示,他并不打算将“接近性”的尺度简单地作为我们对整体相似性的普通概念。<br />
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例子:<br />
:如果他在早餐时吃多一点,他在上午11点就不会饿。<br />
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根据刘易斯的说法,这个陈述的真理在于:在他早餐吃得更多的可能世界中,至少有一个他在上午11点不饿的世界比任何他早餐吃得更多但在上午11点仍然饿的世界更接近我们的世界。<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker的论述与Lewis的论述最明显的不同在于,他接受了“极限(limit)”和“唯一性假设(uniqueness assumptions)”。唯一性假设的论点是:对于任何前件A,在A为真的可能世界中,有一个最接近实际世界的单一(唯一)世界。极限假设的论点是,对于一个给定的前件A,如果存在一个A为真的可能世界链,每个世界都比它的前一个世界更接近实际世界,那么这个链就有一个极限:一个A为真的可能世界比这个链中的所有世界更接近实际世界。(唯一性假设包含了极限假设,但极限假设并不包含唯一性假设)。根据Stalnaker的观点,当且仅当在最接近A为真的世界中,C为真时,A>C才是非空洞的真。因此,上面的例子是真的,只是在他吃了更多早餐的唯一最接近的世界中,他在上午11点不觉得饿。虽然有争议,但Lewis拒绝了极限假设(因此也拒绝了唯一性假设),因为它排除了这样一种可能性,即可能存在着越来越接近实际世界的世界,而没有极限。例如,可能会有一系列无限的世界,每个世界的咖啡杯都在其实际位置的左边小几分之一英寸,但其中没有一个是唯一最接近的。(参见Lewis 1973: 20)。<br />
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Stalnaker接受唯一性假设的一个结果是,如果排除中间律是真的,那么公式(A>C)∨(A>¬C)的所有实例都是真的。排他性中间律的论题是:对于所有命题p,p∨¬p都是真的。如果唯一性假设为真,那么对于每一个前件A,都有一个唯一最接近的世界,其中A为真。如果排除中间法则是真的,任何结果C在A为真的那个世界里要么是真,要么是假。所以对于每一个反事实A>C,要么A>C,要么A>¬C为真。这就是所谓的条件排除中间法(CEM)。例子:<br />
<br />
:(1) 如果公平的硬币被抛出,它将会正面朝上。<br />
:(2) 如果公平的硬币被抛出,它将会反面朝上(即不是正面朝上)。<br />
<br />
根据Stalnaker的分析,存在一个最接近的世界,在这个世界里,(1)和(2)中提到的公平的硬币被抛出,硬币要么正面朝上,要么反面朝上。因此,要么(1)是真,(2)是假,要么(1)是假,(2)是真。然而,根据Lewis的分析,(1)和(2)都是假的,因为公平的硬币正面朝上的世界并不比反面朝上的世界更接近或更远离。对Lewis来说,“如果硬币被抛出,它将正面朝上或反面朝上”是真的,但这并不意味着“如果硬币被抛出,它将落在正面”,或“如果硬币被抛出,它就会反面朝上”。<br />
<br />
=== 其他考虑===<br />
<br />
====因果模型====<br />
<br />
<font color="#ff8000">因果模型框架 Causal Models Framework</font>从<font color="#ff8000">结构方程(structural equations)Structural Equation Model</font>系统的角度分析反事实。在一个方程系统中,每个变量都被分配了一个值,这个值是系统中其他变量的显式函数。给定这样一个模型,“如果X是X,Y就会是Y(''Y'' would be ''y'' had ''X'' been ''x'')”这个句子 (形式上为 ''X = x'' > ''Y = y'' )被定义为断言。如果我们用一个常数''X = x''取代当前决定 ''X''的方程,并求解变量''Y''的方程组,得到的解将是''Y = y''。这个定义已被证明与可能世界语义学的公理兼容,并构成自然科学和社会科学中因果推理的基础。因为这些领域的每个结构方程都对应于一个熟悉的因果机制,这个因果机制可以被研究者进行有意义地推理。这种方法是由Judea Pearl(2000)提出的,作为编码关于因果关系的细粒度直觉的手段,这些直觉在其他提议的系统中难以捕捉。<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
<br />
====信念修正====<br />
<br />
在信念修正框架中,反事实是用 ''Ramsey检验''的形式化实现来处理的。在这些系统中,当且仅当在当前的知识体系添加 ''A''后得到的结果是B时,反事实''A'' > ''B''成立。这个条件将反事实条件与信念修正联系起来,因为对''A'' > ''B''的评价可以通过首先用''A''修正当前的知识,然后检查''B''在什么结果中是否为真。当''A''与当前的信念一致时,修正是很容易的,但在其他情况下可能会很难。每一个用于信念修正的语义都可以用于评价条件语句。反过来说,每一种评价条件语句的方法都可以被看作是一种执行修正的方法。<br />
<br />
<br />
====Ginsberg====<br />
<br />
Ginsberg(1986)提出了一种条件句的语义,它假定当前的信念形成了一组命题公式,考虑这些公式中与''A''一致的最大集合,并在每个集合中加入''A''。其理由是,这些最大集合中的每一个都代表了一种可能的信念状态,在这种状态下,''A''为真,且与原始状态尽可能相似。因此,当且仅当''B''在所有这些集合中都为真时,条件陈述句''A'' > ''B''才成立。<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref></div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22793反事实2021-06-01T12:02:58Z<p>Wei:/* 案例 */</p>
<hr />
<div><br />
'''<font color="#ff8000"> 反事实条件句 Counterfactual conditionals</font>'''(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的<font color="#ff8000"> 条件句 conditional sentence</font>。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
<br />
反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是显而易见的事实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
<br />
<br />
==概述==<br />
<br />
<br />
===案例 ===<br />
<br />
<br />
指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
<br />
# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
<br />
# '''一般过去时的反事实''':如果现在正在下雨,那么Sally应该在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
<br />
这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
<br />
英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
<br />
# '''过去完成时的反事实''':如果昨天下了雨,那么Sally当时应该会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
<br />
另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
<br />
# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
<br />
过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
<br />
<br />
# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
<br />
# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
<br />
===术语===<br />
<br />
“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的前件条件是假的或不可能的。<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
<br />
# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
<br />
这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
<br />
''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
<br />
最近有研究提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为''O-Marked''条件语,反映了它们的''o''普通标记。<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
<br />
<br />
一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
<br />
==逻辑和语义==<br />
<br />
===经典问题===<br />
<br />
====反事实的问题====<br />
<br />
根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
<br />
# 如果那块黄油被加热到150度,它就会融化。<br />
# 如果那块黄油被加热到150度,它就不会融化。<br />
<br />
更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
<br />
====上下文依赖和含糊不清====<br />
<br />
反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
<br />
# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
<br />
====非单调性====<br />
<br />
反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
<br />
# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
<br />
对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
<br />
* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
<br />
===考虑可能存在的世界===<br />
<br />
反事实的最常见的逻辑解释是'''<font color="#ff8000"> 可能世界语义 Possible World Semantics</font>'''。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
<br />
大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,学术上有多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
<br />
====严格的条件====<br />
<br />
严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
<br />
* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
<br />
与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活跃"的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
<br />
严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
<br />
这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
<br />
Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
<br />
# 如果Natalia明天离开,她会准时到达。<br />
<br />
# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
<br />
Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
<br />
====可变严格条件====<br />
<br />
在可变严格方法中,条件''A'' > ''B''的语义是由一些函数给出的,一方面是A为真、B为真的世界,另一方面是A为真、B为假的世界的相对接近程度。<br />
<br />
在刘易斯的论述中,A > C 是(a)空洞的真实,只有在没有A为真的世界时(例如,如果A在逻辑上或形而上学上是不可能的);(b)非空洞的真实,只有在A为真的世界中,一些C为真的世界比任何C不为真的世界更接近实际世界;或者(c)虚假,在其他世界里。尽管在刘易斯的《反事实》中,他对“接近性(closeness)”的意思并不清晰,但在后来的著作中,刘易斯明确表示,他并不打算将“接近性”的尺度简单地作为我们对整体相似性的普通概念。<br />
<br />
例子:<br />
:如果他在早餐时吃多一点,他在上午11点就不会饿。<br />
<br />
根据刘易斯的说法,这个陈述的真理在于:在他早餐吃得更多的可能世界中,至少有一个他在上午11点不饿的世界比任何他早餐吃得更多但在上午11点仍然饿的世界更接近我们的世界。<br />
<br />
过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
<br />
Stalnaker的论述与Lewis的论述最明显的不同在于,他接受了“极限(limit)”和“唯一性假设(uniqueness assumptions)”。唯一性假设的论点是:对于任何前件A,在A为真的可能世界中,有一个最接近实际世界的单一(唯一)世界。极限假设的论点是,对于一个给定的前件A,如果存在一个A为真的可能世界链,每个世界都比它的前一个世界更接近实际世界,那么这个链就有一个极限:一个A为真的可能世界比这个链中的所有世界更接近实际世界。(唯一性假设包含了极限假设,但极限假设并不包含唯一性假设)。根据Stalnaker的观点,当且仅当在最接近A为真的世界中,C为真时,A>C才是非空洞的真。因此,上面的例子是真的,只是在他吃了更多早餐的唯一最接近的世界中,他在上午11点不觉得饿。虽然有争议,但Lewis拒绝了极限假设(因此也拒绝了唯一性假设),因为它排除了这样一种可能性,即可能存在着越来越接近实际世界的世界,而没有极限。例如,可能会有一系列无限的世界,每个世界的咖啡杯都在其实际位置的左边小几分之一英寸,但其中没有一个是唯一最接近的。(参见Lewis 1973: 20)。<br />
<br />
Stalnaker接受唯一性假设的一个结果是,如果排除中间律是真的,那么公式(A>C)∨(A>¬C)的所有实例都是真的。排他性中间律的论题是:对于所有命题p,p∨¬p都是真的。如果唯一性假设为真,那么对于每一个前件A,都有一个唯一最接近的世界,其中A为真。如果排除中间法则是真的,任何结果C在A为真的那个世界里要么是真,要么是假。所以对于每一个反事实A>C,要么A>C,要么A>¬C为真。这就是所谓的条件排除中间法(CEM)。例子:<br />
<br />
:(1) 如果公平的硬币被抛出,它将会正面朝上。<br />
:(2) 如果公平的硬币被抛出,它将会反面朝上(即不是正面朝上)。<br />
<br />
根据Stalnaker的分析,存在一个最接近的世界,在这个世界里,(1)和(2)中提到的公平的硬币被抛出,硬币要么正面朝上,要么反面朝上。因此,要么(1)是真,(2)是假,要么(1)是假,(2)是真。然而,根据Lewis的分析,(1)和(2)都是假的,因为公平的硬币正面朝上的世界并不比反面朝上的世界更接近或更远离。对Lewis来说,“如果硬币被抛出,它将正面朝上或反面朝上”是真的,但这并不意味着“如果硬币被抛出,它将落在正面”,或“如果硬币被抛出,它就会反面朝上”。<br />
<br />
=== 其他考虑===<br />
<br />
====因果模型====<br />
<br />
''<font color="#ff8000">因果模型框架 Causal Models Framework</font>''从<font color="#ff8000">结构方程(structural equations)Structural Equation Model</font>系统的角度分析反事实。在一个方程系统中,每个变量都被分配了一个值,这个值是系统中其他变量的显式函数。给定这样一个模型,“如果X是X,Y就会是Y(''Y'' would be ''y'' had ''X'' been ''x'')”这个句子 (形式上为 ''X = x'' > ''Y = y'' )被定义为断言。如果我们用一个常数''X = x''取代当前决定 ''X''的方程,并求解变量''Y''的方程组,得到的解将是''Y = y''。这个定义已被证明与可能世界语义学的公理兼容,并构成自然科学和社会科学中因果推理的基础。因为这些领域的每个结构方程都对应于一个熟悉的因果机制,这个因果机制可以被研究者进行有意义地推理。这种方法是由Judea Pearl(2000)提出的,作为编码关于因果关系的细粒度直觉的手段,这些直觉在其他提议的系统中难以捕捉。<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
<br />
====信念修正====<br />
<br />
在信念修正框架中,反事实是用 ''Ramsey检验''的形式化实现来处理的。在这些系统中,当且仅当在当前的知识体系添加 ''A''后得到的结果是B时,反事实''A'' > ''B''成立。这个条件将反事实条件与信念修正联系起来,因为对''A'' > ''B''的评价可以通过首先用''A''修正当前的知识,然后检查''B''在什么结果中是否为真。当''A''与当前的信念一致时,修正是很容易的,但在其他情况下可能会很难。每一个用于信念修正的语义都可以用于评价条件语句。反过来说,每一种评价条件语句的方法都可以被看作是一种执行修正的方法。<br />
<br />
<br />
====Ginsberg====<br />
<br />
Ginsberg(1986)提出了一种条件句的语义,它假定当前的信念形成了一组命题公式,考虑这些公式中与''A''一致的最大集合,并在每个集合中加入''A''。其理由是,这些最大集合中的每一个都代表了一种可能的信念状态,在这种状态下,''A''为真,且与原始状态尽可能相似。因此,当且仅当''B''在所有这些集合中都为真时,条件陈述句''A'' > ''B''才成立。<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref></div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22792反事实2021-06-01T12:02:03Z<p>Wei:/* 非单调性 */</p>
<hr />
<div><br />
'''<font color="#ff8000"> 反事实条件句 Counterfactual conditionals</font>'''(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的<font color="#ff8000"> 条件句 conditional sentence</font>。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
<br />
反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是显而易见的事实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
<br />
<br />
==概述==<br />
<br />
<br />
===案例 ===<br />
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<br />
指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
<br />
# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
<br />
# '''一般过去时的反事实''':如果现在正在下雨,那么Sally应该在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
<br />
这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
<br />
英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
<br />
# '''过去完成时的反事实''':如果昨天下了雨,那么Sally当时应该会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
<br />
另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
<br />
# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
<br />
过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
<br />
<br />
# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
<br />
# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
<br />
===术语===<br />
<br />
“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的前件条件是假的或不可能的。<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
<br />
# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
<br />
这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
<br />
''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
<br />
最近有研究提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为''O-Marked''条件语,反映了它们的''o''普通标记。<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
<br />
<br />
一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
<br />
==逻辑和语义==<br />
<br />
===经典问题===<br />
<br />
====反事实的问题====<br />
<br />
根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
<br />
# 如果那块黄油被加热到150度,它就会融化。<br />
# 如果那块黄油被加热到150度,它就不会融化。<br />
<br />
更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
<br />
====上下文依赖和含糊不清====<br />
<br />
反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
<br />
# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
<br />
====非单调性====<br />
<br />
反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
<br />
# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
<br />
对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
<br />
* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
<br />
===考虑可能存在的世界===<br />
<br />
反事实的最常见的逻辑解释是'''<font color="#ff8000"> 可能世界语义 Possible World Semantics</font>'''。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
<br />
大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,学术上有多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
<br />
====严格的条件====<br />
<br />
严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
<br />
* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
<br />
与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活跃"的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
<br />
严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
<br />
这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
<br />
Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
<br />
# 如果Natalia明天离开,她会准时到达。<br />
<br />
# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
<br />
Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
<br />
====可变严格条件====<br />
<br />
在可变严格方法中,条件''A'' > ''B''的语义是由一些函数给出的,一方面是A为真、B为真的世界,另一方面是A为真、B为假的世界的相对接近程度。<br />
<br />
在刘易斯的论述中,A > C 是(a)空洞的真实,只有在没有A为真的世界时(例如,如果A在逻辑上或形而上学上是不可能的);(b)非空洞的真实,只有在A为真的世界中,一些C为真的世界比任何C不为真的世界更接近实际世界;或者(c)虚假,在其他世界里。尽管在刘易斯的《反事实》中,他对“接近性(closeness)”的意思并不清晰,但在后来的著作中,刘易斯明确表示,他并不打算将“接近性”的尺度简单地作为我们对整体相似性的普通概念。<br />
<br />
例子:<br />
:如果他在早餐时吃多一点,他在上午11点就不会饿。<br />
<br />
根据刘易斯的说法,这个陈述的真理在于:在他早餐吃得更多的可能世界中,至少有一个他在上午11点不饿的世界比任何他早餐吃得更多但在上午11点仍然饿的世界更接近我们的世界。<br />
<br />
过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
<br />
Stalnaker的论述与Lewis的论述最明显的不同在于,他接受了“极限(limit)”和“唯一性假设(uniqueness assumptions)”。唯一性假设的论点是:对于任何前件A,在A为真的可能世界中,有一个最接近实际世界的单一(唯一)世界。极限假设的论点是,对于一个给定的前件A,如果存在一个A为真的可能世界链,每个世界都比它的前一个世界更接近实际世界,那么这个链就有一个极限:一个A为真的可能世界比这个链中的所有世界更接近实际世界。(唯一性假设包含了极限假设,但极限假设并不包含唯一性假设)。根据Stalnaker的观点,当且仅当在最接近A为真的世界中,C为真时,A>C才是非空洞的真。因此,上面的例子是真的,只是在他吃了更多早餐的唯一最接近的世界中,他在上午11点不觉得饿。虽然有争议,但Lewis拒绝了极限假设(因此也拒绝了唯一性假设),因为它排除了这样一种可能性,即可能存在着越来越接近实际世界的世界,而没有极限。例如,可能会有一系列无限的世界,每个世界的咖啡杯都在其实际位置的左边小几分之一英寸,但其中没有一个是唯一最接近的。(参见Lewis 1973: 20)。<br />
<br />
Stalnaker接受唯一性假设的一个结果是,如果排除中间律是真的,那么公式(A>C)∨(A>¬C)的所有实例都是真的。排他性中间律的论题是:对于所有命题p,p∨¬p都是真的。如果唯一性假设为真,那么对于每一个前件A,都有一个唯一最接近的世界,其中A为真。如果排除中间法则是真的,任何结果C在A为真的那个世界里要么是真,要么是假。所以对于每一个反事实A>C,要么A>C,要么A>¬C为真。这就是所谓的条件排除中间法(CEM)。例子:<br />
<br />
:(1) 如果公平的硬币被抛出,它将会正面朝上。<br />
:(2) 如果公平的硬币被抛出,它将会反面朝上(即不是正面朝上)。<br />
<br />
根据Stalnaker的分析,存在一个最接近的世界,在这个世界里,(1)和(2)中提到的公平的硬币被抛出,硬币要么正面朝上,要么反面朝上。因此,要么(1)是真,(2)是假,要么(1)是假,(2)是真。然而,根据Lewis的分析,(1)和(2)都是假的,因为公平的硬币正面朝上的世界并不比反面朝上的世界更接近或更远离。对Lewis来说,“如果硬币被抛出,它将正面朝上或反面朝上”是真的,但这并不意味着“如果硬币被抛出,它将落在正面”,或“如果硬币被抛出,它就会反面朝上”。<br />
<br />
=== 其他考虑===<br />
<br />
====因果模型====<br />
<br />
''<font color="#ff8000">因果模型框架 Causal Models Framework</font>''从<font color="#ff8000">结构方程(structural equations)Structural Equation Model</font>系统的角度分析反事实。在一个方程系统中,每个变量都被分配了一个值,这个值是系统中其他变量的显式函数。给定这样一个模型,“如果X是X,Y就会是Y(''Y'' would be ''y'' had ''X'' been ''x'')”这个句子 (形式上为 ''X = x'' > ''Y = y'' )被定义为断言。如果我们用一个常数''X = x''取代当前决定 ''X''的方程,并求解变量''Y''的方程组,得到的解将是''Y = y''。这个定义已被证明与可能世界语义学的公理兼容,并构成自然科学和社会科学中因果推理的基础。因为这些领域的每个结构方程都对应于一个熟悉的因果机制,这个因果机制可以被研究者进行有意义地推理。这种方法是由Judea Pearl(2000)提出的,作为编码关于因果关系的细粒度直觉的手段,这些直觉在其他提议的系统中难以捕捉。<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
<br />
====信念修正====<br />
<br />
在信念修正框架中,反事实是用 ''Ramsey检验''的形式化实现来处理的。在这些系统中,当且仅当在当前的知识体系添加 ''A''后得到的结果是B时,反事实''A'' > ''B''成立。这个条件将反事实条件与信念修正联系起来,因为对''A'' > ''B''的评价可以通过首先用''A''修正当前的知识,然后检查''B''在什么结果中是否为真。当''A''与当前的信念一致时,修正是很容易的,但在其他情况下可能会很难。每一个用于信念修正的语义都可以用于评价条件语句。反过来说,每一种评价条件语句的方法都可以被看作是一种执行修正的方法。<br />
<br />
<br />
====Ginsberg====<br />
<br />
Ginsberg(1986)提出了一种条件句的语义,它假定当前的信念形成了一组命题公式,考虑这些公式中与''A''一致的最大集合,并在每个集合中加入''A''。其理由是,这些最大集合中的每一个都代表了一种可能的信念状态,在这种状态下,''A''为真,且与原始状态尽可能相似。因此,当且仅当''B''在所有这些集合中都为真时,条件陈述句''A'' > ''B''才成立。<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref></div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22791反事实2021-06-01T11:59:08Z<p>Wei:/* 上下文依赖和含糊不清(Context dependence and vagueness) */</p>
<hr />
<div><br />
'''<font color="#ff8000"> 反事实条件句 Counterfactual conditionals</font>'''(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的<font color="#ff8000"> 条件句 conditional sentence</font>。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
<br />
反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是显而易见的事实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
<br />
<br />
==概述==<br />
<br />
<br />
===案例 ===<br />
<br />
<br />
指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
<br />
# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
<br />
# '''一般过去时的反事实''':如果现在正在下雨,那么Sally应该在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
<br />
这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
<br />
英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
<br />
# '''过去完成时的反事实''':如果昨天下了雨,那么Sally当时应该会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
<br />
另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
<br />
# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
<br />
过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
<br />
<br />
# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
<br />
# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
<br />
===术语===<br />
<br />
“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的前件条件是假的或不可能的。<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
<br />
# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
<br />
这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
<br />
''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
<br />
最近有研究提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为''O-Marked''条件语,反映了它们的''o''普通标记。<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
<br />
<br />
一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
<br />
==逻辑和语义==<br />
<br />
===经典问题===<br />
<br />
====反事实的问题====<br />
<br />
根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
<br />
# 如果那块黄油被加热到150度,它就会融化。<br />
# 如果那块黄油被加热到150度,它就不会融化。<br />
<br />
更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
<br />
====上下文依赖和含糊不清====<br />
<br />
反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
<br />
# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
<br />
====非单调性====<br />
<br />
反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
<br />
# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
<br />
对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
<br />
* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
<br />
===考虑可能存在的世界===<br />
<br />
反事实的最常见的逻辑解释是'''<font color="#ff8000"> 可能世界语义 Possible World Semantics</font>'''。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
<br />
大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,学术上有多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
<br />
====严格的条件====<br />
<br />
严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
<br />
* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
<br />
与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活跃"的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
<br />
严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
<br />
这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
<br />
Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
<br />
# 如果Natalia明天离开,她会准时到达。<br />
<br />
# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
<br />
Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
<br />
====可变严格条件====<br />
<br />
在可变严格方法中,条件''A'' > ''B''的语义是由一些函数给出的,一方面是A为真、B为真的世界,另一方面是A为真、B为假的世界的相对接近程度。<br />
<br />
在刘易斯的论述中,A > C 是(a)空洞的真实,只有在没有A为真的世界时(例如,如果A在逻辑上或形而上学上是不可能的);(b)非空洞的真实,只有在A为真的世界中,一些C为真的世界比任何C不为真的世界更接近实际世界;或者(c)虚假,在其他世界里。尽管在刘易斯的《反事实》中,他对“接近性(closeness)”的意思并不清晰,但在后来的著作中,刘易斯明确表示,他并不打算将“接近性”的尺度简单地作为我们对整体相似性的普通概念。<br />
<br />
例子:<br />
:如果他在早餐时吃多一点,他在上午11点就不会饿。<br />
<br />
根据刘易斯的说法,这个陈述的真理在于:在他早餐吃得更多的可能世界中,至少有一个他在上午11点不饿的世界比任何他早餐吃得更多但在上午11点仍然饿的世界更接近我们的世界。<br />
<br />
过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
<br />
Stalnaker的论述与Lewis的论述最明显的不同在于,他接受了“极限(limit)”和“唯一性假设(uniqueness assumptions)”。唯一性假设的论点是:对于任何前件A,在A为真的可能世界中,有一个最接近实际世界的单一(唯一)世界。极限假设的论点是,对于一个给定的前件A,如果存在一个A为真的可能世界链,每个世界都比它的前一个世界更接近实际世界,那么这个链就有一个极限:一个A为真的可能世界比这个链中的所有世界更接近实际世界。(唯一性假设包含了极限假设,但极限假设并不包含唯一性假设)。根据Stalnaker的观点,当且仅当在最接近A为真的世界中,C为真时,A>C才是非空洞的真。因此,上面的例子是真的,只是在他吃了更多早餐的唯一最接近的世界中,他在上午11点不觉得饿。虽然有争议,但Lewis拒绝了极限假设(因此也拒绝了唯一性假设),因为它排除了这样一种可能性,即可能存在着越来越接近实际世界的世界,而没有极限。例如,可能会有一系列无限的世界,每个世界的咖啡杯都在其实际位置的左边小几分之一英寸,但其中没有一个是唯一最接近的。(参见Lewis 1973: 20)。<br />
<br />
Stalnaker接受唯一性假设的一个结果是,如果排除中间律是真的,那么公式(A>C)∨(A>¬C)的所有实例都是真的。排他性中间律的论题是:对于所有命题p,p∨¬p都是真的。如果唯一性假设为真,那么对于每一个前件A,都有一个唯一最接近的世界,其中A为真。如果排除中间法则是真的,任何结果C在A为真的那个世界里要么是真,要么是假。所以对于每一个反事实A>C,要么A>C,要么A>¬C为真。这就是所谓的条件排除中间法(CEM)。例子:<br />
<br />
:(1) 如果公平的硬币被抛出,它将会正面朝上。<br />
:(2) 如果公平的硬币被抛出,它将会反面朝上(即不是正面朝上)。<br />
<br />
根据Stalnaker的分析,存在一个最接近的世界,在这个世界里,(1)和(2)中提到的公平的硬币被抛出,硬币要么正面朝上,要么反面朝上。因此,要么(1)是真,(2)是假,要么(1)是假,(2)是真。然而,根据Lewis的分析,(1)和(2)都是假的,因为公平的硬币正面朝上的世界并不比反面朝上的世界更接近或更远离。对Lewis来说,“如果硬币被抛出,它将正面朝上或反面朝上”是真的,但这并不意味着“如果硬币被抛出,它将落在正面”,或“如果硬币被抛出,它就会反面朝上”。<br />
<br />
=== 其他考虑===<br />
<br />
====因果模型====<br />
<br />
''<font color="#ff8000">因果模型框架 Causal Models Framework</font>''从<font color="#ff8000">结构方程(structural equations)Structural Equation Model</font>系统的角度分析反事实。在一个方程系统中,每个变量都被分配了一个值,这个值是系统中其他变量的显式函数。给定这样一个模型,“如果X是X,Y就会是Y(''Y'' would be ''y'' had ''X'' been ''x'')”这个句子 (形式上为 ''X = x'' > ''Y = y'' )被定义为断言。如果我们用一个常数''X = x''取代当前决定 ''X''的方程,并求解变量''Y''的方程组,得到的解将是''Y = y''。这个定义已被证明与可能世界语义学的公理兼容,并构成自然科学和社会科学中因果推理的基础。因为这些领域的每个结构方程都对应于一个熟悉的因果机制,这个因果机制可以被研究者进行有意义地推理。这种方法是由Judea Pearl(2000)提出的,作为编码关于因果关系的细粒度直觉的手段,这些直觉在其他提议的系统中难以捕捉。<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
<br />
====信念修正====<br />
<br />
在信念修正框架中,反事实是用 ''Ramsey检验''的形式化实现来处理的。在这些系统中,当且仅当在当前的知识体系添加 ''A''后得到的结果是B时,反事实''A'' > ''B''成立。这个条件将反事实条件与信念修正联系起来,因为对''A'' > ''B''的评价可以通过首先用''A''修正当前的知识,然后检查''B''在什么结果中是否为真。当''A''与当前的信念一致时,修正是很容易的,但在其他情况下可能会很难。每一个用于信念修正的语义都可以用于评价条件语句。反过来说,每一种评价条件语句的方法都可以被看作是一种执行修正的方法。<br />
<br />
<br />
====Ginsberg====<br />
<br />
Ginsberg(1986)提出了一种条件句的语义,它假定当前的信念形成了一组命题公式,考虑这些公式中与''A''一致的最大集合,并在每个集合中加入''A''。其理由是,这些最大集合中的每一个都代表了一种可能的信念状态,在这种状态下,''A''为真,且与原始状态尽可能相似。因此,当且仅当''B''在所有这些集合中都为真时,条件陈述句''A'' > ''B''才成立。<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref></div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22790反事实2021-06-01T11:58:53Z<p>Wei:</p>
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'''<font color="#ff8000"> 反事实条件句 Counterfactual conditionals</font>'''(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的<font color="#ff8000"> 条件句 conditional sentence</font>。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是显而易见的事实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==概述==<br />
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===案例 ===<br />
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指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
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# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
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# '''一般过去时的反事实''':如果现在正在下雨,那么Sally应该在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
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英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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# '''过去完成时的反事实''':如果昨天下了雨,那么Sally当时应该会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
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另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
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过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
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# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
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===术语===<br />
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“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的前件条件是假的或不可能的。<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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最近有研究提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为''O-Marked''条件语,反映了它们的''o''普通标记。<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
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==逻辑和语义==<br />
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===经典问题===<br />
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====反事实的问题====<br />
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根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
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# 如果那块黄油被加热到150度,它就会融化。<br />
# 如果那块黄油被加热到150度,它就不会融化。<br />
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更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
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====上下文依赖和含糊不清(Context dependence and vagueness)====<br />
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反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
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# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
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====非单调性====<br />
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反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
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对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
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* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
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===考虑可能存在的世界===<br />
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反事实的最常见的逻辑解释是'''<font color="#ff8000"> 可能世界语义 Possible World Semantics</font>'''。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
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大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,学术上有多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
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====严格的条件====<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
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* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
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与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活跃"的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
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严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
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这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
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Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
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# 如果Natalia明天离开,她会准时到达。<br />
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# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
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Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
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====可变严格条件====<br />
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在可变严格方法中,条件''A'' > ''B''的语义是由一些函数给出的,一方面是A为真、B为真的世界,另一方面是A为真、B为假的世界的相对接近程度。<br />
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在刘易斯的论述中,A > C 是(a)空洞的真实,只有在没有A为真的世界时(例如,如果A在逻辑上或形而上学上是不可能的);(b)非空洞的真实,只有在A为真的世界中,一些C为真的世界比任何C不为真的世界更接近实际世界;或者(c)虚假,在其他世界里。尽管在刘易斯的《反事实》中,他对“接近性(closeness)”的意思并不清晰,但在后来的著作中,刘易斯明确表示,他并不打算将“接近性”的尺度简单地作为我们对整体相似性的普通概念。<br />
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例子:<br />
:如果他在早餐时吃多一点,他在上午11点就不会饿。<br />
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根据刘易斯的说法,这个陈述的真理在于:在他早餐吃得更多的可能世界中,至少有一个他在上午11点不饿的世界比任何他早餐吃得更多但在上午11点仍然饿的世界更接近我们的世界。<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker的论述与Lewis的论述最明显的不同在于,他接受了“极限(limit)”和“唯一性假设(uniqueness assumptions)”。唯一性假设的论点是:对于任何前件A,在A为真的可能世界中,有一个最接近实际世界的单一(唯一)世界。极限假设的论点是,对于一个给定的前件A,如果存在一个A为真的可能世界链,每个世界都比它的前一个世界更接近实际世界,那么这个链就有一个极限:一个A为真的可能世界比这个链中的所有世界更接近实际世界。(唯一性假设包含了极限假设,但极限假设并不包含唯一性假设)。根据Stalnaker的观点,当且仅当在最接近A为真的世界中,C为真时,A>C才是非空洞的真。因此,上面的例子是真的,只是在他吃了更多早餐的唯一最接近的世界中,他在上午11点不觉得饿。虽然有争议,但Lewis拒绝了极限假设(因此也拒绝了唯一性假设),因为它排除了这样一种可能性,即可能存在着越来越接近实际世界的世界,而没有极限。例如,可能会有一系列无限的世界,每个世界的咖啡杯都在其实际位置的左边小几分之一英寸,但其中没有一个是唯一最接近的。(参见Lewis 1973: 20)。<br />
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Stalnaker接受唯一性假设的一个结果是,如果排除中间律是真的,那么公式(A>C)∨(A>¬C)的所有实例都是真的。排他性中间律的论题是:对于所有命题p,p∨¬p都是真的。如果唯一性假设为真,那么对于每一个前件A,都有一个唯一最接近的世界,其中A为真。如果排除中间法则是真的,任何结果C在A为真的那个世界里要么是真,要么是假。所以对于每一个反事实A>C,要么A>C,要么A>¬C为真。这就是所谓的条件排除中间法(CEM)。例子:<br />
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:(1) 如果公平的硬币被抛出,它将会正面朝上。<br />
:(2) 如果公平的硬币被抛出,它将会反面朝上(即不是正面朝上)。<br />
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根据Stalnaker的分析,存在一个最接近的世界,在这个世界里,(1)和(2)中提到的公平的硬币被抛出,硬币要么正面朝上,要么反面朝上。因此,要么(1)是真,(2)是假,要么(1)是假,(2)是真。然而,根据Lewis的分析,(1)和(2)都是假的,因为公平的硬币正面朝上的世界并不比反面朝上的世界更接近或更远离。对Lewis来说,“如果硬币被抛出,它将正面朝上或反面朝上”是真的,但这并不意味着“如果硬币被抛出,它将落在正面”,或“如果硬币被抛出,它就会反面朝上”。<br />
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=== 其他考虑===<br />
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====因果模型====<br />
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''<font color="#ff8000">因果模型框架 Causal Models Framework</font>''从<font color="#ff8000">结构方程(structural equations)Structural Equation Model</font>系统的角度分析反事实。在一个方程系统中,每个变量都被分配了一个值,这个值是系统中其他变量的显式函数。给定这样一个模型,“如果X是X,Y就会是Y(''Y'' would be ''y'' had ''X'' been ''x'')”这个句子 (形式上为 ''X = x'' > ''Y = y'' )被定义为断言。如果我们用一个常数''X = x''取代当前决定 ''X''的方程,并求解变量''Y''的方程组,得到的解将是''Y = y''。这个定义已被证明与可能世界语义学的公理兼容,并构成自然科学和社会科学中因果推理的基础。因为这些领域的每个结构方程都对应于一个熟悉的因果机制,这个因果机制可以被研究者进行有意义地推理。这种方法是由Judea Pearl(2000)提出的,作为编码关于因果关系的细粒度直觉的手段,这些直觉在其他提议的系统中难以捕捉。<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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====信念修正====<br />
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在信念修正框架中,反事实是用 ''Ramsey检验''的形式化实现来处理的。在这些系统中,当且仅当在当前的知识体系添加 ''A''后得到的结果是B时,反事实''A'' > ''B''成立。这个条件将反事实条件与信念修正联系起来,因为对''A'' > ''B''的评价可以通过首先用''A''修正当前的知识,然后检查''B''在什么结果中是否为真。当''A''与当前的信念一致时,修正是很容易的,但在其他情况下可能会很难。每一个用于信念修正的语义都可以用于评价条件语句。反过来说,每一种评价条件语句的方法都可以被看作是一种执行修正的方法。<br />
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====Ginsberg====<br />
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Ginsberg(1986)提出了一种条件句的语义,它假定当前的信念形成了一组命题公式,考虑这些公式中与''A''一致的最大集合,并在每个集合中加入''A''。其理由是,这些最大集合中的每一个都代表了一种可能的信念状态,在这种状态下,''A''为真,且与原始状态尽可能相似。因此,当且仅当''B''在所有这些集合中都为真时,条件陈述句''A'' > ''B''才成立。<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref></div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22752反事实2021-05-31T07:29:05Z<p>Wei:</p>
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{{Short description|Conditionals that discuss what would have been if things were otherwise}}<br />
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{{Redirect|Counterfactual}}<br />
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'''Counterfactual conditionals''' (also ''subjunctive'' or ''X-marked'') are [[conditional sentence]]s which discuss what would have been true under different circumstances, e.g. <!-- this is example is from Iatridou (2000), ex (47c) on p. 244 --> "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with [[indicative conditionals|indicatives]], which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of [[Counterfactual conditional#Fake tense|fake tense morphology]], which some languages use in combination with other kinds of [[Morphology (linguistics)|morphology]] including [[Counterfactual conditional#Fake aspect|aspect]] and [[Counterfactual conditional#mood|mood]].<br />
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反事实条件句(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的条件句。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
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Counterfactuals are one of the most studied phenomena in [[philosophical logic]], [[formal semantics (natural language)|formal semantics]], and [[philosophy of language]]. They were first discussed as a problem for the [[material conditional]] analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic [[possible world]] approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as [[causal model]]s and [[dynamic semantics]]. Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是微不足道的真实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==Overview==<br />
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=== Examples ===<br />
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The difference between [[indicative conditional|indicative]] and counterfactual conditionals can be illustrated by the following [[minimal pair]]:<br />
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指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
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# '''Indicative Conditional''': If it ''is'' raining right now, then Sally ''is'' inside. <br />
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# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
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# '''Simple Past Counterfactual''': If it ''was raining'' <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally ''would be'' inside.<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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# '''一般过去时的反事实''':如果现在正在下雨,那么Sally就会在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "is" in both the "if" clause and the "then" clause. As a result, it conveys that the speaker is agnostic about whether it is raining. The counterfactual example uses the [[fake tense]] form "was" in the "if" clause and the [[modal verb|modal]] "would" in the "then" clause. As a result, it conveys that the speaker does not believe that it is raining.<br />
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这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
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English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the [[pluperfect|past perfect]] counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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# '''Past Perfect Counterfactual''': If it ''had been raining'' yesterday, then Sally ''would have been'' inside.<br />
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# '''过去完成时的反事实''':如果昨天下了雨,那么Sally就会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<br />
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另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<br />
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# '''Irrealis Counterfactual''': If it ''were raining'' right now, then Sally ''would be'' inside.<br />
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# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
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Past perfect and irrealis counterfactuals can undergo ''conditional inversion'':<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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# Were it raining, Sally would be inside.<br />
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# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
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# Had it rained, Sally would be inside.<br />
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# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
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=== Terminology ===<br />
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<!——鉴于术语上的巨大但往往是细微的差异,本节必须经过仔细的编辑。在点击“发布更改”之前,请考虑结果文本是否有助于读者理解这些术语是如何使用的。如果结果文本读起来像是“热狗是三明治的辩论吗?”删除所有字符提示后,请不要点击”发布更改”。特别是,请确保(1)明确区分事实主张和术语定义(2)记住,不同的来源可以以不同的方式使用单一术语(3)对术语的每个术语或用法进行不偏不倚的框架性解释。--><br />
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The term ''counterfactual conditional'' is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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The term counterfactual conditional is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<br />
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“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的先行词是假的或不可能的。<br />
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# '''Anderson Case''': If the patient had taken arsenic, he would have blue spots.<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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Anderson Case: If the patient had taken arsenic, he would have blue spots.<br />
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# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<br />
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Such conditionals are also widely referred to as ''subjunctive conditionals'', though this term is likewise acknowledged as a misnomer even by those who use it.<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref> Many languages do not have a morphological [[subjunctive]] (e.g. [[Danish grammar|Danish]] and [[Dutch grammar|Dutch]]) and many that do have it don’t use it for this sort of conditional (e.g. [[French grammar|French]], [[Swahili grammar|Swahili]], all [[Indo-Aryan languages]] that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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Such conditionals are also widely referred to as subjunctive conditionals, though this term is likewise acknowledged as a misnomer even by those who use it. Many languages do not have a morphological subjunctive (e.g. Danish and Dutch) and many that do have it don’t use it for this sort of conditional (e.g. French, Swahili, all Indo-Aryan languages that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<br />
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这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<br />
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The terms ''counterfactual'' and ''subjunctive'' have sometimes been repurposed for more specific uses. For instance, the term "counterfactual" is sometimes applied to conditionals that express a contrary-to-fact meaning, regardless of their grammatical structure.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" /> Along similar lines, the term "subjunctive" is sometimes used to refer to conditionals that bear fake past or irrealis marking, regardless of the meaning they convey.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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Recently the term X-Marked has been proposed as a replacement, evoking the extra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as O-Marked conditionals, reflecting their ordinary marking.<br />
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''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<br />
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最近有人提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为O-Marked条件语,反映了它们的普通标记。<br />
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Recently the term ''X-Marked'' has been proposed as a replacement, evoking the ''ex''tra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as ''O-Marked'' conditionals, reflecting their ''o''rdinary marking.<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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The ''antecedent'' of a conditional is sometimes referred to as its ''"if"-clause'' or ''protasis''. The ''consequent'' of a conditional is sometimes referred to as a ''"then"''-clause or as an apodosis.<br />
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一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
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==Logic and semantics==<br />
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===经典问题(Classic puzzles)===<br />
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====反事实的问题(The problem of counterfactuals)====<br />
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According to the material conditional analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated. <br />
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根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
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If that piece of butter had been heated to 150º, it would have melted.<br />
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如果那块黄油被加热到150度,它就会融化。<br />
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Counterfactuals were first discussed by [[Nelson Goodman]] as a problem for the [[material conditional]] used in [[classical logic]]. Because of these problems, early work such as that of [[W.V. Quine]] held that counterfactuals aren't strictly logical, and do not make true or false claims about the world. However, in the 1970s, [[David Lewis (philosopher)|David Lewis]] showed that these problems are surmountable given an appropriate logical framework. Work since then in [[formal semantics (linguistics)|formal semantics]], [[philosophical logic]], [[philosophy of language]], and [[cognitive science]] has built on Lewis's insight, taking it in a variety of different directions.<ref name="Counterfactuals">{{cite encyclopedia |last1=Starr |first1=Will |editor-last1=Zalta |editor-first1=Edward N.|encyclopedia=The Stanford Encyclopedia of Philosophy|title=Counterfactuals|year=2019 |url=https://plato.stanford.edu/archives/fall2019/entries/counterfactuals}}</ref><br />
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If that piece of butter had been heated to 150º, it would not have melted.<br />
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如果那块黄油被加热到150度,它就不会融化。<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<br />
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更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
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====上下文依赖和含糊不清(Context dependence and vagueness)====<br />
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Counterfactuals are ''context dependent'' and ''[[vague]]''. For example, either of the following statements can be reasonably held true, though not at the same time:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<br />
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If Caesar had been in command in Korea, he would have used the atom bomb.<br />
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# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
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If Caesar had been in command in Korea, he would have used catapults.<br />
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# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
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====非单调性(Non-monotonicity)====<br />
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Counterfactuals are ''non-monotonic'' in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by ''[[Jordan Howard Sobel|Sobel sequences]]'' such as the following:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<br />
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If Hannah had drunk coffee, she would be happy.<br />
If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
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One way of formalizing this fact is to say that the principle of ''Antecedent Strengthening'' should '''not''' hold for any connective > intended as a formalization of natural language conditionals.<br />
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对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
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* '''Antecedent Strengthening''': <math> P > Q \models (P \land R) > Q </math><br />
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* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
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===考虑可能存在的世界Possible worlds accounts===<br />
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The most common logical accounts of counterfactuals are couched in the [[possible world semantics]]. Broadly speaking, these approaches have in common that they treat a counterfactual ''A'' > ''B'' as true if ''B'' holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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反事实的最常见的逻辑解释是可能世界语义学。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
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David Lewis's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.<br />
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大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,市场上有许多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
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====严格的条件Strict conditional====<br />
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The [[strict conditional]] analysis treats natural language counterfactuals as being equivalent to the [[modal logic]] formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as [[material conditional|material implication]]. This approach was first proposed in 1912 by [[C.I. Lewis]] as part of his [[Axiomatic system|axiomatic approach]] to modal logic.<ref name="Counterfactuals"/> In modern [[relational semantics]], this means that the strict conditional is true at ''w'' iff the corresponding material conditional is true throughout the worlds accessible from ''w''. More formally:<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
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* Given a model <math>M = \langle W,R,V \rangle</math>, we have that <math> M,w \models \Box(P \rightarrow Q) </math> iff <math>M, v \models P \rightarrow Q </math> for all <math>v</math> such that <math>Rwv</math><br />
* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
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Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.<br />
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与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活 "的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
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The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.<br />
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严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
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This fact led to widespread abandonment of the strict conditional, in particular in favor of Lewis's [[counterfactual conditional#Variably strict conditional|variably strict analysis]]. However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued that ''Sobel sequences'' don't demand a ''non-monotonic'' logic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as the sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. Warmbrōd's idea was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality.<br />
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这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
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Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of [[dynamic semantics]], and given a number of linguistic arguments in favor. One argument is that conditional antecedents license [[Polarity item#Determination of licensing contexts|negative polarity items]], which are thought to be licensed only by monotonic operators.<br />
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Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
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If Natalia leaves tomorrow, she will arrive on time.<br />
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# 如果Natalia明天离开,她会准时到达。<br />
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Another argument in favor of the strict conditional comes from [[Irene Heim|Irene Heim's]] observation that Sobel Sequences are generally [[Felicity (pragmatics)|infelicitous]] (i.e. sound strange) in reverse.<br />
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If Hannah had drunk coffee with gasoline in it, she would not be happy. But if she had drunk coffee, she would be happy.<br />
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# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
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Sarah Moss (2012) and Karen Lewis (2018) have responded to these arguments, showing that a version of the variably strict analysis can account for these patterns, and arguing that such an account is preferable since it can also account for apparent exceptions. As of 2020, this debate continues in the literature, with accounts such as Willer (2019) arguing that a strict conditional account can cover these exceptions as well.<ref name="Counterfactuals"/><br />
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Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
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====可变严格条件 Variably strict conditional====<br />
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In the variably strict approach, the semantics of a conditional ''A'' > ''B'' is given by some function on the relative closeness of worlds where A is true and B is true, on the one hand, and worlds where A is true but B is not, on the other.<br />
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在可变严格方法中,条件''A'' > ''B''的语义是由一些函数给出的,一方面是A为真、B为真的世界,另一方面是A为真、B为假的世界的相对接近程度。<br />
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On Lewis's account, A > C is (a) vacuously true if and only if there are no worlds where A is true (for example, if A is logically or metaphysically impossible); (b) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or (c) false otherwise. Although in Lewis's ''Counterfactuals'' it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did ''not'' intend the metric of 'closeness' to be simply our ordinary notion of [[Similarity (philosophy)#Respective and overall similarity|overall similarity]].<br />
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在刘易斯的论述中,A > C 是(a)空洞的真实,只有在没有A为真的世界时(例如,如果A在逻辑上或形而上学上是不可能的);(b)非空洞的真实,只有在A为真的世界中,一些C为真的世界比任何C不为真的世界更接近实际世界;或者(c)虚假,在其他世界里。尽管在刘易斯的《反事实》中,他对“接近性(closeness)”的意思并不清晰,但在后来的著作中,刘易斯明确表示,他并不打算将“接近性”的尺度简单地作为我们对整体相似性的普通概念。<br />
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Example:<br />
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:If he had eaten more at breakfast, he would not have been hungry at 11 am.<br />
例子:<br />
:如果他在早餐时吃多一点,他在上午11点就不会饿。<br />
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On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where he ate more for breakfast, there is at least one world where he is not hungry at 11 am and which is closer to our world than any world where he ate more for breakfast but is still hungry at 11 am.<br />
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根据刘易斯的说法,这个陈述的真理在于:在他早餐吃得更多的可能世界中,至少有一个他在上午11点不饿的世界比任何他早餐吃得更多但在上午11点仍然饿的世界更接近我们的世界。<br />
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In the past as modal approach, the denotation of the past tense is not fundamentally about time. Rather, it is an underspecified skeleton which can apply either to modal or temporal content. For instance, the particular past as modal proposal of Iatridou (2000), the past tense's core meaning is what's shown schematically below:<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker's account differs from Lewis's most notably in his acceptance of the ''limit'' and ''uniqueness assumptions''. The uniqueness assumption is the thesis that, for any antecedent A, among the possible worlds where A is true, there is a single (''unique'') one that is ''closest'' to the actual world. The limit assumption is the thesis that, for a given antecedent A, if there is a chain of possible worlds where A is true, each closer to the actual world than its predecessor, then the chain has a ''limit'': a possible world where A is true that is closer to the actual worlds than all worlds in the chain. (The uniqueness assumption [[logical consequence|entails]] the limit assumption, but the limit assumption does not entail the uniqueness assumption.) On Stalnaker's account, A > C is non-vacuously true if and only if, at the closest world where A is true, C is true. So, the above example is true just in case at the single, closest world where he ate more breakfast, he does not feel hungry at 11 am. Although it is controversial, Lewis rejected the limit assumption (and therefore the uniqueness assumption) because it rules out the possibility that there might be worlds that get closer and closer to the actual world without limit. For example, there might be an infinite series of worlds, each with a coffee cup a smaller fraction of an inch to the left of its actual position, but none of which is uniquely the closest. (See Lewis 1973: 20.)<br />
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Stalnaker的论述与Lewis的论述最明显的不同在于,他接受了“极限(limit)”和“唯一性假设(uniqueness assumptions)”。唯一性假设的论点是:对于任何前件A,在A为真的可能世界中,有一个最接近实际世界的单一(唯一)世界。极限假设的论点是,对于一个给定的前件A,如果存在一个A为真的可能世界链,每个世界都比它的前一个世界更接近实际世界,那么这个链就有一个极限:一个A为真的可能世界比这个链中的所有世界更接近实际世界。(唯一性假设包含了极限假设,但极限假设并不包含唯一性假设)。根据Stalnaker的观点,当且仅当在最接近A为真的世界中,C为真时,A>C才是非空洞的真。因此,上面的例子是真的,只是在他吃了更多早餐的唯一最接近的世界中,他在上午11点不觉得饿。虽然有争议,但Lewis拒绝了极限假设(因此也拒绝了唯一性假设),因为它排除了这样一种可能性,即可能存在着越来越接近实际世界的世界,而没有极限。例如,可能会有一系列无限的世界,每个世界的咖啡杯都在其实际位置的左边小几分之一英寸,但其中没有一个是唯一最接近的。(见Lewis 1973: 20)。<br />
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One consequence of Stalnaker's acceptance of the uniqueness assumption is that, if the [[law of excluded middle]] is true, then all instances of the formula (A > C) ∨ (A > ¬C) are true. The law of excluded middle is the thesis that for all propositions p, p ∨ ¬p is true. If the uniqueness assumption is true, then for every antecedent A, there is a uniquely closest world where A is true. If the law of excluded middle is true, any consequent C is either true or false at that world where A is true. So for every counterfactual A > C, either A > C or A > ¬C is true. This is called conditional excluded middle (CEM). Example:<br />
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Stalnaker接受唯一性假设的一个结果是,如果排除中间律是真的,那么公式(A>C)∨(A>¬C)的所有实例都是真的。排他性中间律的论题是:对于所有命题p,p∨¬p都是真的。如果唯一性假设为真,那么对于每一个前件A,都有一个唯一最接近的世界,其中A为真。如果排除中间法则是真的,任何结果C在A为真的那个世界里要么是真,要么是假。所以对于每一个反事实A>C,要么A>C,要么A>¬C为真。这就是所谓的条件排除中间法(CEM)。例子:<br />
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:(1) If the fair coin had been flipped, it would have landed heads.<br />
:(2) If the fair coin had been flipped, it would have landed tails (i.e. not heads).<br />
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:(1) 如果公平的硬币被抛出,它将会正面朝上。<br />
:(2) 如果公平的硬币被抛出,它将会反面朝上(即不是正面朝上)。<br />
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On Stalnaker's analysis, there is a closest world where the fair coin mentioned in (1) and (2) is flipped and at that world either it lands heads or it lands tails. So either (1) is true and (2) is false or (1) is false and (2) true. On Lewis's analysis, however, both (1) and (2) are false, for the worlds where the fair coin lands heads are no more or less close than the worlds where they land tails. For Lewis, "If the coin had been flipped, it would have landed heads or tails" is true, but this does not entail that "If the coin had been flipped, it would have landed heads, or: If the coin had been flipped it would have landed tails."<br />
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根据Stalnaker的分析,存在一个最接近的世界,在这个世界里,(1)和(2)中提到的公平的硬币被抛出,硬币要么正面朝上,要么反面朝上。因此,要么(1)是真,(2)是假,要么(1)是假,(2)是真。然而,根据Lewis的分析,(1)和(2)都是假的,因为公平的硬币正面朝上的世界并不比反面朝上的世界更接近或更远离。对Lewis来说,“如果硬币被抛出,它将正面朝上或反面朝上”是真的,但这并不意味着“如果硬币被抛出,它将落在正面”,或“如果硬币被抛出,它就会反面朝上”。<br />
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=== 其他考虑 Other accounts ===<br />
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====因果模型 Causal models====<br />
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The ''causal models framework'' analyzes counterfactuals in terms of systems of [[structural equation model|structural equations]]. In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence "''Y'' would be ''y'' had ''X'' been ''x''" (formally, ''X = x'' > ''Y = y'' ) is defined as the assertion: If we replace the equation currently determining ''X'' with a constant ''X = x'', and solve the set of equations for variable ''Y'', the solution obtained will be ''Y = y''. This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators. This approach was developed by [[Judea Pearl]] (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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''因果模型框架''从结构方程(structural equations)系统的角度分析反事实。在一个方程系统中,每个变量都被分配了一个值,这个值是系统中其他变量的显式函数。给定这样一个模型,“如果X是X,Y就会是Y(''Y'' would be ''y'' had ''X'' been ''x'')”这个句子 (形式上为 ''X = x'' > ''Y = y'' )被定义为断言。如果我们用一个常数''X = x''取代当前决定 ''X''的方程,并求解变量''Y''的方程组,得到的解将是''Y = y''。这个定义已被证明与可能世界语义学的公理兼容,并构成自然科学和社会科学中因果推理的基础。因为这些领域的每个结构方程都对应于一个熟悉的因果机制,这个因果机制可以被研究者进行有意义地推理。这种方法是由Judea Pearl(2000)提出的,作为编码关于因果关系的细粒度直觉的手段,这些直觉在其他提议的系统中难以捕捉。<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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====信念修正 Belief revision====<br />
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In the [[belief revision]] framework, counterfactuals are treated using a formal implementation of the ''Ramsey test''. In these systems, a counterfactual ''A'' > ''B'' holds if and only if the addition of ''A'' to the current body of knowledge has ''B'' as a consequence. This condition relates counterfactual conditionals to [[belief revision]], as the evaluation of ''A'' > ''B'' can be done by first revising the current knowledge with ''A'' and then checking whether ''B'' is true in what results. Revising is easy when ''A'' is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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在信念修正框架中,反事实是用 ''Ramsey检验''的形式化实现来处理的。在这些系统中,当且仅当在当前的知识体系添加 ''A''后得到的结果是B时,反事实''A'' > ''B''成立。这个条件将反事实条件与信念修正联系起来,因为对''A'' > ''B''的评价可以通过首先用''A''修正当前的知识,然后检查''B''在什么结果中是否为真。当''A''与当前的信念一致时,修正是很容易的,但在其他情况下可能会很难。每一个用于信念修正的语义都可以用于评价条件语句。反过来说,每一种评价条件语句的方法都可以被看作是一种执行修正的方法。<br />
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====Ginsberg====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of [[propositional formula]]e, considering the maximal sets of these formulae that are consistent with ''A'', and adding ''A'' to each. The rationale is that each of these maximal sets represents a possible state of belief in which ''A'' is true that is as similar as possible to the original one. The conditional statement ''A'' > ''B'' therefore holds if and only if ''B'' is true in all such sets.<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref><br />
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Ginsberg(1986)提出了一种条件句的语义,它假定当前的信念形成了一组命题公式,考虑这些公式中与''A''一致的最大集合,并在每个集合中加入''A''。其理由是,这些最大集合中的每一个都代表了一种可能的信念状态,在这种状态下,''A''为真,且与原始状态尽可能相似。因此,当且仅当''B''在所有这些集合中都为真时,条件陈述句''A'' > ''B''才成立。</div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22751反事实2021-05-31T07:22:42Z<p>Wei:/* Other accounts */</p>
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{{Short description|Conditionals that discuss what would have been if things were otherwise}}<br />
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{{Redirect|Counterfactual}}<br />
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'''Counterfactual conditionals''' (also ''subjunctive'' or ''X-marked'') are [[conditional sentence]]s which discuss what would have been true under different circumstances, e.g. <!-- this is example is from Iatridou (2000), ex (47c) on p. 244 --> "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with [[indicative conditionals|indicatives]], which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of [[Counterfactual conditional#Fake tense|fake tense morphology]], which some languages use in combination with other kinds of [[Morphology (linguistics)|morphology]] including [[Counterfactual conditional#Fake aspect|aspect]] and [[Counterfactual conditional#mood|mood]].<br />
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反事实条件句(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的条件句。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
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Counterfactuals are one of the most studied phenomena in [[philosophical logic]], [[formal semantics (natural language)|formal semantics]], and [[philosophy of language]]. They were first discussed as a problem for the [[material conditional]] analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic [[possible world]] approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as [[causal model]]s and [[dynamic semantics]]. Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是微不足道的真实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==Overview==<br />
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=== Examples ===<br />
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The difference between [[indicative conditional|indicative]] and counterfactual conditionals can be illustrated by the following [[minimal pair]]:<br />
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指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
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# '''Indicative Conditional''': If it ''is'' raining right now, then Sally ''is'' inside. <br />
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# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
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# '''Simple Past Counterfactual''': If it ''was raining'' <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally ''would be'' inside.<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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# '''一般过去时的反事实''':如果现在正在下雨,那么Sally就会在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "is" in both the "if" clause and the "then" clause. As a result, it conveys that the speaker is agnostic about whether it is raining. The counterfactual example uses the [[fake tense]] form "was" in the "if" clause and the [[modal verb|modal]] "would" in the "then" clause. As a result, it conveys that the speaker does not believe that it is raining.<br />
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这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
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English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the [[pluperfect|past perfect]] counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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# '''Past Perfect Counterfactual''': If it ''had been raining'' yesterday, then Sally ''would have been'' inside.<br />
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# '''过去完成时的反事实''':如果昨天下了雨,那么Sally就会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<br />
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另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<br />
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# '''Irrealis Counterfactual''': If it ''were raining'' right now, then Sally ''would be'' inside.<br />
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# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
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Past perfect and irrealis counterfactuals can undergo ''conditional inversion'':<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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# Were it raining, Sally would be inside.<br />
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# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
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# Had it rained, Sally would be inside.<br />
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# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
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=== Terminology ===<br />
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<!——鉴于术语上的巨大但往往是细微的差异,本节必须经过仔细的编辑。在点击“发布更改”之前,请考虑结果文本是否有助于读者理解这些术语是如何使用的。如果结果文本读起来像是“热狗是三明治的辩论吗?”删除所有字符提示后,请不要点击”发布更改”。特别是,请确保(1)明确区分事实主张和术语定义(2)记住,不同的来源可以以不同的方式使用单一术语(3)对术语的每个术语或用法进行不偏不倚的框架性解释。--><br />
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The term ''counterfactual conditional'' is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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The term counterfactual conditional is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<br />
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“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的先行词是假的或不可能的。<br />
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# '''Anderson Case''': If the patient had taken arsenic, he would have blue spots.<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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Anderson Case: If the patient had taken arsenic, he would have blue spots.<br />
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# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<br />
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Such conditionals are also widely referred to as ''subjunctive conditionals'', though this term is likewise acknowledged as a misnomer even by those who use it.<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref> Many languages do not have a morphological [[subjunctive]] (e.g. [[Danish grammar|Danish]] and [[Dutch grammar|Dutch]]) and many that do have it don’t use it for this sort of conditional (e.g. [[French grammar|French]], [[Swahili grammar|Swahili]], all [[Indo-Aryan languages]] that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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Such conditionals are also widely referred to as subjunctive conditionals, though this term is likewise acknowledged as a misnomer even by those who use it. Many languages do not have a morphological subjunctive (e.g. Danish and Dutch) and many that do have it don’t use it for this sort of conditional (e.g. French, Swahili, all Indo-Aryan languages that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<br />
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这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<br />
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The terms ''counterfactual'' and ''subjunctive'' have sometimes been repurposed for more specific uses. For instance, the term "counterfactual" is sometimes applied to conditionals that express a contrary-to-fact meaning, regardless of their grammatical structure.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" /> Along similar lines, the term "subjunctive" is sometimes used to refer to conditionals that bear fake past or irrealis marking, regardless of the meaning they convey.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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Recently the term X-Marked has been proposed as a replacement, evoking the extra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as O-Marked conditionals, reflecting their ordinary marking.<br />
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''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<br />
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最近有人提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为O-Marked条件语,反映了它们的普通标记。<br />
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Recently the term ''X-Marked'' has been proposed as a replacement, evoking the ''ex''tra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as ''O-Marked'' conditionals, reflecting their ''o''rdinary marking.<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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The ''antecedent'' of a conditional is sometimes referred to as its ''"if"-clause'' or ''protasis''. The ''consequent'' of a conditional is sometimes referred to as a ''"then"''-clause or as an apodosis.<br />
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一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
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==Logic and semantics==<br />
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===经典问题(Classic puzzles)===<br />
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====反事实的问题(The problem of counterfactuals)====<br />
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According to the material conditional analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated. <br />
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根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
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If that piece of butter had been heated to 150º, it would have melted.<br />
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如果那块黄油被加热到150度,它就会融化。<br />
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Counterfactuals were first discussed by [[Nelson Goodman]] as a problem for the [[material conditional]] used in [[classical logic]]. Because of these problems, early work such as that of [[W.V. Quine]] held that counterfactuals aren't strictly logical, and do not make true or false claims about the world. However, in the 1970s, [[David Lewis (philosopher)|David Lewis]] showed that these problems are surmountable given an appropriate logical framework. Work since then in [[formal semantics (linguistics)|formal semantics]], [[philosophical logic]], [[philosophy of language]], and [[cognitive science]] has built on Lewis's insight, taking it in a variety of different directions.<ref name="Counterfactuals">{{cite encyclopedia |last1=Starr |first1=Will |editor-last1=Zalta |editor-first1=Edward N.|encyclopedia=The Stanford Encyclopedia of Philosophy|title=Counterfactuals|year=2019 |url=https://plato.stanford.edu/archives/fall2019/entries/counterfactuals}}</ref><br />
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If that piece of butter had been heated to 150º, it would not have melted.<br />
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如果那块黄油被加热到150度,它就不会融化。<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<br />
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更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
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====上下文依赖和含糊不清(Context dependence and vagueness)====<br />
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Counterfactuals are ''context dependent'' and ''[[vague]]''. For example, either of the following statements can be reasonably held true, though not at the same time:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<br />
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If Caesar had been in command in Korea, he would have used the atom bomb.<br />
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# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
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If Caesar had been in command in Korea, he would have used catapults.<br />
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# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
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====非单调性(Non-monotonicity)====<br />
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Counterfactuals are ''non-monotonic'' in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by ''[[Jordan Howard Sobel|Sobel sequences]]'' such as the following:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<br />
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If Hannah had drunk coffee, she would be happy.<br />
If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
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One way of formalizing this fact is to say that the principle of ''Antecedent Strengthening'' should '''not''' hold for any connective > intended as a formalization of natural language conditionals.<br />
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对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
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* '''Antecedent Strengthening''': <math> P > Q \models (P \land R) > Q </math><br />
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* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
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===考虑可能存在的世界Possible worlds accounts===<br />
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The most common logical accounts of counterfactuals are couched in the [[possible world semantics]]. Broadly speaking, these approaches have in common that they treat a counterfactual ''A'' > ''B'' as true if ''B'' holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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反事实的最常见的逻辑解释是可能世界语义学。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
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David Lewis's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.<br />
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大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,市场上有许多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
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====严格的条件Strict conditional====<br />
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The [[strict conditional]] analysis treats natural language counterfactuals as being equivalent to the [[modal logic]] formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as [[material conditional|material implication]]. This approach was first proposed in 1912 by [[C.I. Lewis]] as part of his [[Axiomatic system|axiomatic approach]] to modal logic.<ref name="Counterfactuals"/> In modern [[relational semantics]], this means that the strict conditional is true at ''w'' iff the corresponding material conditional is true throughout the worlds accessible from ''w''. More formally:<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
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* Given a model <math>M = \langle W,R,V \rangle</math>, we have that <math> M,w \models \Box(P \rightarrow Q) </math> iff <math>M, v \models P \rightarrow Q </math> for all <math>v</math> such that <math>Rwv</math><br />
* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
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Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.<br />
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与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活 "的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
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The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.<br />
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严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
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This fact led to widespread abandonment of the strict conditional, in particular in favor of Lewis's [[counterfactual conditional#Variably strict conditional|variably strict analysis]]. However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued that ''Sobel sequences'' don't demand a ''non-monotonic'' logic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as the sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. Warmbrōd's idea was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality.<br />
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这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
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Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of [[dynamic semantics]], and given a number of linguistic arguments in favor. One argument is that conditional antecedents license [[Polarity item#Determination of licensing contexts|negative polarity items]], which are thought to be licensed only by monotonic operators.<br />
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Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
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If Natalia leaves tomorrow, she will arrive on time.<br />
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# 如果Natalia明天离开,她会准时到达。<br />
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Another argument in favor of the strict conditional comes from [[Irene Heim|Irene Heim's]] observation that Sobel Sequences are generally [[Felicity (pragmatics)|infelicitous]] (i.e. sound strange) in reverse.<br />
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If Hannah had drunk coffee with gasoline in it, she would not be happy. But if she had drunk coffee, she would be happy.<br />
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# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
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Sarah Moss (2012) and Karen Lewis (2018) have responded to these arguments, showing that a version of the variably strict analysis can account for these patterns, and arguing that such an account is preferable since it can also account for apparent exceptions. As of 2020, this debate continues in the literature, with accounts such as Willer (2019) arguing that a strict conditional account can cover these exceptions as well.<ref name="Counterfactuals"/><br />
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Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
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====可变严格条件 Variably strict conditional====<br />
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In the variably strict approach, the semantics of a conditional ''A'' > ''B'' is given by some function on the relative closeness of worlds where A is true and B is true, on the one hand, and worlds where A is true but B is not, on the other.<br />
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在可变严格方法中,条件''A'' > ''B''的语义是由一些函数给出的,一方面是A为真、B为真的世界,另一方面是A为真、B为假的世界的相对接近程度。<br />
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On Lewis's account, A > C is (a) vacuously true if and only if there are no worlds where A is true (for example, if A is logically or metaphysically impossible); (b) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or (c) false otherwise. Although in Lewis's ''Counterfactuals'' it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did ''not'' intend the metric of 'closeness' to be simply our ordinary notion of [[Similarity (philosophy)#Respective and overall similarity|overall similarity]].<br />
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在刘易斯的论述中,A > C 是(a)空洞的真实,只有在没有A为真的世界时(例如,如果A在逻辑上或形而上学上是不可能的);(b)非空洞的真实,只有在A为真的世界中,一些C为真的世界比任何C不为真的世界更接近实际世界;或者(c)虚假,在其他世界里。尽管在刘易斯的《反事实》中,他对“接近性(closeness)”的意思并不清晰,但在后来的著作中,刘易斯明确表示,他并不打算将“接近性”的尺度简单地作为我们对整体相似性的普通概念。<br />
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Example:<br />
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:If he had eaten more at breakfast, he would not have been hungry at 11 am.<br />
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:如果他在早餐时吃多一点,他在上午11点就不会饿。<br />
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On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where he ate more for breakfast, there is at least one world where he is not hungry at 11 am and which is closer to our world than any world where he ate more for breakfast but is still hungry at 11 am.<br />
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根据刘易斯的说法,这个陈述的真理在于:在他早餐吃得更多的可能世界中,至少有一个他在上午11点不饿的世界比任何他早餐吃得更多但在上午11点仍然饿的世界更接近我们的世界。<br />
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In the past as modal approach, the denotation of the past tense is not fundamentally about time. Rather, it is an underspecified skeleton which can apply either to modal or temporal content. For instance, the particular past as modal proposal of Iatridou (2000), the past tense's core meaning is what's shown schematically below:<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker's account differs from Lewis's most notably in his acceptance of the ''limit'' and ''uniqueness assumptions''. The uniqueness assumption is the thesis that, for any antecedent A, among the possible worlds where A is true, there is a single (''unique'') one that is ''closest'' to the actual world. The limit assumption is the thesis that, for a given antecedent A, if there is a chain of possible worlds where A is true, each closer to the actual world than its predecessor, then the chain has a ''limit'': a possible world where A is true that is closer to the actual worlds than all worlds in the chain. (The uniqueness assumption [[logical consequence|entails]] the limit assumption, but the limit assumption does not entail the uniqueness assumption.) On Stalnaker's account, A > C is non-vacuously true if and only if, at the closest world where A is true, C is true. So, the above example is true just in case at the single, closest world where he ate more breakfast, he does not feel hungry at 11 am. Although it is controversial, Lewis rejected the limit assumption (and therefore the uniqueness assumption) because it rules out the possibility that there might be worlds that get closer and closer to the actual world without limit. For example, there might be an infinite series of worlds, each with a coffee cup a smaller fraction of an inch to the left of its actual position, but none of which is uniquely the closest. (See Lewis 1973: 20.)<br />
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Stalnaker的论述与Lewis的论述最明显的不同在于,他接受了“极限(limit)”和“唯一性假设(uniqueness assumptions)”。唯一性假设的论点是:对于任何前件A,在A为真的可能世界中,有一个最接近实际世界的单一(唯一)世界。极限假设的论点是,对于一个给定的前件A,如果存在一个A为真的可能世界链,每个世界都比它的前一个世界更接近实际世界,那么这个链就有一个极限:一个A为真的可能世界比这个链中的所有世界更接近实际世界。(唯一性假设包含了极限假设,但极限假设并不包含唯一性假设)。根据Stalnaker的观点,当且仅当在最接近A为真的世界中,C为真时,A>C才是非空洞的真。因此,上面的例子是真的,只是在他吃了更多早餐的唯一最接近的世界中,他在上午11点不觉得饿。虽然有争议,但Lewis拒绝了极限假设(因此也拒绝了唯一性假设),因为它排除了这样一种可能性,即可能存在着越来越接近实际世界的世界,而没有极限。例如,可能会有一系列无限的世界,每个世界的咖啡杯都在其实际位置的左边小几分之一英寸,但其中没有一个是唯一最接近的。(见Lewis 1973: 20)。<br />
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One consequence of Stalnaker's acceptance of the uniqueness assumption is that, if the [[law of excluded middle]] is true, then all instances of the formula (A > C) ∨ (A > ¬C) are true. The law of excluded middle is the thesis that for all propositions p, p ∨ ¬p is true. If the uniqueness assumption is true, then for every antecedent A, there is a uniquely closest world where A is true. If the law of excluded middle is true, any consequent C is either true or false at that world where A is true. So for every counterfactual A > C, either A > C or A > ¬C is true. This is called conditional excluded middle (CEM). Example:<br />
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Stalnaker接受唯一性假设的一个结果是,如果排除中间律是真的,那么公式(A>C)∨(A>¬C)的所有实例都是真的。排他性中间律的论题是:对于所有命题p,p∨¬p都是真的。如果唯一性假设为真,那么对于每一个前件A,都有一个唯一最接近的世界,其中A为真。如果排除中间法则是真的,任何结果C在A为真的那个世界里要么是真,要么是假。所以对于每一个反事实A>C,要么A>C,要么A>¬C为真。这就是所谓的条件排除中间法(CEM)。例子:<br />
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:(1) If the fair coin had been flipped, it would have landed heads.<br />
:(2) If the fair coin had been flipped, it would have landed tails (i.e. not heads).<br />
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:(1) 如果公平的硬币被抛出,它将会正面朝上。<br />
:(2) 如果公平的硬币被抛出,它将会反面朝上(即不是正面朝上)。<br />
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On Stalnaker's analysis, there is a closest world where the fair coin mentioned in (1) and (2) is flipped and at that world either it lands heads or it lands tails. So either (1) is true and (2) is false or (1) is false and (2) true. On Lewis's analysis, however, both (1) and (2) are false, for the worlds where the fair coin lands heads are no more or less close than the worlds where they land tails. For Lewis, "If the coin had been flipped, it would have landed heads or tails" is true, but this does not entail that "If the coin had been flipped, it would have landed heads, or: If the coin had been flipped it would have landed tails."<br />
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根据Stalnaker的分析,存在一个最接近的世界,在这个世界里,(1)和(2)中提到的公平的硬币被抛出,硬币要么正面朝上,要么反面朝上。因此,要么(1)是真,(2)是假,要么(1)是假,(2)是真。然而,根据Lewis的分析,(1)和(2)都是假的,因为公平的硬币正面朝上的世界并不比反面朝上的世界更接近或更远离。对Lewis来说,“如果硬币被抛出,它将正面朝上或反面朝上”是真的,但这并不意味着“如果硬币被抛出,它将落在正面”,或“如果硬币被抛出,它就会反面朝上”。<br />
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=== 其他考虑 Other accounts ===<br />
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====因果模型 Causal models====<br />
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The ''causal models framework'' analyzes counterfactuals in terms of systems of [[structural equation model|structural equations]]. In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence "''Y'' would be ''y'' had ''X'' been ''x''" (formally, ''X = x'' > ''Y = y'' ) is defined as the assertion: If we replace the equation currently determining ''X'' with a constant ''X = x'', and solve the set of equations for variable ''Y'', the solution obtained will be ''Y = y''. This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators. This approach was developed by [[Judea Pearl]] (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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''因果模型框架''从结构方程(structural equations)系统的角度分析反事实。在一个方程系统中,每个变量都被分配了一个值,这个值是系统中其他变量的显式函数。给定这样一个模型,“如果X是X,Y就会是Y(''Y'' would be ''y'' had ''X'' been ''x'')”这个句子 (形式上为 ''X = x'' > ''Y = y'' )被定义为断言。如果我们用一个常数''X = x''取代当前决定 ''X''的方程,并求解变量''Y''的方程组,得到的解将是''Y = y''。这个定义已被证明与可能世界语义学的公理兼容,并构成自然科学和社会科学中因果推理的基础。因为这些领域的每个结构方程都对应于一个熟悉的因果机制,这个因果机制可以被研究者进行有意义地推理。这种方法是由Judea Pearl(2000)提出的,作为编码关于因果关系的细粒度直觉的手段,这些直觉在其他提议的系统中难以捕捉。<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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====信念修正 Belief revision====<br />
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In the [[belief revision]] framework, counterfactuals are treated using a formal implementation of the ''Ramsey test''. In these systems, a counterfactual ''A'' > ''B'' holds if and only if the addition of ''A'' to the current body of knowledge has ''B'' as a consequence. This condition relates counterfactual conditionals to [[belief revision]], as the evaluation of ''A'' > ''B'' can be done by first revising the current knowledge with ''A'' and then checking whether ''B'' is true in what results. Revising is easy when ''A'' is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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在信念修正框架中,反事实是用 ''Ramsey检验''的形式化实现来处理的。在这些系统中,当且仅当在当前的知识体系添加 ''A''后得到的结果是B时,反事实''A'' > ''B''成立。这个条件将反事实条件与信念修正联系起来,因为对''A'' > ''B''的评价可以通过首先用''A''修正当前的知识,然后检查''B''在什么结果中是否为真。当''A''与当前的信念一致时,修正是很容易的,但在其他情况下可能会很难。每一个用于信念修正的语义都可以用于评价条件语句。反过来说,每一种评价条件语句的方法都可以被看作是一种执行修正的方法。<br />
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====Ginsberg====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of [[propositional formula]]e, considering the maximal sets of these formulae that are consistent with ''A'', and adding ''A'' to each. The rationale is that each of these maximal sets represents a possible state of belief in which ''A'' is true that is as similar as possible to the original one. The conditional statement ''A'' > ''B'' therefore holds if and only if ''B'' is true in all such sets.<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref><br />
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Ginsberg(1986)提出了一种条件句的语义,它假定当前的信念形成了一组命题公式,考虑这些公式中与''A''一致的最大集合,并在每个集合中加入''A''。其理由是,这些最大集合中的每一个都代表了一种可能的信念状态,在这种状态下,''A''为真,且与原始状态尽可能相似。因此,当且仅当''B''在所有这些集合中都为真时,条件陈述句''A'' > ''B''才成立。<br />
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== The grammar of counterfactuality ==<br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual [[morphemes]], while others recruit morphemes which otherwise express [[grammatical tense|tense]], [[grammatical aspect|aspect]], [[grammatical mood|mood]], or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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=== Fake tense ===<br />
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==== Description ====<br />
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In many languages, counterfactuality is marked by [[past tense]] morphology.<ref name = "palmer">{{cite book |last=Palmer |first=Frank Robert |date=1986 |title=Mood and modality |publisher= Cambridge University Press}}</ref> Since these uses of the past tense do not convey their typical temporal meaning, they are called ''fake past'' or ''fake tense''.<ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref> English is one language which uses fake past to mark counterfactuality, as shown in the following [[minimal pair]].<ref>English fake past is sometimes erroneously referred to as "subjunctive", even though it is not the [[English subjunctive|subjunctive mood]].</ref> In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<ref name = palmer /><ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref><br />
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# Indicative: If Natalia '''leaves''' tomorrow, she '''will''' arrive on time.<br />
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# Counterfactual: If Natalia '''left''' tomorrow, she '''would''' arrive on time.<br />
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[[Hebrew language|Modern Hebrew]] is another language where counterfactuality is marked with a fake past morpheme:<ref name="karawani">{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><br />
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Category:Conditionals in linguistics<br />
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范畴: 语言学中的条件句<br />
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:: {| <br />
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Category:Grammar<br />
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分类: 语法<br />
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| || im || Dani || '''haya''' || ba-bayit || maχa ɾ || '''hayinu''' || mevakRim || oto<br />
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Category:Semantics<br />
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分类: 语义学<br />
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Category:Belief revision<br />
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类别: 信念修正<br />
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| || if || Dani || be.'''pst'''.3sm || in-home || tomorrow || be.'''pst'''.1pl || visit.ptc.pl || he.acc<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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Category:Linguistic modality<br />
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类别: 情态<br />
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<small>This page was moved from [[wikipedia:en:Counterfactual conditional]]. Its edit history can be viewed at [[反事实/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22720反事实2021-05-30T18:19:45Z<p>Wei:/* Variably strict conditional */</p>
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{{Short description|Conditionals that discuss what would have been if things were otherwise}}<br />
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{{Redirect|Counterfactual}}<br />
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'''Counterfactual conditionals''' (also ''subjunctive'' or ''X-marked'') are [[conditional sentence]]s which discuss what would have been true under different circumstances, e.g. <!-- this is example is from Iatridou (2000), ex (47c) on p. 244 --> "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with [[indicative conditionals|indicatives]], which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of [[Counterfactual conditional#Fake tense|fake tense morphology]], which some languages use in combination with other kinds of [[Morphology (linguistics)|morphology]] including [[Counterfactual conditional#Fake aspect|aspect]] and [[Counterfactual conditional#mood|mood]].<br />
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反事实条件句(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的条件句。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
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Counterfactuals are one of the most studied phenomena in [[philosophical logic]], [[formal semantics (natural language)|formal semantics]], and [[philosophy of language]]. They were first discussed as a problem for the [[material conditional]] analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic [[possible world]] approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as [[causal model]]s and [[dynamic semantics]]. Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是微不足道的真实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==Overview==<br />
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=== Examples ===<br />
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The difference between [[indicative conditional|indicative]] and counterfactual conditionals can be illustrated by the following [[minimal pair]]:<br />
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指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
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# '''Indicative Conditional''': If it ''is'' raining right now, then Sally ''is'' inside. <br />
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# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
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# '''Simple Past Counterfactual''': If it ''was raining'' <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally ''would be'' inside.<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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# '''一般过去时的反事实''':如果现在正在下雨,那么Sally就会在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "is" in both the "if" clause and the "then" clause. As a result, it conveys that the speaker is agnostic about whether it is raining. The counterfactual example uses the [[fake tense]] form "was" in the "if" clause and the [[modal verb|modal]] "would" in the "then" clause. As a result, it conveys that the speaker does not believe that it is raining.<br />
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这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
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English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the [[pluperfect|past perfect]] counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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# '''Past Perfect Counterfactual''': If it ''had been raining'' yesterday, then Sally ''would have been'' inside.<br />
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# '''过去完成时的反事实''':如果昨天下了雨,那么Sally就会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<br />
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另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<br />
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# '''Irrealis Counterfactual''': If it ''were raining'' right now, then Sally ''would be'' inside.<br />
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# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
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Past perfect and irrealis counterfactuals can undergo ''conditional inversion'':<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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# Were it raining, Sally would be inside.<br />
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# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
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# Had it rained, Sally would be inside.<br />
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# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
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=== Terminology ===<br />
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<!-- Given the vast but often subtle differences in terminology, this section has to be edited with a lot of care. Before clicking "publish changes", please consider whether the resulting text will help a reader understand how these terms are used. If the resulting text reads like a "is a hotdog a sandwich debate?" with all the character cues removed, please don't click "publish changes". In particular, please be sure to (1) clearly distinguish factual claims from definitions of terms (2) remember that different sources may use a single term in different ways (3) situate each term or usage of a term by giving a framework-neutral explanation of how it is used.--><br />
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<!——鉴于术语上的巨大但往往是细微的差异,本节必须经过仔细的编辑。在点击“发布更改”之前,请考虑结果文本是否有助于读者理解这些术语是如何使用的。如果结果文本读起来像是“热狗是三明治的辩论吗?”删除所有字符提示后,请不要点击”发布更改”。特别是,请确保(1)明确区分事实主张和术语定义(2)记住,不同的来源可以以不同的方式使用单一术语(3)对术语的每个术语或用法进行不偏不倚的框架性解释。--><br />
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The term ''counterfactual conditional'' is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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The term counterfactual conditional is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<br />
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“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的先行词是假的或不可能的。<br />
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# '''Anderson Case''': If the patient had taken arsenic, he would have blue spots.<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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Anderson Case: If the patient had taken arsenic, he would have blue spots.<br />
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# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<br />
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Such conditionals are also widely referred to as ''subjunctive conditionals'', though this term is likewise acknowledged as a misnomer even by those who use it.<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref> Many languages do not have a morphological [[subjunctive]] (e.g. [[Danish grammar|Danish]] and [[Dutch grammar|Dutch]]) and many that do have it don’t use it for this sort of conditional (e.g. [[French grammar|French]], [[Swahili grammar|Swahili]], all [[Indo-Aryan languages]] that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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Such conditionals are also widely referred to as subjunctive conditionals, though this term is likewise acknowledged as a misnomer even by those who use it. Many languages do not have a morphological subjunctive (e.g. Danish and Dutch) and many that do have it don’t use it for this sort of conditional (e.g. French, Swahili, all Indo-Aryan languages that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<br />
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这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<br />
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The terms ''counterfactual'' and ''subjunctive'' have sometimes been repurposed for more specific uses. For instance, the term "counterfactual" is sometimes applied to conditionals that express a contrary-to-fact meaning, regardless of their grammatical structure.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" /> Along similar lines, the term "subjunctive" is sometimes used to refer to conditionals that bear fake past or irrealis marking, regardless of the meaning they convey.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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Recently the term X-Marked has been proposed as a replacement, evoking the extra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as O-Marked conditionals, reflecting their ordinary marking.<br />
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''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<br />
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最近有人提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为O-Marked条件语,反映了它们的普通标记。<br />
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Recently the term ''X-Marked'' has been proposed as a replacement, evoking the ''ex''tra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as ''O-Marked'' conditionals, reflecting their ''o''rdinary marking.<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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The ''antecedent'' of a conditional is sometimes referred to as its ''"if"-clause'' or ''protasis''. The ''consequent'' of a conditional is sometimes referred to as a ''"then"''-clause or as an apodosis.<br />
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一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
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==Logic and semantics==<br />
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===经典问题(Classic puzzles)===<br />
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====反事实的问题(The problem of counterfactuals)====<br />
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According to the material conditional analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated. <br />
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根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
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If that piece of butter had been heated to 150º, it would have melted.<br />
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如果那块黄油被加热到150度,它就会融化。<br />
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Counterfactuals were first discussed by [[Nelson Goodman]] as a problem for the [[material conditional]] used in [[classical logic]]. Because of these problems, early work such as that of [[W.V. Quine]] held that counterfactuals aren't strictly logical, and do not make true or false claims about the world. However, in the 1970s, [[David Lewis (philosopher)|David Lewis]] showed that these problems are surmountable given an appropriate logical framework. Work since then in [[formal semantics (linguistics)|formal semantics]], [[philosophical logic]], [[philosophy of language]], and [[cognitive science]] has built on Lewis's insight, taking it in a variety of different directions.<ref name="Counterfactuals">{{cite encyclopedia |last1=Starr |first1=Will |editor-last1=Zalta |editor-first1=Edward N.|encyclopedia=The Stanford Encyclopedia of Philosophy|title=Counterfactuals|year=2019 |url=https://plato.stanford.edu/archives/fall2019/entries/counterfactuals}}</ref><br />
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If that piece of butter had been heated to 150º, it would not have melted.<br />
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如果那块黄油被加热到150度,它就不会融化。<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<br />
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更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
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====上下文依赖和含糊不清(Context dependence and vagueness)====<br />
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Counterfactuals are ''context dependent'' and ''[[vague]]''. For example, either of the following statements can be reasonably held true, though not at the same time:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<br />
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If Caesar had been in command in Korea, he would have used the atom bomb.<br />
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# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
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If Caesar had been in command in Korea, he would have used catapults.<br />
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# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
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====非单调性(Non-monotonicity)====<br />
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Counterfactuals are ''non-monotonic'' in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by ''[[Jordan Howard Sobel|Sobel sequences]]'' such as the following:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<br />
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If Hannah had drunk coffee, she would be happy.<br />
If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
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One way of formalizing this fact is to say that the principle of ''Antecedent Strengthening'' should '''not''' hold for any connective > intended as a formalization of natural language conditionals.<br />
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对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
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* '''Antecedent Strengthening''': <math> P > Q \models (P \land R) > Q </math><br />
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* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
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===考虑可能存在的世界Possible worlds accounts===<br />
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The most common logical accounts of counterfactuals are couched in the [[possible world semantics]]. Broadly speaking, these approaches have in common that they treat a counterfactual ''A'' > ''B'' as true if ''B'' holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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反事实的最常见的逻辑解释是可能世界语义学。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
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David Lewis's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.<br />
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大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,市场上有许多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
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====严格的条件Strict conditional====<br />
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The [[strict conditional]] analysis treats natural language counterfactuals as being equivalent to the [[modal logic]] formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as [[material conditional|material implication]]. This approach was first proposed in 1912 by [[C.I. Lewis]] as part of his [[Axiomatic system|axiomatic approach]] to modal logic.<ref name="Counterfactuals"/> In modern [[relational semantics]], this means that the strict conditional is true at ''w'' iff the corresponding material conditional is true throughout the worlds accessible from ''w''. More formally:<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
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* Given a model <math>M = \langle W,R,V \rangle</math>, we have that <math> M,w \models \Box(P \rightarrow Q) </math> iff <math>M, v \models P \rightarrow Q </math> for all <math>v</math> such that <math>Rwv</math><br />
* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
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Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.<br />
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与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活 "的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
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The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.<br />
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严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
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This fact led to widespread abandonment of the strict conditional, in particular in favor of Lewis's [[counterfactual conditional#Variably strict conditional|variably strict analysis]]. However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued that ''Sobel sequences'' don't demand a ''non-monotonic'' logic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as the sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. Warmbrōd's idea was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality.<br />
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这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
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Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of [[dynamic semantics]], and given a number of linguistic arguments in favor. One argument is that conditional antecedents license [[Polarity item#Determination of licensing contexts|negative polarity items]], which are thought to be licensed only by monotonic operators.<br />
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Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
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If Natalia leaves tomorrow, she will arrive on time.<br />
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# 如果Natalia明天离开,她会准时到达。<br />
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Another argument in favor of the strict conditional comes from [[Irene Heim|Irene Heim's]] observation that Sobel Sequences are generally [[Felicity (pragmatics)|infelicitous]] (i.e. sound strange) in reverse.<br />
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If Hannah had drunk coffee with gasoline in it, she would not be happy. But if she had drunk coffee, she would be happy.<br />
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# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
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Sarah Moss (2012) and Karen Lewis (2018) have responded to these arguments, showing that a version of the variably strict analysis can account for these patterns, and arguing that such an account is preferable since it can also account for apparent exceptions. As of 2020, this debate continues in the literature, with accounts such as Willer (2019) arguing that a strict conditional account can cover these exceptions as well.<ref name="Counterfactuals"/><br />
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Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
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====可变严格条件 Variably strict conditional====<br />
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In the variably strict approach, the semantics of a conditional ''A'' > ''B'' is given by some function on the relative closeness of worlds where A is true and B is true, on the one hand, and worlds where A is true but B is not, on the other.<br />
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在可变严格方法中,条件''A'' > ''B''的语义是由一些函数给出的,一方面是A为真、B为真的世界,另一方面是A为真、B为假的世界的相对接近程度。<br />
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On Lewis's account, A > C is (a) vacuously true if and only if there are no worlds where A is true (for example, if A is logically or metaphysically impossible); (b) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or (c) false otherwise. Although in Lewis's ''Counterfactuals'' it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did ''not'' intend the metric of 'closeness' to be simply our ordinary notion of [[Similarity (philosophy)#Respective and overall similarity|overall similarity]].<br />
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在刘易斯的论述中,A > C 是(a)空洞的真实,只有在没有A为真的世界时(例如,如果A在逻辑上或形而上学上是不可能的);(b)非空洞的真实,只有在A为真的世界中,一些C为真的世界比任何C不为真的世界更接近实际世界;或者(c)虚假,在其他世界里。尽管在刘易斯的《反事实》中,他对“接近性(closeness)”的意思并不清晰,但在后来的著作中,刘易斯明确表示,他并不打算将“接近性”的尺度简单地作为我们对整体相似性的普通概念。<br />
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Example:<br />
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:If he had eaten more at breakfast, he would not have been hungry at 11 am.<br />
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:如果他在早餐时吃多一点,他在上午11点就不会饿。<br />
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On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where he ate more for breakfast, there is at least one world where he is not hungry at 11 am and which is closer to our world than any world where he ate more for breakfast but is still hungry at 11 am.<br />
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根据刘易斯的说法,这个陈述的真理在于:在他早餐吃得更多的可能世界中,至少有一个他在上午11点不饿的世界比任何他早餐吃得更多但在上午11点仍然饿的世界更接近我们的世界。<br />
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In the past as modal approach, the denotation of the past tense is not fundamentally about time. Rather, it is an underspecified skeleton which can apply either to modal or temporal content. For instance, the particular past as modal proposal of Iatridou (2000), the past tense's core meaning is what's shown schematically below:<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker's account differs from Lewis's most notably in his acceptance of the ''limit'' and ''uniqueness assumptions''. The uniqueness assumption is the thesis that, for any antecedent A, among the possible worlds where A is true, there is a single (''unique'') one that is ''closest'' to the actual world. The limit assumption is the thesis that, for a given antecedent A, if there is a chain of possible worlds where A is true, each closer to the actual world than its predecessor, then the chain has a ''limit'': a possible world where A is true that is closer to the actual worlds than all worlds in the chain. (The uniqueness assumption [[logical consequence|entails]] the limit assumption, but the limit assumption does not entail the uniqueness assumption.) On Stalnaker's account, A > C is non-vacuously true if and only if, at the closest world where A is true, C is true. So, the above example is true just in case at the single, closest world where he ate more breakfast, he does not feel hungry at 11 am. Although it is controversial, Lewis rejected the limit assumption (and therefore the uniqueness assumption) because it rules out the possibility that there might be worlds that get closer and closer to the actual world without limit. For example, there might be an infinite series of worlds, each with a coffee cup a smaller fraction of an inch to the left of its actual position, but none of which is uniquely the closest. (See Lewis 1973: 20.)<br />
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Stalnaker的论述与Lewis的论述最明显的不同在于,他接受了“极限(limit)”和“唯一性假设(uniqueness assumptions)”。唯一性假设的论点是:对于任何前件A,在A为真的可能世界中,有一个最接近实际世界的单一(唯一)世界。极限假设的论点是,对于一个给定的前件A,如果存在一个A为真的可能世界链,每个世界都比它的前一个世界更接近实际世界,那么这个链就有一个极限:一个A为真的可能世界比这个链中的所有世界更接近实际世界。(唯一性假设包含了极限假设,但极限假设并不包含唯一性假设)。根据Stalnaker的观点,当且仅当在最接近A为真的世界中,C为真时,A>C才是非空洞的真。因此,上面的例子是真的,只是在他吃了更多早餐的唯一最接近的世界中,他在上午11点不觉得饿。虽然有争议,但Lewis拒绝了极限假设(因此也拒绝了唯一性假设),因为它排除了这样一种可能性,即可能存在着越来越接近实际世界的世界,而没有极限。例如,可能会有一系列无限的世界,每个世界的咖啡杯都在其实际位置的左边小几分之一英寸,但其中没有一个是唯一最接近的。(见Lewis 1973: 20)。<br />
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One consequence of Stalnaker's acceptance of the uniqueness assumption is that, if the [[law of excluded middle]] is true, then all instances of the formula (A > C) ∨ (A > ¬C) are true. The law of excluded middle is the thesis that for all propositions p, p ∨ ¬p is true. If the uniqueness assumption is true, then for every antecedent A, there is a uniquely closest world where A is true. If the law of excluded middle is true, any consequent C is either true or false at that world where A is true. So for every counterfactual A > C, either A > C or A > ¬C is true. This is called conditional excluded middle (CEM). Example:<br />
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Stalnaker接受唯一性假设的一个结果是,如果排除中间律是真的,那么公式(A>C)∨(A>¬C)的所有实例都是真的。排他性中间律的论题是:对于所有命题p,p∨¬p都是真的。如果唯一性假设为真,那么对于每一个前件A,都有一个唯一最接近的世界,其中A为真。如果排除中间法则是真的,任何结果C在A为真的那个世界里要么是真,要么是假。所以对于每一个反事实A>C,要么A>C,要么A>¬C为真。这就是所谓的条件排除中间法(CEM)。例子:<br />
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:(1) If the fair coin had been flipped, it would have landed heads.<br />
:(2) If the fair coin had been flipped, it would have landed tails (i.e. not heads).<br />
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:(1) 如果公平的硬币被抛出,它将会正面朝上。<br />
:(2) 如果公平的硬币被抛出,它将会反面朝上(即不是正面朝上)。<br />
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On Stalnaker's analysis, there is a closest world where the fair coin mentioned in (1) and (2) is flipped and at that world either it lands heads or it lands tails. So either (1) is true and (2) is false or (1) is false and (2) true. On Lewis's analysis, however, both (1) and (2) are false, for the worlds where the fair coin lands heads are no more or less close than the worlds where they land tails. For Lewis, "If the coin had been flipped, it would have landed heads or tails" is true, but this does not entail that "If the coin had been flipped, it would have landed heads, or: If the coin had been flipped it would have landed tails."<br />
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根据Stalnaker的分析,存在一个最接近的世界,在这个世界里,(1)和(2)中提到的公平的硬币被抛出,硬币要么正面朝上,要么反面朝上。因此,要么(1)是真,(2)是假,要么(1)是假,(2)是真。然而,根据Lewis的分析,(1)和(2)都是假的,因为公平的硬币正面朝上的世界并不比反面朝上的世界更接近或更远离。对Lewis来说,“如果硬币被抛出,它将正面朝上或反面朝上”是真的,但这并不意味着“如果硬币被抛出,它将落在正面”,或“如果硬币被抛出,它就会反面朝上”。<br />
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=== Other accounts ===<br />
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Fake aspect often accompanies fake tense in languages that mark aspect. In some languages (e.g. Modern Greek, Zulu, and the Romance languages) this fake aspect is imperfective. In other languages (e.g. Palestinian Arabic) it is perfective. However, in other languages including Russian and Polish, counterfactuals can have either perfective or imperfective aspect. In other experiments, participants were asked to read short stories that contained counterfactual conditionals, e.g., ‘If there had been roses in the flower shop then there would have been lilies’. Later in the story, they read sentences corresponding to the presupposed facts, e.g., ‘there were no roses and there were no lilies’. The counterfactual conditional primed them to read the sentence corresponding to the presupposed facts very rapidly; no such priming effect occurred for indicative conditionals. They spent different amounts of time 'updating' a story that contains a counterfactual conditional compared to one that contains factual information and focused on different parts of counterfactual conditionals.<br />
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在标记体的语言中,假体往往伴随着假时态。在某些语言中(例如:。现代希腊语、祖鲁语和罗曼语)这个虚构的部分是不完整的。用其他语言(例如:。巴勒斯坦阿拉伯语)这是完美的。然而,在包括俄语和波兰语在内的其他语言中,反事实可以是完成体或非完整体。在其他实验中,参与者被要求阅读包含反事实条件的短篇小说,例如,如果花店里有玫瑰,那么就会有百合花。在故事的后半部分,他们阅读与预设事实相对应的句子,例如,没有玫瑰,也没有百合。反事实条件让他们非常快速地阅读与预设事实相对应的句子; 指示性条件句则没有这样的启动效应。他们花了不同数量的时间更新一个包含反事实条件的故事,而不是一个包含事实信息的故事,并且关注不同部分的反事实条件句。<br />
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====Causal models====<br />
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Experiments have compared the inferences people make from counterfactual conditionals and indicative conditionals. Given a counterfactual conditional, e.g., 'If there had been a circle on the blackboard then there would have been a triangle', and the subsequent information 'in fact there was no triangle', participants make the modus tollens inference 'there was no circle' more often than they do from an indicative conditional. Given the counterfactual conditional and the subsequent information 'in fact there was a circle', participants make the modus ponens inference as often as they do from an indicative conditional. See counterfactual thinking.<br />
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实验比较了人们从反事实条件句和指示性条件句中得出的推论。给定一个反事实条件,例如,如果黑板上有一个圆,那么就会有一个三角形,并且随后的信息事实上没有三角形,参与者做这种推断的频率比他们从一个直陈条件推断的频率更高。考虑到反事实条件和随后的信息‘事实上存在一个循环’,参与者做这种推理的频率和他们从直陈条件推理的频率一样高。参见反事实思维。<br />
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{{Further|Causal model#Counterfactuals}}<br />
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{{Expand section|date=September 2020}}<br />
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Byrne argues that people construct mental representations that encompass two possibilities when they understand, and reason from, a counterfactual conditional, e.g., 'if Oswald had not shot Kennedy, then someone else would have'. They envisage the conjecture 'Oswald did not shoot Kennedy and someone else did' and they also think about the presupposed facts 'Oswald did shoot Kennedy and someone else did not'. According to the mental model theory of reasoning, they construct mental models of the alternative possibilities.<br />
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认为人们构建的心理表征包括两种可能性,一种是他们理解的反事实条件,另一种是推理,例如,如果 Oswald 没有射杀 Kennedy,那么其他人也会射杀 Kennedy。他们猜想肯尼迪不是奥斯瓦尔德杀的,而是别人杀的,他们还想到了预先假定的事实奥斯瓦尔德确实杀了肯尼迪,而别人没有。根据心理模型推理理论,他们构建了可选择可能性的心理模型。<br />
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The ''causal models framework'' analyzes counterfactuals in terms of systems of [[structural equation model|structural equations]]. In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence "''Y'' would be ''y'' had ''X'' been ''x''" (formally, ''X = x'' > ''Y = y'' ) is defined as the assertion: If we replace the equation currently determining ''X'' with a constant ''X = x'', and solve the set of equations for variable ''Y'', the solution obtained will be ''Y = y''. This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators. This approach was developed by [[Judea Pearl]] (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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====Belief revision====<br />
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{{Further|Belief revision#The Ramsey test}}<br />
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{{Expand section|date=September 2020}}<br />
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In the [[belief revision]] framework, counterfactuals are treated using a formal implementation of the ''Ramsey test''. In these systems, a counterfactual ''A'' > ''B'' holds if and only if the addition of ''A'' to the current body of knowledge has ''B'' as a consequence. This condition relates counterfactual conditionals to [[belief revision]], as the evaluation of ''A'' > ''B'' can be done by first revising the current knowledge with ''A'' and then checking whether ''B'' is true in what results. Revising is easy when ''A'' is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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====Ginsberg====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of [[propositional formula]]e, considering the maximal sets of these formulae that are consistent with ''A'', and adding ''A'' to each. The rationale is that each of these maximal sets represents a possible state of belief in which ''A'' is true that is as similar as possible to the original one. The conditional statement ''A'' > ''B'' therefore holds if and only if ''B'' is true in all such sets.<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref><br />
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== The grammar of counterfactuality ==<br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual [[morphemes]], while others recruit morphemes which otherwise express [[grammatical tense|tense]], [[grammatical aspect|aspect]], [[grammatical mood|mood]], or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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=== Fake tense ===<br />
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==== Description ====<br />
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In many languages, counterfactuality is marked by [[past tense]] morphology.<ref name = "palmer">{{cite book |last=Palmer |first=Frank Robert |date=1986 |title=Mood and modality |publisher= Cambridge University Press}}</ref> Since these uses of the past tense do not convey their typical temporal meaning, they are called ''fake past'' or ''fake tense''.<ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref> English is one language which uses fake past to mark counterfactuality, as shown in the following [[minimal pair]].<ref>English fake past is sometimes erroneously referred to as "subjunctive", even though it is not the [[English subjunctive|subjunctive mood]].</ref> In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<ref name = palmer /><ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref><br />
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# Indicative: If Natalia '''leaves''' tomorrow, she '''will''' arrive on time.<br />
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# Counterfactual: If Natalia '''left''' tomorrow, she '''would''' arrive on time.<br />
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[[Hebrew language|Modern Hebrew]] is another language where counterfactuality is marked with a fake past morpheme:<ref name="karawani">{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><br />
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Category:Conditionals in linguistics<br />
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范畴: 语言学中的条件句<br />
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Category:Grammar<br />
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分类: 语法<br />
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| || im || Dani || '''haya''' || ba-bayit || maχa ɾ || '''hayinu''' || mevakRim || oto<br />
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Category:Semantics<br />
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分类: 语义学<br />
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Category:Belief revision<br />
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类别: 信念修正<br />
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| || if || Dani || be.'''pst'''.3sm || in-home || tomorrow || be.'''pst'''.1pl || visit.ptc.pl || he.acc<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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Category:Linguistic modality<br />
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类别: 情态<br />
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<small>This page was moved from [[wikipedia:en:Counterfactual conditional]]. Its edit history can be viewed at [[反事实/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22719反事实2021-05-30T18:01:15Z<p>Wei:/* 严格的条件Strict conditional */</p>
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{{Short description|Conditionals that discuss what would have been if things were otherwise}}<br />
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{{Redirect|Counterfactual}}<br />
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'''Counterfactual conditionals''' (also ''subjunctive'' or ''X-marked'') are [[conditional sentence]]s which discuss what would have been true under different circumstances, e.g. <!-- this is example is from Iatridou (2000), ex (47c) on p. 244 --> "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with [[indicative conditionals|indicatives]], which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of [[Counterfactual conditional#Fake tense|fake tense morphology]], which some languages use in combination with other kinds of [[Morphology (linguistics)|morphology]] including [[Counterfactual conditional#Fake aspect|aspect]] and [[Counterfactual conditional#mood|mood]].<br />
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反事实条件句(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的条件句。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
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Counterfactuals are one of the most studied phenomena in [[philosophical logic]], [[formal semantics (natural language)|formal semantics]], and [[philosophy of language]]. They were first discussed as a problem for the [[material conditional]] analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic [[possible world]] approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as [[causal model]]s and [[dynamic semantics]]. Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是微不足道的真实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==Overview==<br />
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=== Examples ===<br />
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The difference between [[indicative conditional|indicative]] and counterfactual conditionals can be illustrated by the following [[minimal pair]]:<br />
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指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
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# '''Indicative Conditional''': If it ''is'' raining right now, then Sally ''is'' inside. <br />
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# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
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# '''Simple Past Counterfactual''': If it ''was raining'' <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally ''would be'' inside.<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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# '''一般过去时的反事实''':如果现在正在下雨,那么Sally就会在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "is" in both the "if" clause and the "then" clause. As a result, it conveys that the speaker is agnostic about whether it is raining. The counterfactual example uses the [[fake tense]] form "was" in the "if" clause and the [[modal verb|modal]] "would" in the "then" clause. As a result, it conveys that the speaker does not believe that it is raining.<br />
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这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
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English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the [[pluperfect|past perfect]] counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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# '''Past Perfect Counterfactual''': If it ''had been raining'' yesterday, then Sally ''would have been'' inside.<br />
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# '''过去完成时的反事实''':如果昨天下了雨,那么Sally就会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<br />
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另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<br />
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# '''Irrealis Counterfactual''': If it ''were raining'' right now, then Sally ''would be'' inside.<br />
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# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
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Past perfect and irrealis counterfactuals can undergo ''conditional inversion'':<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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# Were it raining, Sally would be inside.<br />
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# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
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# Had it rained, Sally would be inside.<br />
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# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
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=== Terminology ===<br />
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<!——鉴于术语上的巨大但往往是细微的差异,本节必须经过仔细的编辑。在点击“发布更改”之前,请考虑结果文本是否有助于读者理解这些术语是如何使用的。如果结果文本读起来像是“热狗是三明治的辩论吗?”删除所有字符提示后,请不要点击”发布更改”。特别是,请确保(1)明确区分事实主张和术语定义(2)记住,不同的来源可以以不同的方式使用单一术语(3)对术语的每个术语或用法进行不偏不倚的框架性解释。--><br />
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The term ''counterfactual conditional'' is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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The term counterfactual conditional is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<br />
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“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的先行词是假的或不可能的。<br />
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# '''Anderson Case''': If the patient had taken arsenic, he would have blue spots.<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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Anderson Case: If the patient had taken arsenic, he would have blue spots.<br />
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# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<br />
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Such conditionals are also widely referred to as ''subjunctive conditionals'', though this term is likewise acknowledged as a misnomer even by those who use it.<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref> Many languages do not have a morphological [[subjunctive]] (e.g. [[Danish grammar|Danish]] and [[Dutch grammar|Dutch]]) and many that do have it don’t use it for this sort of conditional (e.g. [[French grammar|French]], [[Swahili grammar|Swahili]], all [[Indo-Aryan languages]] that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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Such conditionals are also widely referred to as subjunctive conditionals, though this term is likewise acknowledged as a misnomer even by those who use it. Many languages do not have a morphological subjunctive (e.g. Danish and Dutch) and many that do have it don’t use it for this sort of conditional (e.g. French, Swahili, all Indo-Aryan languages that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<br />
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这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<br />
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The terms ''counterfactual'' and ''subjunctive'' have sometimes been repurposed for more specific uses. For instance, the term "counterfactual" is sometimes applied to conditionals that express a contrary-to-fact meaning, regardless of their grammatical structure.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" /> Along similar lines, the term "subjunctive" is sometimes used to refer to conditionals that bear fake past or irrealis marking, regardless of the meaning they convey.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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Recently the term X-Marked has been proposed as a replacement, evoking the extra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as O-Marked conditionals, reflecting their ordinary marking.<br />
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''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<br />
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最近有人提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为O-Marked条件语,反映了它们的普通标记。<br />
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Recently the term ''X-Marked'' has been proposed as a replacement, evoking the ''ex''tra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as ''O-Marked'' conditionals, reflecting their ''o''rdinary marking.<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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The ''antecedent'' of a conditional is sometimes referred to as its ''"if"-clause'' or ''protasis''. The ''consequent'' of a conditional is sometimes referred to as a ''"then"''-clause or as an apodosis.<br />
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一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
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==Logic and semantics==<br />
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===经典问题(Classic puzzles)===<br />
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====反事实的问题(The problem of counterfactuals)====<br />
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According to the material conditional analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated. <br />
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根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
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If that piece of butter had been heated to 150º, it would have melted.<br />
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如果那块黄油被加热到150度,它就会融化。<br />
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Counterfactuals were first discussed by [[Nelson Goodman]] as a problem for the [[material conditional]] used in [[classical logic]]. Because of these problems, early work such as that of [[W.V. Quine]] held that counterfactuals aren't strictly logical, and do not make true or false claims about the world. However, in the 1970s, [[David Lewis (philosopher)|David Lewis]] showed that these problems are surmountable given an appropriate logical framework. Work since then in [[formal semantics (linguistics)|formal semantics]], [[philosophical logic]], [[philosophy of language]], and [[cognitive science]] has built on Lewis's insight, taking it in a variety of different directions.<ref name="Counterfactuals">{{cite encyclopedia |last1=Starr |first1=Will |editor-last1=Zalta |editor-first1=Edward N.|encyclopedia=The Stanford Encyclopedia of Philosophy|title=Counterfactuals|year=2019 |url=https://plato.stanford.edu/archives/fall2019/entries/counterfactuals}}</ref><br />
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If that piece of butter had been heated to 150º, it would not have melted.<br />
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如果那块黄油被加热到150度,它就不会融化。<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<br />
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更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
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====上下文依赖和含糊不清(Context dependence and vagueness)====<br />
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Counterfactuals are ''context dependent'' and ''[[vague]]''. For example, either of the following statements can be reasonably held true, though not at the same time:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<br />
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If Caesar had been in command in Korea, he would have used the atom bomb.<br />
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# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
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If Caesar had been in command in Korea, he would have used catapults.<br />
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# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
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====非单调性(Non-monotonicity)====<br />
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Counterfactuals are ''non-monotonic'' in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by ''[[Jordan Howard Sobel|Sobel sequences]]'' such as the following:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<br />
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If Hannah had drunk coffee, she would be happy.<br />
If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
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One way of formalizing this fact is to say that the principle of ''Antecedent Strengthening'' should '''not''' hold for any connective > intended as a formalization of natural language conditionals.<br />
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对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
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* '''Antecedent Strengthening''': <math> P > Q \models (P \land R) > Q </math><br />
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* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
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===考虑可能存在的世界Possible worlds accounts===<br />
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The most common logical accounts of counterfactuals are couched in the [[possible world semantics]]. Broadly speaking, these approaches have in common that they treat a counterfactual ''A'' > ''B'' as true if ''B'' holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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反事实的最常见的逻辑解释是可能世界语义学。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
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David Lewis's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.<br />
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大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,市场上有许多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
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====严格的条件Strict conditional====<br />
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The [[strict conditional]] analysis treats natural language counterfactuals as being equivalent to the [[modal logic]] formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as [[material conditional|material implication]]. This approach was first proposed in 1912 by [[C.I. Lewis]] as part of his [[Axiomatic system|axiomatic approach]] to modal logic.<ref name="Counterfactuals"/> In modern [[relational semantics]], this means that the strict conditional is true at ''w'' iff the corresponding material conditional is true throughout the worlds accessible from ''w''. More formally:<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
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* Given a model <math>M = \langle W,R,V \rangle</math>, we have that <math> M,w \models \Box(P \rightarrow Q) </math> iff <math>M, v \models P \rightarrow Q </math> for all <math>v</math> such that <math>Rwv</math><br />
* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
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Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.<br />
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与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界<math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活 "的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
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The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.<br />
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严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
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This fact led to widespread abandonment of the strict conditional, in particular in favor of Lewis's [[counterfactual conditional#Variably strict conditional|variably strict analysis]]. However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued that ''Sobel sequences'' don't demand a ''non-monotonic'' logic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as the sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. Warmbrōd's idea was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality.<br />
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这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
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Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of [[dynamic semantics]], and given a number of linguistic arguments in favor. One argument is that conditional antecedents license [[Polarity item#Determination of licensing contexts|negative polarity items]], which are thought to be licensed only by monotonic operators.<br />
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Kai von Fintel(2001)、Thony Gillies(2007)和Malte Willer(2019)的后续工作在动态语义学的框架内将这一想法正式化,并给出了一些支持的语言学论据。其中一个论点是,条件前置词许可否定性词语,而这些词被认为只能由单调性运算符许可。<br />
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If Natalia leaves tomorrow, she will arrive on time.<br />
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# 如果Natalia明天离开,她会准时到达。<br />
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Another argument in favor of the strict conditional comes from [[Irene Heim|Irene Heim's]] observation that Sobel Sequences are generally [[Felicity (pragmatics)|infelicitous]] (i.e. sound strange) in reverse.<br />
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If Hannah had drunk coffee with gasoline in it, she would not be happy. But if she had drunk coffee, she would be happy.<br />
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# 如果Hannah喝了含有汽油的咖啡,她就不会高兴。但如果她喝了咖啡,她就会高兴。<br />
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Sarah Moss (2012) and Karen Lewis (2018) have responded to these arguments, showing that a version of the variably strict analysis can account for these patterns, and arguing that such an account is preferable since it can also account for apparent exceptions. As of 2020, this debate continues in the literature, with accounts such as Willer (2019) arguing that a strict conditional account can cover these exceptions as well.<ref name="Counterfactuals"/><br />
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Sarah Moss(2012)和Karen Lewis(2018)对这些论点做出了回应,表明一个版本的可变严格分析可以解释这些模式,并认为这样的解释是可取的,因为它也可以解释明显的例外情况。截至2020年,这一争论在文献中仍在继续,Willer(2019)等人认为,严格条件账户也可以涵盖这些例外情况。<br />
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====Variably strict conditional====<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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如果丹妮明天在家,我们就会去看他了<br />
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In the variably strict approach, the semantics of a conditional ''A'' > ''B'' is given by some function on the relative closeness of worlds where A is true and B is true, on the one hand, and worlds where A is true but B is not, on the other.<br />
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Palestinian Arabic is another:<br />
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巴勒斯坦阿拉伯语是另一个例子:<br />
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On Lewis's account, A > C is (a) vacuously true if and only if there are no worlds where A is true (for example, if A is logically or metaphysically impossible); (b) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or (c) false otherwise. Although in Lewis's ''Counterfactuals'' it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did ''not'' intend the metric of 'closeness' to be simply our ordinary notion of [[Similarity (philosophy)#Respective and overall similarity|overall similarity]].<br />
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Example:<br />
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In formal semantics and philosophical logic, fake past is regarded as a puzzle, since it is not obvious why so many unrelated languages would repurpose a tense morpheme to mark counterfactuality. Proposed solutions to this puzzle divide into two camps: past as modal and past as past. These approaches differ in whether or not they take the past tense's core meaning to be about time.<br />
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在形式语义学和哲学逻辑中,虚假的过去被认为是一个谜,因为不明显的是为什么这么多不相关的语言重新使用一个时态语素来标记反事实性。针对这一难题提出的解决办法分为两个阵营: 过去为模式和过去为过去。这些方法的不同之处在于它们是否将过去时的核心意思理解为与时间有关。<br />
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:If he had eaten more at breakfast, he would not have been hungry at 11 am.<br />
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On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where he ate more for breakfast, there is at least one world where he is not hungry at 11 am and which is closer to our world than any world where he ate more for breakfast but is still hungry at 11 am.<br />
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In the past as modal approach, the denotation of the past tense is not fundamentally about time. Rather, it is an underspecified skeleton which can apply either to modal or temporal content. For instance, the particular past as modal proposal of Iatridou (2000), the past tense's core meaning is what's shown schematically below:<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker's account differs from Lewis's most notably in his acceptance of the ''limit'' and ''uniqueness assumptions''. The uniqueness assumption is the thesis that, for any antecedent A, among the possible worlds where A is true, there is a single (''unique'') one that is ''closest'' to the actual world. The limit assumption is the thesis that, for a given antecedent A, if there is a chain of possible worlds where A is true, each closer to the actual world than its predecessor, then the chain has a ''limit'': a possible world where A is true that is closer to the actual worlds than all worlds in the chain. (The uniqueness assumption [[logical consequence|entails]] the limit assumption, but the limit assumption does not entail the uniqueness assumption.) On Stalnaker's account, A > C is non-vacuously true if and only if, at the closest world where A is true, C is true. So, the above example is true just in case at the single, closest world where he ate more breakfast, he does not feel hungry at 11 am. Although it is controversial, Lewis rejected the limit assumption (and therefore the uniqueness assumption) because it rules out the possibility that there might be worlds that get closer and closer to the actual world without limit. For example, there might be an infinite series of worlds, each with a coffee cup a smaller fraction of an inch to the left of its actual position, but none of which is uniquely the closest. (See Lewis 1973: 20.)<br />
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The topic x is not the contextually-provided x<br />
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主题 x 不是上下文提供的 x<br />
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One consequence of Stalnaker's acceptance of the uniqueness assumption is that, if the [[law of excluded middle]] is true, then all instances of the formula (A > C) ∨ (A > ¬C) are true. The law of excluded middle is the thesis that for all propositions p, p ∨ ¬p is true. If the uniqueness assumption is true, then for every antecedent A, there is a uniquely closest world where A is true. If the law of excluded middle is true, any consequent C is either true or false at that world where A is true. So for every counterfactual A > C, either A > C or A > ¬C is true. This is called conditional excluded middle (CEM). Example:<br />
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Depending on how this denotation composes, x can be a time interval or a possible world. When x is a time, the past tense will convey that the sentence is talking about non-current times, i.e. the past. When x is a world, it will convey that the sentence is talking about a potentially non-actual possibility. The latter is what allows for a counterfactual meaning.<br />
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根据这个指称的组成,x 可以是时间间隔,也可以是可能世界。当 x 是时间时,过去时态表示句子指的是非现在时间,也就是说,过去时态指的是非现在时间。过去。当 x 是一个世界时,它将传达出这个句子所指的是一种潜在的不真实的可能性。后者是允许反事实意义的东西。<br />
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:(1) If the fair coin had been flipped, it would have landed heads.<br />
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The past as past approach treats the past tense as having an inherently temporal denotation. On this approach, so-called fake tense isn't actually fake. It differs from "real" tense only in how it takes scope, i.e. which component of the sentence's meaning is shifted to an earlier time. When a sentence has "real" past marking, it discusses something that happened at an earlier time; when a sentence has so-called fake past marking, it discusses possibilities that were accessible at an earlier time but may no longer be.<br />
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过去时作为过去时的方法认为过去时具有内在的时间外延。在这种方法中,所谓的假时态实际上并不是假的。它与“真实”时态的区别仅在于它如何占据范围,即。句子的哪个部分的意思转移到了更早的时间。当一个句子有“真实的”过去标记时,它讨论的是发生在更早的时间的事情; 当一个句子有所谓的“假过去标记”时,它讨论的可能性在更早的时间是可以接受的,但可能不再是。<br />
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:(2) If the fair coin had been flipped, it would have landed tails (i.e. not heads).<br />
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On Stalnaker's analysis, there is a closest world where the fair coin mentioned in (1) and (2) is flipped and at that world either it lands heads or it lands tails. So either (1) is true and (2) is false or (1) is false and (2) true. On Lewis's analysis, however, both (1) and (2) are false, for the worlds where the fair coin lands heads are no more or less close than the worlds where they land tails. For Lewis, "If the coin had been flipped, it would have landed heads or tails" is true, but this does not entail that "If the coin had been flipped, it would have landed heads, or: If the coin had been flipped it would have landed tails."<br />
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=== Other accounts ===<br />
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Fake aspect often accompanies fake tense in languages that mark aspect. In some languages (e.g. Modern Greek, Zulu, and the Romance languages) this fake aspect is imperfective. In other languages (e.g. Palestinian Arabic) it is perfective. However, in other languages including Russian and Polish, counterfactuals can have either perfective or imperfective aspect. In other experiments, participants were asked to read short stories that contained counterfactual conditionals, e.g., ‘If there had been roses in the flower shop then there would have been lilies’. Later in the story, they read sentences corresponding to the presupposed facts, e.g., ‘there were no roses and there were no lilies’. The counterfactual conditional primed them to read the sentence corresponding to the presupposed facts very rapidly; no such priming effect occurred for indicative conditionals. They spent different amounts of time 'updating' a story that contains a counterfactual conditional compared to one that contains factual information and focused on different parts of counterfactual conditionals.<br />
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在标记体的语言中,假体往往伴随着假时态。在某些语言中(例如:。现代希腊语、祖鲁语和罗曼语)这个虚构的部分是不完整的。用其他语言(例如:。巴勒斯坦阿拉伯语)这是完美的。然而,在包括俄语和波兰语在内的其他语言中,反事实可以是完成体或非完整体。在其他实验中,参与者被要求阅读包含反事实条件的短篇小说,例如,如果花店里有玫瑰,那么就会有百合花。在故事的后半部分,他们阅读与预设事实相对应的句子,例如,没有玫瑰,也没有百合。反事实条件让他们非常快速地阅读与预设事实相对应的句子; 指示性条件句则没有这样的启动效应。他们花了不同数量的时间更新一个包含反事实条件的故事,而不是一个包含事实信息的故事,并且关注不同部分的反事实条件句。<br />
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====Causal models====<br />
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Experiments have compared the inferences people make from counterfactual conditionals and indicative conditionals. Given a counterfactual conditional, e.g., 'If there had been a circle on the blackboard then there would have been a triangle', and the subsequent information 'in fact there was no triangle', participants make the modus tollens inference 'there was no circle' more often than they do from an indicative conditional. Given the counterfactual conditional and the subsequent information 'in fact there was a circle', participants make the modus ponens inference as often as they do from an indicative conditional. See counterfactual thinking.<br />
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实验比较了人们从反事实条件句和指示性条件句中得出的推论。给定一个反事实条件,例如,如果黑板上有一个圆,那么就会有一个三角形,并且随后的信息事实上没有三角形,参与者做这种推断的频率比他们从一个直陈条件推断的频率更高。考虑到反事实条件和随后的信息‘事实上存在一个循环’,参与者做这种推理的频率和他们从直陈条件推理的频率一样高。参见反事实思维。<br />
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{{Further|Causal model#Counterfactuals}}<br />
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{{Expand section|date=September 2020}}<br />
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Byrne argues that people construct mental representations that encompass two possibilities when they understand, and reason from, a counterfactual conditional, e.g., 'if Oswald had not shot Kennedy, then someone else would have'. They envisage the conjecture 'Oswald did not shoot Kennedy and someone else did' and they also think about the presupposed facts 'Oswald did shoot Kennedy and someone else did not'. According to the mental model theory of reasoning, they construct mental models of the alternative possibilities.<br />
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认为人们构建的心理表征包括两种可能性,一种是他们理解的反事实条件,另一种是推理,例如,如果 Oswald 没有射杀 Kennedy,那么其他人也会射杀 Kennedy。他们猜想肯尼迪不是奥斯瓦尔德杀的,而是别人杀的,他们还想到了预先假定的事实奥斯瓦尔德确实杀了肯尼迪,而别人没有。根据心理模型推理理论,他们构建了可选择可能性的心理模型。<br />
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The ''causal models framework'' analyzes counterfactuals in terms of systems of [[structural equation model|structural equations]]. In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence "''Y'' would be ''y'' had ''X'' been ''x''" (formally, ''X = x'' > ''Y = y'' ) is defined as the assertion: If we replace the equation currently determining ''X'' with a constant ''X = x'', and solve the set of equations for variable ''Y'', the solution obtained will be ''Y = y''. This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators. This approach was developed by [[Judea Pearl]] (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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====Belief revision====<br />
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{{Further|Belief revision#The Ramsey test}}<br />
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{{Expand section|date=September 2020}}<br />
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In the [[belief revision]] framework, counterfactuals are treated using a formal implementation of the ''Ramsey test''. In these systems, a counterfactual ''A'' > ''B'' holds if and only if the addition of ''A'' to the current body of knowledge has ''B'' as a consequence. This condition relates counterfactual conditionals to [[belief revision]], as the evaluation of ''A'' > ''B'' can be done by first revising the current knowledge with ''A'' and then checking whether ''B'' is true in what results. Revising is easy when ''A'' is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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====Ginsberg====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of [[propositional formula]]e, considering the maximal sets of these formulae that are consistent with ''A'', and adding ''A'' to each. The rationale is that each of these maximal sets represents a possible state of belief in which ''A'' is true that is as similar as possible to the original one. The conditional statement ''A'' > ''B'' therefore holds if and only if ''B'' is true in all such sets.<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref><br />
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== The grammar of counterfactuality ==<br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual [[morphemes]], while others recruit morphemes which otherwise express [[grammatical tense|tense]], [[grammatical aspect|aspect]], [[grammatical mood|mood]], or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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=== Fake tense ===<br />
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==== Description ====<br />
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In many languages, counterfactuality is marked by [[past tense]] morphology.<ref name = "palmer">{{cite book |last=Palmer |first=Frank Robert |date=1986 |title=Mood and modality |publisher= Cambridge University Press}}</ref> Since these uses of the past tense do not convey their typical temporal meaning, they are called ''fake past'' or ''fake tense''.<ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref> English is one language which uses fake past to mark counterfactuality, as shown in the following [[minimal pair]].<ref>English fake past is sometimes erroneously referred to as "subjunctive", even though it is not the [[English subjunctive|subjunctive mood]].</ref> In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<ref name = palmer /><ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref><br />
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# Indicative: If Natalia '''leaves''' tomorrow, she '''will''' arrive on time.<br />
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# Counterfactual: If Natalia '''left''' tomorrow, she '''would''' arrive on time.<br />
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[[Hebrew language|Modern Hebrew]] is another language where counterfactuality is marked with a fake past morpheme:<ref name="karawani">{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><br />
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Category:Conditionals in linguistics<br />
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范畴: 语言学中的条件句<br />
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:: {| <br />
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Category:Grammar<br />
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分类: 语法<br />
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| || im || Dani || '''haya''' || ba-bayit || maχa ɾ || '''hayinu''' || mevakRim || oto<br />
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Category:Semantics<br />
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分类: 语义学<br />
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Category:Belief revision<br />
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类别: 信念修正<br />
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| || if || Dani || be.'''pst'''.3sm || in-home || tomorrow || be.'''pst'''.1pl || visit.ptc.pl || he.acc<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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Category:Linguistic modality<br />
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类别: 情态<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Counterfactual conditional]]. Its edit history can be viewed at [[反事实/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22718反事实2021-05-30T17:41:09Z<p>Wei:/* 逻辑和语义 */</p>
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{{Short description|Conditionals that discuss what would have been if things were otherwise}}<br />
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{{Redirect|Counterfactual}}<br />
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'''Counterfactual conditionals''' (also ''subjunctive'' or ''X-marked'') are [[conditional sentence]]s which discuss what would have been true under different circumstances, e.g. <!-- this is example is from Iatridou (2000), ex (47c) on p. 244 --> "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with [[indicative conditionals|indicatives]], which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of [[Counterfactual conditional#Fake tense|fake tense morphology]], which some languages use in combination with other kinds of [[Morphology (linguistics)|morphology]] including [[Counterfactual conditional#Fake aspect|aspect]] and [[Counterfactual conditional#mood|mood]].<br />
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反事实条件句(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的条件句。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
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Counterfactuals are one of the most studied phenomena in [[philosophical logic]], [[formal semantics (natural language)|formal semantics]], and [[philosophy of language]]. They were first discussed as a problem for the [[material conditional]] analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic [[possible world]] approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as [[causal model]]s and [[dynamic semantics]]. Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是微不足道的真实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==Overview==<br />
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=== Examples ===<br />
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The difference between [[indicative conditional|indicative]] and counterfactual conditionals can be illustrated by the following [[minimal pair]]:<br />
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指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
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# '''Indicative Conditional''': If it ''is'' raining right now, then Sally ''is'' inside. <br />
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# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
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# '''Simple Past Counterfactual''': If it ''was raining'' <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally ''would be'' inside.<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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# '''一般过去时的反事实''':如果现在正在下雨,那么Sally就会在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "is" in both the "if" clause and the "then" clause. As a result, it conveys that the speaker is agnostic about whether it is raining. The counterfactual example uses the [[fake tense]] form "was" in the "if" clause and the [[modal verb|modal]] "would" in the "then" clause. As a result, it conveys that the speaker does not believe that it is raining.<br />
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这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
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English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the [[pluperfect|past perfect]] counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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# '''Past Perfect Counterfactual''': If it ''had been raining'' yesterday, then Sally ''would have been'' inside.<br />
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# '''过去完成时的反事实''':如果昨天下了雨,那么Sally就会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<br />
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另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<br />
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# '''Irrealis Counterfactual''': If it ''were raining'' right now, then Sally ''would be'' inside.<br />
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# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
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Past perfect and irrealis counterfactuals can undergo ''conditional inversion'':<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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# Were it raining, Sally would be inside.<br />
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# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
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# Had it rained, Sally would be inside.<br />
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# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
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=== Terminology ===<br />
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The term ''counterfactual conditional'' is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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The term counterfactual conditional is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<br />
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“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的先行词是假的或不可能的。<br />
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# '''Anderson Case''': If the patient had taken arsenic, he would have blue spots.<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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Anderson Case: If the patient had taken arsenic, he would have blue spots.<br />
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# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<br />
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Such conditionals are also widely referred to as ''subjunctive conditionals'', though this term is likewise acknowledged as a misnomer even by those who use it.<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref> Many languages do not have a morphological [[subjunctive]] (e.g. [[Danish grammar|Danish]] and [[Dutch grammar|Dutch]]) and many that do have it don’t use it for this sort of conditional (e.g. [[French grammar|French]], [[Swahili grammar|Swahili]], all [[Indo-Aryan languages]] that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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Such conditionals are also widely referred to as subjunctive conditionals, though this term is likewise acknowledged as a misnomer even by those who use it. Many languages do not have a morphological subjunctive (e.g. Danish and Dutch) and many that do have it don’t use it for this sort of conditional (e.g. French, Swahili, all Indo-Aryan languages that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<br />
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这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<br />
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The terms ''counterfactual'' and ''subjunctive'' have sometimes been repurposed for more specific uses. For instance, the term "counterfactual" is sometimes applied to conditionals that express a contrary-to-fact meaning, regardless of their grammatical structure.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" /> Along similar lines, the term "subjunctive" is sometimes used to refer to conditionals that bear fake past or irrealis marking, regardless of the meaning they convey.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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Recently the term X-Marked has been proposed as a replacement, evoking the extra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as O-Marked conditionals, reflecting their ordinary marking.<br />
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''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<br />
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最近有人提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为O-Marked条件语,反映了它们的普通标记。<br />
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Recently the term ''X-Marked'' has been proposed as a replacement, evoking the ''ex''tra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as ''O-Marked'' conditionals, reflecting their ''o''rdinary marking.<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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The ''antecedent'' of a conditional is sometimes referred to as its ''"if"-clause'' or ''protasis''. The ''consequent'' of a conditional is sometimes referred to as a ''"then"''-clause or as an apodosis.<br />
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一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
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==Logic and semantics==<br />
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===经典问题(Classic puzzles)===<br />
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====反事实的问题(The problem of counterfactuals)====<br />
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According to the material conditional analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated. <br />
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根据实质条件的分析,自然语言条件句即“如果p,那么q(if P then Q)”的陈述,只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下,用下面的一对例子来说明这一点。<br />
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If that piece of butter had been heated to 150º, it would have melted.<br />
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如果那块黄油被加热到150度,它就会融化。<br />
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Counterfactuals were first discussed by [[Nelson Goodman]] as a problem for the [[material conditional]] used in [[classical logic]]. Because of these problems, early work such as that of [[W.V. Quine]] held that counterfactuals aren't strictly logical, and do not make true or false claims about the world. However, in the 1970s, [[David Lewis (philosopher)|David Lewis]] showed that these problems are surmountable given an appropriate logical framework. Work since then in [[formal semantics (linguistics)|formal semantics]], [[philosophical logic]], [[philosophy of language]], and [[cognitive science]] has built on Lewis's insight, taking it in a variety of different directions.<ref name="Counterfactuals">{{cite encyclopedia |last1=Starr |first1=Will |editor-last1=Zalta |editor-first1=Edward N.|encyclopedia=The Stanford Encyclopedia of Philosophy|title=Counterfactuals|year=2019 |url=https://plato.stanford.edu/archives/fall2019/entries/counterfactuals}}</ref><br />
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If that piece of butter had been heated to 150º, it would not have melted.<br />
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如果那块黄油被加热到150度,它就不会融化。<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<br />
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更一般地说,这些例子表明反事实不具备真理功能。换句话说,知道前件和结果是否为真并不足以确定反事实本身是否为真。<br />
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====上下文依赖和含糊不清(Context dependence and vagueness)====<br />
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Counterfactuals are ''context dependent'' and ''[[vague]]''. For example, either of the following statements can be reasonably held true, though not at the same time:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
反事实是依赖于上下文且含糊不清的。例如,以下任一陈述都可以合理地成立,但不能同时成立:<br />
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If Caesar had been in command in Korea, he would have used the atom bomb.<br />
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# 如果凯撒(Caesar)当时在朝鲜指挥,他会使用原子弹。<br />
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If Caesar had been in command in Korea, he would have used catapults.<br />
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# 如果凯撒在朝鲜指挥,他会使用弹弓。<br />
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====非单调性(Non-monotonicity)====<br />
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Counterfactuals are ''non-monotonic'' in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by ''[[Jordan Howard Sobel|Sobel sequences]]'' such as the following:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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反事实是非单调的,因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明,例如:<br />
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If Hannah had drunk coffee, she would be happy.<br />
If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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# 如果汉娜喝了咖啡,她会很高兴。<br />
# 如果汉娜喝了咖啡,而且咖啡里有汽油,她会很伤心。<br />
# 如果汉娜喝了咖啡,咖啡里有汽油,而汉娜是一个喝汽油的机器人,她会很高兴。<br />
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One way of formalizing this fact is to say that the principle of ''Antecedent Strengthening'' should '''not''' hold for any connective > intended as a formalization of natural language conditionals.<br />
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对此事实进行形式化的一种方法是说,''前件增强(Antecedent Strengthening)''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。<br />
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* '''Antecedent Strengthening''': <math> P > Q \models (P \land R) > Q </math><br />
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* '''前件增强''': <math> P > Q \models (P \land R) > Q </math><br />
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===考虑可能存在的世界Possible worlds accounts===<br />
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The most common logical accounts of counterfactuals are couched in the [[possible world semantics]]. Broadly speaking, these approaches have in common that they treat a counterfactual ''A'' > ''B'' as true if ''B'' holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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反事实的最常见的逻辑解释是可能世界语义学。一般来说,这些方法的共同点是,如果B在A成立的某些可能世界中成立,那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。<br />
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David Lewis's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.<br />
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大卫·刘易斯(David Lewis)严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策(Angelika Kratzer)提出的紧密相关的前提语义常常被视为语言学中的标准。然而,市场上有许多可能世界的方法,包括最初被Lewis摒弃的严格条件分析的动态变体。<br />
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====严格的条件Strict conditional====<br />
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The [[strict conditional]] analysis treats natural language counterfactuals as being equivalent to the [[modal logic]] formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as [[material conditional|material implication]]. This approach was first proposed in 1912 by [[C.I. Lewis]] as part of his [[Axiomatic system|axiomatic approach]] to modal logic.<ref name="Counterfactuals"/> In modern [[relational semantics]], this means that the strict conditional is true at ''w'' iff the corresponding material conditional is true throughout the worlds accessible from ''w''. More formally:<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中, <math>\Box</math>表示必要性,<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的,作为他对模态逻辑的公理化方法的一部分。<br />
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* Given a model <math>M = \langle W,R,V \rangle</math>, we have that <math> M,w \models \Box(P \rightarrow Q) </math> iff <math>M, v \models P \rightarrow Q </math> for all <math>v</math> such that <math>Rwv</math><br />
* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>, 当且仅当<math>M, v \models P \rightarrow Q </math> ,我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。<br />
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Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.<br />
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与实质条件不同,严格条件在其前件为假时严格为真。要知道为什么,请观察,如果有一些可能世界math>v</math>,其中<math>P</math>为真,<math>Q</math>为假,那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的,至少在给定关系语义(或类似的东西)时是如此。在关系框架中,可及性关系是评价的参数,它编码了在上下文中被视为 "活 "的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系,所以严格条件的这一特征可以用来捕捉上下文的依赖性。<br />
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The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.<br />
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严格条件分析遇到了许多已知的问题,特别是单调性。在经典的关系框架中,当使用标准的蕴涵概念时,严格条件是单调的,也就是说,它验证了''前件增强''。要知道为什么,观察一下,如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此,我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。<br />
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This fact led to widespread abandonment of the strict conditional, in particular in favor of Lewis's [[counterfactual conditional#Variably strict conditional|variably strict analysis]]. However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued that ''Sobel sequences'' don't demand a ''non-monotonic'' logic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as the sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. Warmbrōd's idea was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality.<br />
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这一事实导致了对严格条件的广泛放弃,特别是支持刘易斯的可变严格分析。然而,随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd(1981)开创的,他认为''Sobel序列'' 并不要求非单调逻辑,而事实上,随着序列的进行,说话人可以切换到更宽松的可及性关系来解释。在他的系统中,像“如果Hannah喝了咖啡,她会很高兴”这样的反事实,通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡,而咖啡里有汽油……”的话语,这个第二个条件就会被认为是微不足道的真实,因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是,说话人将转向一个具有更宽松的可及性关系的模型,以避免这种琐碎性。<br />
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Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of [[dynamic semantics]], and given a number of linguistic arguments in favor. One argument is that conditional antecedents license [[Polarity item#Determination of licensing contexts|negative polarity items]], which are thought to be licensed only by monotonic operators.<br />
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Indicative: If Natalia leaves tomorrow, she will arrive on time.<br />
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如果娜塔莉亚明天离开,她会准时到达。<br />
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# If Hannah had drunk any coffee, she would be happy.<br />
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Counterfactual: If Natalia left tomorrow, she would arrive on time.<br />
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反事实: 如果娜塔莉亚明天离开,她会准时到达。<br />
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Another argument in favor of the strict conditional comes from [[Irene Heim|Irene Heim's]] observation that Sobel Sequences are generally [[Felicity (pragmatics)|infelicitous]] (i.e. sound strange) in reverse.<br />
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Modern Hebrew is another language where counterfactuality is marked with a fake past morpheme:<br />
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现代希伯来语是另一种用假的过去语素标记反事实性的语言:<br />
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# If Hannah had drunk coffee with gasoline in it, she would not be happy. But if she had drunk coffee, she would be happy.<br />
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| || im || Dani || haya || ba-bayit || maχa ɾ || hayinu || mevakRim || oto<br />
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Sarah Moss (2012) and Karen Lewis (2018) have responded to these arguments, showing that a version of the variably strict analysis can account for these patterns, and arguing that such an account is preferable since it can also account for apparent exceptions. As of 2020, this debate continues in the literature, with accounts such as Willer (2019) arguing that a strict conditional account can cover these exceptions as well.<ref name="Counterfactuals"/><br />
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| || if || Dani || be.pst.3sm || in-home || tomorrow || be.pst.1pl || visit.ptc.pl || he.acc<br />
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如果达尼在家里,明天,在家里,在家里,在家里,在家里<br />
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====Variably strict conditional====<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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如果丹妮明天在家,我们就会去看他了<br />
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In the variably strict approach, the semantics of a conditional ''A'' > ''B'' is given by some function on the relative closeness of worlds where A is true and B is true, on the one hand, and worlds where A is true but B is not, on the other.<br />
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Palestinian Arabic is another:<br />
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巴勒斯坦阿拉伯语是另一个例子:<br />
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On Lewis's account, A > C is (a) vacuously true if and only if there are no worlds where A is true (for example, if A is logically or metaphysically impossible); (b) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or (c) false otherwise. Although in Lewis's ''Counterfactuals'' it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did ''not'' intend the metric of 'closeness' to be simply our ordinary notion of [[Similarity (philosophy)#Respective and overall similarity|overall similarity]].<br />
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Example:<br />
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In formal semantics and philosophical logic, fake past is regarded as a puzzle, since it is not obvious why so many unrelated languages would repurpose a tense morpheme to mark counterfactuality. Proposed solutions to this puzzle divide into two camps: past as modal and past as past. These approaches differ in whether or not they take the past tense's core meaning to be about time.<br />
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在形式语义学和哲学逻辑中,虚假的过去被认为是一个谜,因为不明显的是为什么这么多不相关的语言重新使用一个时态语素来标记反事实性。针对这一难题提出的解决办法分为两个阵营: 过去为模式和过去为过去。这些方法的不同之处在于它们是否将过去时的核心意思理解为与时间有关。<br />
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:If he had eaten more at breakfast, he would not have been hungry at 11 am.<br />
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On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where he ate more for breakfast, there is at least one world where he is not hungry at 11 am and which is closer to our world than any world where he ate more for breakfast but is still hungry at 11 am.<br />
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In the past as modal approach, the denotation of the past tense is not fundamentally about time. Rather, it is an underspecified skeleton which can apply either to modal or temporal content. For instance, the particular past as modal proposal of Iatridou (2000), the past tense's core meaning is what's shown schematically below:<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker's account differs from Lewis's most notably in his acceptance of the ''limit'' and ''uniqueness assumptions''. The uniqueness assumption is the thesis that, for any antecedent A, among the possible worlds where A is true, there is a single (''unique'') one that is ''closest'' to the actual world. The limit assumption is the thesis that, for a given antecedent A, if there is a chain of possible worlds where A is true, each closer to the actual world than its predecessor, then the chain has a ''limit'': a possible world where A is true that is closer to the actual worlds than all worlds in the chain. (The uniqueness assumption [[logical consequence|entails]] the limit assumption, but the limit assumption does not entail the uniqueness assumption.) On Stalnaker's account, A > C is non-vacuously true if and only if, at the closest world where A is true, C is true. So, the above example is true just in case at the single, closest world where he ate more breakfast, he does not feel hungry at 11 am. Although it is controversial, Lewis rejected the limit assumption (and therefore the uniqueness assumption) because it rules out the possibility that there might be worlds that get closer and closer to the actual world without limit. For example, there might be an infinite series of worlds, each with a coffee cup a smaller fraction of an inch to the left of its actual position, but none of which is uniquely the closest. (See Lewis 1973: 20.)<br />
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The topic x is not the contextually-provided x<br />
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主题 x 不是上下文提供的 x<br />
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One consequence of Stalnaker's acceptance of the uniqueness assumption is that, if the [[law of excluded middle]] is true, then all instances of the formula (A > C) ∨ (A > ¬C) are true. The law of excluded middle is the thesis that for all propositions p, p ∨ ¬p is true. If the uniqueness assumption is true, then for every antecedent A, there is a uniquely closest world where A is true. If the law of excluded middle is true, any consequent C is either true or false at that world where A is true. So for every counterfactual A > C, either A > C or A > ¬C is true. This is called conditional excluded middle (CEM). Example:<br />
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Depending on how this denotation composes, x can be a time interval or a possible world. When x is a time, the past tense will convey that the sentence is talking about non-current times, i.e. the past. When x is a world, it will convey that the sentence is talking about a potentially non-actual possibility. The latter is what allows for a counterfactual meaning.<br />
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根据这个指称的组成,x 可以是时间间隔,也可以是可能世界。当 x 是时间时,过去时态表示句子指的是非现在时间,也就是说,过去时态指的是非现在时间。过去。当 x 是一个世界时,它将传达出这个句子所指的是一种潜在的不真实的可能性。后者是允许反事实意义的东西。<br />
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:(1) If the fair coin had been flipped, it would have landed heads.<br />
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The past as past approach treats the past tense as having an inherently temporal denotation. On this approach, so-called fake tense isn't actually fake. It differs from "real" tense only in how it takes scope, i.e. which component of the sentence's meaning is shifted to an earlier time. When a sentence has "real" past marking, it discusses something that happened at an earlier time; when a sentence has so-called fake past marking, it discusses possibilities that were accessible at an earlier time but may no longer be.<br />
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过去时作为过去时的方法认为过去时具有内在的时间外延。在这种方法中,所谓的假时态实际上并不是假的。它与“真实”时态的区别仅在于它如何占据范围,即。句子的哪个部分的意思转移到了更早的时间。当一个句子有“真实的”过去标记时,它讨论的是发生在更早的时间的事情; 当一个句子有所谓的“假过去标记”时,它讨论的可能性在更早的时间是可以接受的,但可能不再是。<br />
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:(2) If the fair coin had been flipped, it would have landed tails (i.e. not heads).<br />
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On Stalnaker's analysis, there is a closest world where the fair coin mentioned in (1) and (2) is flipped and at that world either it lands heads or it lands tails. So either (1) is true and (2) is false or (1) is false and (2) true. On Lewis's analysis, however, both (1) and (2) are false, for the worlds where the fair coin lands heads are no more or less close than the worlds where they land tails. For Lewis, "If the coin had been flipped, it would have landed heads or tails" is true, but this does not entail that "If the coin had been flipped, it would have landed heads, or: If the coin had been flipped it would have landed tails."<br />
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=== Other accounts ===<br />
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Fake aspect often accompanies fake tense in languages that mark aspect. In some languages (e.g. Modern Greek, Zulu, and the Romance languages) this fake aspect is imperfective. In other languages (e.g. Palestinian Arabic) it is perfective. However, in other languages including Russian and Polish, counterfactuals can have either perfective or imperfective aspect. In other experiments, participants were asked to read short stories that contained counterfactual conditionals, e.g., ‘If there had been roses in the flower shop then there would have been lilies’. Later in the story, they read sentences corresponding to the presupposed facts, e.g., ‘there were no roses and there were no lilies’. The counterfactual conditional primed them to read the sentence corresponding to the presupposed facts very rapidly; no such priming effect occurred for indicative conditionals. They spent different amounts of time 'updating' a story that contains a counterfactual conditional compared to one that contains factual information and focused on different parts of counterfactual conditionals.<br />
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在标记体的语言中,假体往往伴随着假时态。在某些语言中(例如:。现代希腊语、祖鲁语和罗曼语)这个虚构的部分是不完整的。用其他语言(例如:。巴勒斯坦阿拉伯语)这是完美的。然而,在包括俄语和波兰语在内的其他语言中,反事实可以是完成体或非完整体。在其他实验中,参与者被要求阅读包含反事实条件的短篇小说,例如,如果花店里有玫瑰,那么就会有百合花。在故事的后半部分,他们阅读与预设事实相对应的句子,例如,没有玫瑰,也没有百合。反事实条件让他们非常快速地阅读与预设事实相对应的句子; 指示性条件句则没有这样的启动效应。他们花了不同数量的时间更新一个包含反事实条件的故事,而不是一个包含事实信息的故事,并且关注不同部分的反事实条件句。<br />
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====Causal models====<br />
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Experiments have compared the inferences people make from counterfactual conditionals and indicative conditionals. Given a counterfactual conditional, e.g., 'If there had been a circle on the blackboard then there would have been a triangle', and the subsequent information 'in fact there was no triangle', participants make the modus tollens inference 'there was no circle' more often than they do from an indicative conditional. Given the counterfactual conditional and the subsequent information 'in fact there was a circle', participants make the modus ponens inference as often as they do from an indicative conditional. See counterfactual thinking.<br />
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实验比较了人们从反事实条件句和指示性条件句中得出的推论。给定一个反事实条件,例如,如果黑板上有一个圆,那么就会有一个三角形,并且随后的信息事实上没有三角形,参与者做这种推断的频率比他们从一个直陈条件推断的频率更高。考虑到反事实条件和随后的信息‘事实上存在一个循环’,参与者做这种推理的频率和他们从直陈条件推理的频率一样高。参见反事实思维。<br />
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{{Further|Causal model#Counterfactuals}}<br />
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{{Expand section|date=September 2020}}<br />
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Byrne argues that people construct mental representations that encompass two possibilities when they understand, and reason from, a counterfactual conditional, e.g., 'if Oswald had not shot Kennedy, then someone else would have'. They envisage the conjecture 'Oswald did not shoot Kennedy and someone else did' and they also think about the presupposed facts 'Oswald did shoot Kennedy and someone else did not'. According to the mental model theory of reasoning, they construct mental models of the alternative possibilities.<br />
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认为人们构建的心理表征包括两种可能性,一种是他们理解的反事实条件,另一种是推理,例如,如果 Oswald 没有射杀 Kennedy,那么其他人也会射杀 Kennedy。他们猜想肯尼迪不是奥斯瓦尔德杀的,而是别人杀的,他们还想到了预先假定的事实奥斯瓦尔德确实杀了肯尼迪,而别人没有。根据心理模型推理理论,他们构建了可选择可能性的心理模型。<br />
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The ''causal models framework'' analyzes counterfactuals in terms of systems of [[structural equation model|structural equations]]. In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence "''Y'' would be ''y'' had ''X'' been ''x''" (formally, ''X = x'' > ''Y = y'' ) is defined as the assertion: If we replace the equation currently determining ''X'' with a constant ''X = x'', and solve the set of equations for variable ''Y'', the solution obtained will be ''Y = y''. This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators. This approach was developed by [[Judea Pearl]] (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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====Belief revision====<br />
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{{Further|Belief revision#The Ramsey test}}<br />
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{{Expand section|date=September 2020}}<br />
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In the [[belief revision]] framework, counterfactuals are treated using a formal implementation of the ''Ramsey test''. In these systems, a counterfactual ''A'' > ''B'' holds if and only if the addition of ''A'' to the current body of knowledge has ''B'' as a consequence. This condition relates counterfactual conditionals to [[belief revision]], as the evaluation of ''A'' > ''B'' can be done by first revising the current knowledge with ''A'' and then checking whether ''B'' is true in what results. Revising is easy when ''A'' is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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====Ginsberg====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of [[propositional formula]]e, considering the maximal sets of these formulae that are consistent with ''A'', and adding ''A'' to each. The rationale is that each of these maximal sets represents a possible state of belief in which ''A'' is true that is as similar as possible to the original one. The conditional statement ''A'' > ''B'' therefore holds if and only if ''B'' is true in all such sets.<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref><br />
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== The grammar of counterfactuality ==<br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual [[morphemes]], while others recruit morphemes which otherwise express [[grammatical tense|tense]], [[grammatical aspect|aspect]], [[grammatical mood|mood]], or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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=== Fake tense ===<br />
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==== Description ====<br />
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In many languages, counterfactuality is marked by [[past tense]] morphology.<ref name = "palmer">{{cite book |last=Palmer |first=Frank Robert |date=1986 |title=Mood and modality |publisher= Cambridge University Press}}</ref> Since these uses of the past tense do not convey their typical temporal meaning, they are called ''fake past'' or ''fake tense''.<ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref> English is one language which uses fake past to mark counterfactuality, as shown in the following [[minimal pair]].<ref>English fake past is sometimes erroneously referred to as "subjunctive", even though it is not the [[English subjunctive|subjunctive mood]].</ref> In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<ref name = palmer /><ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref><br />
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# Indicative: If Natalia '''leaves''' tomorrow, she '''will''' arrive on time.<br />
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# Counterfactual: If Natalia '''left''' tomorrow, she '''would''' arrive on time.<br />
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[[Hebrew language|Modern Hebrew]] is another language where counterfactuality is marked with a fake past morpheme:<ref name="karawani">{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><br />
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Category:Conditionals in linguistics<br />
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范畴: 语言学中的条件句<br />
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Category:Grammar<br />
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分类: 语法<br />
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| || im || Dani || '''haya''' || ba-bayit || maχa ɾ || '''hayinu''' || mevakRim || oto<br />
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Category:Semantics<br />
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分类: 语义学<br />
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Category:Belief revision<br />
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类别: 信念修正<br />
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| || if || Dani || be.'''pst'''.3sm || in-home || tomorrow || be.'''pst'''.1pl || visit.ptc.pl || he.acc<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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Category:Linguistic modality<br />
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类别: 情态<br />
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<small>This page was moved from [[wikipedia:en:Counterfactual conditional]]. Its edit history can be viewed at [[反事实/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22717反事实2021-05-30T16:38:18Z<p>Wei:/* Terminology */</p>
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{{Short description|Conditionals that discuss what would have been if things were otherwise}}<br />
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{{Redirect|Counterfactual}}<br />
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'''Counterfactual conditionals''' (also ''subjunctive'' or ''X-marked'') are [[conditional sentence]]s which discuss what would have been true under different circumstances, e.g. <!-- this is example is from Iatridou (2000), ex (47c) on p. 244 --> "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with [[indicative conditionals|indicatives]], which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of [[Counterfactual conditional#Fake tense|fake tense morphology]], which some languages use in combination with other kinds of [[Morphology (linguistics)|morphology]] including [[Counterfactual conditional#Fake aspect|aspect]] and [[Counterfactual conditional#mood|mood]].<br />
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反事实条件句(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的条件句。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
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Counterfactuals are one of the most studied phenomena in [[philosophical logic]], [[formal semantics (natural language)|formal semantics]], and [[philosophy of language]]. They were first discussed as a problem for the [[material conditional]] analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic [[possible world]] approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as [[causal model]]s and [[dynamic semantics]]. Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是微不足道的真实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==Overview==<br />
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=== Examples ===<br />
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The difference between [[indicative conditional|indicative]] and counterfactual conditionals can be illustrated by the following [[minimal pair]]:<br />
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指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
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# '''Indicative Conditional''': If it ''is'' raining right now, then Sally ''is'' inside. <br />
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# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
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# '''Simple Past Counterfactual''': If it ''was raining'' <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally ''would be'' inside.<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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# '''一般过去时的反事实''':如果现在正在下雨,那么Sally就会在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "is" in both the "if" clause and the "then" clause. As a result, it conveys that the speaker is agnostic about whether it is raining. The counterfactual example uses the [[fake tense]] form "was" in the "if" clause and the [[modal verb|modal]] "would" in the "then" clause. As a result, it conveys that the speaker does not believe that it is raining.<br />
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这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
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English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the [[pluperfect|past perfect]] counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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# '''Past Perfect Counterfactual''': If it ''had been raining'' yesterday, then Sally ''would have been'' inside.<br />
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# '''过去完成时的反事实''':如果昨天下了雨,那么Sally就会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<br />
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另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<br />
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# '''Irrealis Counterfactual''': If it ''were raining'' right now, then Sally ''would be'' inside.<br />
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# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
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Past perfect and irrealis counterfactuals can undergo ''conditional inversion'':<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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# Were it raining, Sally would be inside.<br />
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# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
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# Had it rained, Sally would be inside.<br />
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# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
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=== Terminology ===<br />
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<!-- Given the vast but often subtle differences in terminology, this section has to be edited with a lot of care. Before clicking "publish changes", please consider whether the resulting text will help a reader understand how these terms are used. If the resulting text reads like a "is a hotdog a sandwich debate?" with all the character cues removed, please don't click "publish changes". In particular, please be sure to (1) clearly distinguish factual claims from definitions of terms (2) remember that different sources may use a single term in different ways (3) situate each term or usage of a term by giving a framework-neutral explanation of how it is used.--><br />
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<!——鉴于术语上的巨大但往往是细微的差异,本节必须经过仔细的编辑。在点击“发布更改”之前,请考虑结果文本是否有助于读者理解这些术语是如何使用的。如果结果文本读起来像是“热狗是三明治的辩论吗?”删除所有字符提示后,请不要点击”发布更改”。特别是,请确保(1)明确区分事实主张和术语定义(2)记住,不同的来源可以以不同的方式使用单一术语(3)对术语的每个术语或用法进行不偏不倚的框架性解释。--><br />
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The term ''counterfactual conditional'' is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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The term counterfactual conditional is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<br />
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“反事实条件(counterfactual conditional)”这一术语被广泛用作上述各类句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,被称为“ Anderson 案例”的经典例子具有反事实条件的典型语法形式,但是并不表明它的先行词是假的或不可能的。<br />
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# '''Anderson Case''': If the patient had taken arsenic, he would have blue spots.<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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Anderson Case: If the patient had taken arsenic, he would have blue spots.<br />
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# '''Anderson案例''':如果病人服用了砒霜,他会长出蓝斑(If the patient had taken arsenic, he would have blue spots)。<br />
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Such conditionals are also widely referred to as ''subjunctive conditionals'', though this term is likewise acknowledged as a misnomer even by those who use it.<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref> Many languages do not have a morphological [[subjunctive]] (e.g. [[Danish grammar|Danish]] and [[Dutch grammar|Dutch]]) and many that do have it don’t use it for this sort of conditional (e.g. [[French grammar|French]], [[Swahili grammar|Swahili]], all [[Indo-Aryan languages]] that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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Such conditionals are also widely referred to as subjunctive conditionals, though this term is likewise acknowledged as a misnomer even by those who use it. Many languages do not have a morphological subjunctive (e.g. Danish and Dutch) and many that do have it don’t use it for this sort of conditional (e.g. French, Swahili, all Indo-Aryan languages that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<br />
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这种条件句也被广泛地称为''虚拟条件句(subjunctive conditionals)'',尽管这个术语同样被使用者认为是用词不当<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref>。许多语言都没有虚拟语气(如丹麦语和荷兰语),许多有从句的语言也不把它用于这种条件句(如法语、斯瓦希里语、所有有从句的印度-雅利安语)。此外,只有将虚拟语气用于此类条件的语言才具有特定的过去虚拟语气形式。因此,虚拟标记既不是必要的,也不是充分的。<br />
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The terms ''counterfactual'' and ''subjunctive'' have sometimes been repurposed for more specific uses. For instance, the term "counterfactual" is sometimes applied to conditionals that express a contrary-to-fact meaning, regardless of their grammatical structure.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" /> Along similar lines, the term "subjunctive" is sometimes used to refer to conditionals that bear fake past or irrealis marking, regardless of the meaning they convey.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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Recently the term X-Marked has been proposed as a replacement, evoking the extra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as O-Marked conditionals, reflecting their ordinary marking.<br />
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''反事实(counterfactual)'' and ''从句(subjunctive)''这两个术语有时被重新用于更具体的用途。例如,不管其语法结构如何,"反事实"这个术语有时被用于表达与事实相反的意思的条件语<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" />。按照类似的思路,不管其表达的意思如何,"从句"这个术语有时被用于指带有虚拟过去或非现实标记的条件语。<br />
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最近有人提出用术语 X-Marked这个词来替代,以概括这些条件语所带有的额外标记。采用这个术语的人把指示性条件语称为O-Marked条件语,反映了它们的普通标记。<br />
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Recently the term ''X-Marked'' has been proposed as a replacement, evoking the ''ex''tra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as ''O-Marked'' conditionals, reflecting their ''o''rdinary marking.<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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The ''antecedent'' of a conditional is sometimes referred to as its ''"if"-clause'' or ''protasis''. The ''consequent'' of a conditional is sometimes referred to as a ''"then"''-clause or as an apodosis.<br />
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一个条件的 ''前件(antecedent)''有时被称为 "如果"从句或条件子句。条件的结果有时被称为"那么"子句或结论子句。<br />
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==Logic and semantics==<br />
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According to the material conditional analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated. <br />
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根据实质条件的分析,自然语言条件句---- 形式为如果 p 那么 q 的陈述---- 只要其先行词 p 为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是真空的。古德曼用下面的一对来说明这一点,在这个背景下,我们知道正在讨论的那块黄油并没有被加热。<br />
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If that piece of butter had been heated to 150º, it would have melted.<br />
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如果那块黄油被加热到150度,它就会融化。<br />
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Counterfactuals were first discussed by [[Nelson Goodman]] as a problem for the [[material conditional]] used in [[classical logic]]. Because of these problems, early work such as that of [[W.V. Quine]] held that counterfactuals aren't strictly logical, and do not make true or false claims about the world. However, in the 1970s, [[David Lewis (philosopher)|David Lewis]] showed that these problems are surmountable given an appropriate logical framework. Work since then in [[formal semantics (linguistics)|formal semantics]], [[philosophical logic]], [[philosophy of language]], and [[cognitive science]] has built on Lewis's insight, taking it in a variety of different directions.<ref name="Counterfactuals">{{cite encyclopedia |last1=Starr |first1=Will |editor-last1=Zalta |editor-first1=Edward N.|encyclopedia=The Stanford Encyclopedia of Philosophy|title=Counterfactuals|year=2019 |url=https://plato.stanford.edu/archives/fall2019/entries/counterfactuals}}</ref><br />
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If that piece of butter had been heated to 150º, it would not have melted.<br />
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如果那块黄油被加热到150度,它就不会融化。<br />
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===Classic puzzles===<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<br />
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更一般地说,这些例子表明反事实并不是真理功能的。换句话说,知道先行词和结果是否真实并不足以确定反事实本身是否真实。<br />
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====The problem of counterfactuals====<br />
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If Caesar had been in command in Korea, he would have used the atom bomb.<br />
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如果凯撒当时在朝鲜指挥,他会使用原子弹。<br />
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If Caesar had been in command in Korea, he would have used catapults.<br />
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如果凯撒在朝鲜指挥,他会使用投石器。<br />
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According to the [[material conditional]] analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated.<ref name="jstor.org">Goodman, N., "[https://www.jstor.org/stable/2019988 The Problem of Counterfactual Conditionals]", ''The Journal of Philosophy'', Vol. 44, No. 5, (27 February 1947), pp. 113–28.</ref> <br />
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# If that piece of butter had been heated to 150º, it would have melted.<br />
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# If that piece of butter had been heated to 150º, it would not have melted.<br />
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Counterfactuals are non-monotonic in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by Sobel sequences such as the following:<br />
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反事实是非单调的,因为它们的真值可以通过在其先行词中添加额外的材料而改变。这一事实可以通过 Sobel 序列得到说明,例如:<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<ref name="Counterfactuals"/><br />
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If Hannah had drunk coffee, she would be happy.<br />
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如果汉娜喝了咖啡,她会很高兴的。<br />
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====Context dependence and vagueness====<br />
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If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
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如果汉娜喝了咖啡,咖啡里加了汽油,她会伤心的。<br />
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If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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如果汉娜喝了咖啡,咖啡里加了汽油,而汉娜是个喝汽油的机器人,她会很高兴的。<br />
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Counterfactuals are ''context dependent'' and ''[[vague]]''. For example, either of the following statements can be reasonably held true, though not at the same time:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
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One way of formalizing this fact is to say that the principle of Antecedent Strengthening should not hold for any connective > intended as a formalization of natural language conditionals.<br />
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形式化这一事实的一种方法是说,先行强化原则不适用于任何连接词,它是自然语言条件句的形式化。<br />
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# If [[Julius Caesar|Caesar]] had been in command in Korea, he would have [[Korean War#US threat of atomic warfare|used the atom bomb]].<br />
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# If Caesar had been in command in Korea, he would have used catapults.<br />
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====Non-monotonicity====<br />
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Counterfactuals are ''non-monotonic'' in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by ''[[Jordan Howard Sobel|Sobel sequences]]'' such as the following:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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The most common logical accounts of counterfactuals are couched in the possible world semantics. Broadly speaking, these approaches have in common that they treat a counterfactual A > B as true if B holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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反事实的最常见的逻辑解释是可能世界语义学。一般来说,这些方法的共同点是,如果 b 持有一些可能的世界集合,其中 a 是真实的,那么它们就把反事实的 a > b 当作真实的。它们主要在如何识别相关的 a 世界集方面有所不同。<br />
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# If Hannah had drunk coffee, she would be happy.<br />
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David Lewis's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.<br />
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大卫 · 刘易斯多变的严格条件被认为是哲学中的经典分析。安吉利卡 · 克拉策提出的前提语义学是语言学中的一个标准。然而,市场上有许多可能的世界方法,包括最初被 Lewis 摒弃的严格条件分析的动态变体。<br />
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# If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
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# If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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One way of formalizing this fact is to say that the principle of ''Antecedent Strengthening'' should '''not''' hold for any connective > intended as a formalization of natural language conditionals.<br />
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The strict conditional analysis treats natural language counterfactuals as being equivalent to the modal logic formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as material implication. This approach was first proposed in 1912 by C.I. Lewis as part of his axiomatic approach to modal logic.<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式。在这个公式中,Box 表示必要性,right tarrow </math > 被理解为实质条件。这种方法最早是在1912年由 c.i. 提出的。刘易斯的公理化方法的一部分,模态逻辑。<br />
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* '''Antecedent Strengthening''': <math> P > Q \models (P \land R) > Q </math><br />
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=== Possible worlds accounts ===<br />
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The most common logical accounts of counterfactuals are couched in the [[possible world semantics]]. Broadly speaking, these approaches have in common that they treat a counterfactual ''A'' > ''B'' as true if ''B'' holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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In the belief revision framework, counterfactuals are treated using a formal implementation of the Ramsey test. In these systems, a counterfactual A > B holds if and only if the addition of A to the current body of knowledge has B as a consequence. This condition relates counterfactual conditionals to belief revision, as the evaluation of A > B can be done by first revising the current knowledge with A and then checking whether B is true in what results. Revising is easy when A is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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在信念修正框架中,我们使用 Ramsey 测试的一个正式实现来处理反事实问题。在这些系统中,一个反事实的 a > b 成立当且仅当 a 加入到当前的知识体系中的结果是 b。这个条件将反事实条件与信念修正联系起来,因为 a > b 的评估可以通过首先用 a 修正当前的知识,然后检查 b 在什么结果中是否为真来完成。当 a 与当前的信念一致时,复习就容易了,否则就很难了。每个信念修正的语义都可以用于条件语句的求值。反过来,每一种条件求值方法都可以看作是一种执行修正的方法。<br />
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[[David Lewis (philosopher)|David Lewis]]'s ''variably strict conditional'' is considered the classic analysis within philosophy. The closely related ''premise semantics'' proposed by [[Angelika Kratzer]] is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including [[dynamic semantics|dynamic]] variants of the ''strict conditional'' analysis originally dismissed by Lewis.<br />
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====Strict conditional====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of propositional formulae, considering the maximal sets of these formulae that are consistent with A, and adding A to each. The rationale is that each of these maximal sets represents a possible state of belief in which A is true that is as similar as possible to the original one. The conditional statement A > B therefore holds if and only if B is true in all such sets.<br />
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Ginsberg (1986)提出了条件句的语义假设,假设当前的信念构成一组命题公式,考虑这些公式的最大集与 a 相一致,并在每个公式中加入 a。其基本原理是,这些最大集合中的每一个都代表了一种可能的信念状态,其中 a 为真,且尽可能与原始信念相似。因此,If判断语句集 a > b 成立的充要条件是 b 在所有这样的集合中都为真。<br />
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The [[strict conditional]] analysis treats natural language counterfactuals as being equivalent to the [[modal logic]] formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as [[material conditional|material implication]]. This approach was first proposed in 1912 by [[C.I. Lewis]] as part of his [[Axiomatic system|axiomatic approach]] to modal logic.<ref name="Counterfactuals"/> In modern [[relational semantics]], this means that the strict conditional is true at ''w'' iff the corresponding material conditional is true throughout the worlds accessible from ''w''. More formally:<br />
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* Given a model <math>M = \langle W,R,V \rangle</math>, we have that <math> M,w \models \Box(P \rightarrow Q) </math> iff <math>M, v \models P \rightarrow Q </math> for all <math>v</math> such that <math>Rwv</math><br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual morphemes, while others recruit morphemes which otherwise express tense, aspect, mood, or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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语言使用不同的策略来表达反事实。一些语素有专门的反事实语素,而另一些语素则表示时态、方面、语气或者它们的组合。自2000年代初以来,语言学家、语言哲学家和哲学逻辑学家对这种语法标记的本质进行了大量的研究,并且一直是一个活跃的研究领域。<br />
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Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.<br />
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The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.<br />
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This fact led to widespread abandonment of the strict conditional, in particular in favor of Lewis's [[counterfactual conditional#Variably strict conditional|variably strict analysis]]. However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued that ''Sobel sequences'' don't demand a ''non-monotonic'' logic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as the sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. Warmbrōd's idea was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality.<br />
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In many languages, counterfactuality is marked by past tense morphology. Since these uses of the past tense do not convey their typical temporal meaning, they are called fake past or fake tense. English is one language which uses fake past to mark counterfactuality, as shown in the following minimal pair. In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<br />
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在许多语言中,反事实性以过去时态形态学为标志。由于过去时的这些用法没有传达其典型的时间意义,所以它们被称为假过去时或假过去时。英语是一种使用虚假过去来标记反事实性的语言,如下面的最小对所示。在陈述句中,粗体词是现在时态的形式。在反事实的例子中,两个词都采用过去时态。过去时的这种用法不可能有普通的时间意义,因为它可以和副词“明天”一起使用,而不会产生矛盾。<br />
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Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of [[dynamic semantics]], and given a number of linguistic arguments in favor. One argument is that conditional antecedents license [[Polarity item#Determination of licensing contexts|negative polarity items]], which are thought to be licensed only by monotonic operators.<br />
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Indicative: If Natalia leaves tomorrow, she will arrive on time.<br />
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如果娜塔莉亚明天离开,她会准时到达。<br />
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# If Hannah had drunk any coffee, she would be happy.<br />
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Counterfactual: If Natalia left tomorrow, she would arrive on time.<br />
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反事实: 如果娜塔莉亚明天离开,她会准时到达。<br />
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Another argument in favor of the strict conditional comes from [[Irene Heim|Irene Heim's]] observation that Sobel Sequences are generally [[Felicity (pragmatics)|infelicitous]] (i.e. sound strange) in reverse.<br />
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Modern Hebrew is another language where counterfactuality is marked with a fake past morpheme:<br />
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现代希伯来语是另一种用假的过去语素标记反事实性的语言:<br />
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# If Hannah had drunk coffee with gasoline in it, she would not be happy. But if she had drunk coffee, she would be happy.<br />
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| || im || Dani || haya || ba-bayit || maχa ɾ || hayinu || mevakRim || oto<br />
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| || im || Dani || haya || ba-bayit || maχa ɾ || hayinu || mevakRim || oto<br />
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Sarah Moss (2012) and Karen Lewis (2018) have responded to these arguments, showing that a version of the variably strict analysis can account for these patterns, and arguing that such an account is preferable since it can also account for apparent exceptions. As of 2020, this debate continues in the literature, with accounts such as Willer (2019) arguing that a strict conditional account can cover these exceptions as well.<ref name="Counterfactuals"/><br />
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| || if || Dani || be.pst.3sm || in-home || tomorrow || be.pst.1pl || visit.ptc.pl || he.acc<br />
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如果达尼在家里,明天,在家里,在家里,在家里,在家里<br />
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====Variably strict conditional====<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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如果丹妮明天在家,我们就会去看他了<br />
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In the variably strict approach, the semantics of a conditional ''A'' > ''B'' is given by some function on the relative closeness of worlds where A is true and B is true, on the one hand, and worlds where A is true but B is not, on the other.<br />
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Palestinian Arabic is another:<br />
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巴勒斯坦阿拉伯语是另一个例子:<br />
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On Lewis's account, A > C is (a) vacuously true if and only if there are no worlds where A is true (for example, if A is logically or metaphysically impossible); (b) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or (c) false otherwise. Although in Lewis's ''Counterfactuals'' it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did ''not'' intend the metric of 'closeness' to be simply our ordinary notion of [[Similarity (philosophy)#Respective and overall similarity|overall similarity]].<br />
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Example:<br />
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In formal semantics and philosophical logic, fake past is regarded as a puzzle, since it is not obvious why so many unrelated languages would repurpose a tense morpheme to mark counterfactuality. Proposed solutions to this puzzle divide into two camps: past as modal and past as past. These approaches differ in whether or not they take the past tense's core meaning to be about time.<br />
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在形式语义学和哲学逻辑中,虚假的过去被认为是一个谜,因为不明显的是为什么这么多不相关的语言重新使用一个时态语素来标记反事实性。针对这一难题提出的解决办法分为两个阵营: 过去为模式和过去为过去。这些方法的不同之处在于它们是否将过去时的核心意思理解为与时间有关。<br />
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:If he had eaten more at breakfast, he would not have been hungry at 11 am.<br />
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On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where he ate more for breakfast, there is at least one world where he is not hungry at 11 am and which is closer to our world than any world where he ate more for breakfast but is still hungry at 11 am.<br />
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In the past as modal approach, the denotation of the past tense is not fundamentally about time. Rather, it is an underspecified skeleton which can apply either to modal or temporal content. For instance, the particular past as modal proposal of Iatridou (2000), the past tense's core meaning is what's shown schematically below:<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker's account differs from Lewis's most notably in his acceptance of the ''limit'' and ''uniqueness assumptions''. The uniqueness assumption is the thesis that, for any antecedent A, among the possible worlds where A is true, there is a single (''unique'') one that is ''closest'' to the actual world. The limit assumption is the thesis that, for a given antecedent A, if there is a chain of possible worlds where A is true, each closer to the actual world than its predecessor, then the chain has a ''limit'': a possible world where A is true that is closer to the actual worlds than all worlds in the chain. (The uniqueness assumption [[logical consequence|entails]] the limit assumption, but the limit assumption does not entail the uniqueness assumption.) On Stalnaker's account, A > C is non-vacuously true if and only if, at the closest world where A is true, C is true. So, the above example is true just in case at the single, closest world where he ate more breakfast, he does not feel hungry at 11 am. Although it is controversial, Lewis rejected the limit assumption (and therefore the uniqueness assumption) because it rules out the possibility that there might be worlds that get closer and closer to the actual world without limit. For example, there might be an infinite series of worlds, each with a coffee cup a smaller fraction of an inch to the left of its actual position, but none of which is uniquely the closest. (See Lewis 1973: 20.)<br />
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The topic x is not the contextually-provided x<br />
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主题 x 不是上下文提供的 x<br />
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One consequence of Stalnaker's acceptance of the uniqueness assumption is that, if the [[law of excluded middle]] is true, then all instances of the formula (A > C) ∨ (A > ¬C) are true. The law of excluded middle is the thesis that for all propositions p, p ∨ ¬p is true. If the uniqueness assumption is true, then for every antecedent A, there is a uniquely closest world where A is true. If the law of excluded middle is true, any consequent C is either true or false at that world where A is true. So for every counterfactual A > C, either A > C or A > ¬C is true. This is called conditional excluded middle (CEM). Example:<br />
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Depending on how this denotation composes, x can be a time interval or a possible world. When x is a time, the past tense will convey that the sentence is talking about non-current times, i.e. the past. When x is a world, it will convey that the sentence is talking about a potentially non-actual possibility. The latter is what allows for a counterfactual meaning.<br />
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根据这个指称的组成,x 可以是时间间隔,也可以是可能世界。当 x 是时间时,过去时态表示句子指的是非现在时间,也就是说,过去时态指的是非现在时间。过去。当 x 是一个世界时,它将传达出这个句子所指的是一种潜在的不真实的可能性。后者是允许反事实意义的东西。<br />
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:(1) If the fair coin had been flipped, it would have landed heads.<br />
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The past as past approach treats the past tense as having an inherently temporal denotation. On this approach, so-called fake tense isn't actually fake. It differs from "real" tense only in how it takes scope, i.e. which component of the sentence's meaning is shifted to an earlier time. When a sentence has "real" past marking, it discusses something that happened at an earlier time; when a sentence has so-called fake past marking, it discusses possibilities that were accessible at an earlier time but may no longer be.<br />
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过去时作为过去时的方法认为过去时具有内在的时间外延。在这种方法中,所谓的假时态实际上并不是假的。它与“真实”时态的区别仅在于它如何占据范围,即。句子的哪个部分的意思转移到了更早的时间。当一个句子有“真实的”过去标记时,它讨论的是发生在更早的时间的事情; 当一个句子有所谓的“假过去标记”时,它讨论的可能性在更早的时间是可以接受的,但可能不再是。<br />
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:(2) If the fair coin had been flipped, it would have landed tails (i.e. not heads).<br />
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On Stalnaker's analysis, there is a closest world where the fair coin mentioned in (1) and (2) is flipped and at that world either it lands heads or it lands tails. So either (1) is true and (2) is false or (1) is false and (2) true. On Lewis's analysis, however, both (1) and (2) are false, for the worlds where the fair coin lands heads are no more or less close than the worlds where they land tails. For Lewis, "If the coin had been flipped, it would have landed heads or tails" is true, but this does not entail that "If the coin had been flipped, it would have landed heads, or: If the coin had been flipped it would have landed tails."<br />
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=== Other accounts ===<br />
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Fake aspect often accompanies fake tense in languages that mark aspect. In some languages (e.g. Modern Greek, Zulu, and the Romance languages) this fake aspect is imperfective. In other languages (e.g. Palestinian Arabic) it is perfective. However, in other languages including Russian and Polish, counterfactuals can have either perfective or imperfective aspect. In other experiments, participants were asked to read short stories that contained counterfactual conditionals, e.g., ‘If there had been roses in the flower shop then there would have been lilies’. Later in the story, they read sentences corresponding to the presupposed facts, e.g., ‘there were no roses and there were no lilies’. The counterfactual conditional primed them to read the sentence corresponding to the presupposed facts very rapidly; no such priming effect occurred for indicative conditionals. They spent different amounts of time 'updating' a story that contains a counterfactual conditional compared to one that contains factual information and focused on different parts of counterfactual conditionals.<br />
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在标记体的语言中,假体往往伴随着假时态。在某些语言中(例如:。现代希腊语、祖鲁语和罗曼语)这个虚构的部分是不完整的。用其他语言(例如:。巴勒斯坦阿拉伯语)这是完美的。然而,在包括俄语和波兰语在内的其他语言中,反事实可以是完成体或非完整体。在其他实验中,参与者被要求阅读包含反事实条件的短篇小说,例如,如果花店里有玫瑰,那么就会有百合花。在故事的后半部分,他们阅读与预设事实相对应的句子,例如,没有玫瑰,也没有百合。反事实条件让他们非常快速地阅读与预设事实相对应的句子; 指示性条件句则没有这样的启动效应。他们花了不同数量的时间更新一个包含反事实条件的故事,而不是一个包含事实信息的故事,并且关注不同部分的反事实条件句。<br />
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====Causal models====<br />
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Experiments have compared the inferences people make from counterfactual conditionals and indicative conditionals. Given a counterfactual conditional, e.g., 'If there had been a circle on the blackboard then there would have been a triangle', and the subsequent information 'in fact there was no triangle', participants make the modus tollens inference 'there was no circle' more often than they do from an indicative conditional. Given the counterfactual conditional and the subsequent information 'in fact there was a circle', participants make the modus ponens inference as often as they do from an indicative conditional. See counterfactual thinking.<br />
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实验比较了人们从反事实条件句和指示性条件句中得出的推论。给定一个反事实条件,例如,如果黑板上有一个圆,那么就会有一个三角形,并且随后的信息事实上没有三角形,参与者做这种推断的频率比他们从一个直陈条件推断的频率更高。考虑到反事实条件和随后的信息‘事实上存在一个循环’,参与者做这种推理的频率和他们从直陈条件推理的频率一样高。参见反事实思维。<br />
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{{Further|Causal model#Counterfactuals}}<br />
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{{Expand section|date=September 2020}}<br />
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Byrne argues that people construct mental representations that encompass two possibilities when they understand, and reason from, a counterfactual conditional, e.g., 'if Oswald had not shot Kennedy, then someone else would have'. They envisage the conjecture 'Oswald did not shoot Kennedy and someone else did' and they also think about the presupposed facts 'Oswald did shoot Kennedy and someone else did not'. According to the mental model theory of reasoning, they construct mental models of the alternative possibilities.<br />
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认为人们构建的心理表征包括两种可能性,一种是他们理解的反事实条件,另一种是推理,例如,如果 Oswald 没有射杀 Kennedy,那么其他人也会射杀 Kennedy。他们猜想肯尼迪不是奥斯瓦尔德杀的,而是别人杀的,他们还想到了预先假定的事实奥斯瓦尔德确实杀了肯尼迪,而别人没有。根据心理模型推理理论,他们构建了可选择可能性的心理模型。<br />
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The ''causal models framework'' analyzes counterfactuals in terms of systems of [[structural equation model|structural equations]]. In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence "''Y'' would be ''y'' had ''X'' been ''x''" (formally, ''X = x'' > ''Y = y'' ) is defined as the assertion: If we replace the equation currently determining ''X'' with a constant ''X = x'', and solve the set of equations for variable ''Y'', the solution obtained will be ''Y = y''. This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators. This approach was developed by [[Judea Pearl]] (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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====Belief revision====<br />
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{{Further|Belief revision#The Ramsey test}}<br />
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{{Expand section|date=September 2020}}<br />
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In the [[belief revision]] framework, counterfactuals are treated using a formal implementation of the ''Ramsey test''. In these systems, a counterfactual ''A'' > ''B'' holds if and only if the addition of ''A'' to the current body of knowledge has ''B'' as a consequence. This condition relates counterfactual conditionals to [[belief revision]], as the evaluation of ''A'' > ''B'' can be done by first revising the current knowledge with ''A'' and then checking whether ''B'' is true in what results. Revising is easy when ''A'' is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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====Ginsberg====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of [[propositional formula]]e, considering the maximal sets of these formulae that are consistent with ''A'', and adding ''A'' to each. The rationale is that each of these maximal sets represents a possible state of belief in which ''A'' is true that is as similar as possible to the original one. The conditional statement ''A'' > ''B'' therefore holds if and only if ''B'' is true in all such sets.<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref><br />
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== The grammar of counterfactuality ==<br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual [[morphemes]], while others recruit morphemes which otherwise express [[grammatical tense|tense]], [[grammatical aspect|aspect]], [[grammatical mood|mood]], or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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=== Fake tense ===<br />
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==== Description ====<br />
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In many languages, counterfactuality is marked by [[past tense]] morphology.<ref name = "palmer">{{cite book |last=Palmer |first=Frank Robert |date=1986 |title=Mood and modality |publisher= Cambridge University Press}}</ref> Since these uses of the past tense do not convey their typical temporal meaning, they are called ''fake past'' or ''fake tense''.<ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref> English is one language which uses fake past to mark counterfactuality, as shown in the following [[minimal pair]].<ref>English fake past is sometimes erroneously referred to as "subjunctive", even though it is not the [[English subjunctive|subjunctive mood]].</ref> In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<ref name = palmer /><ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref><br />
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# Indicative: If Natalia '''leaves''' tomorrow, she '''will''' arrive on time.<br />
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# Counterfactual: If Natalia '''left''' tomorrow, she '''would''' arrive on time.<br />
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[[Hebrew language|Modern Hebrew]] is another language where counterfactuality is marked with a fake past morpheme:<ref name="karawani">{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><br />
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Category:Conditionals in linguistics<br />
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范畴: 语言学中的条件句<br />
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Category:Grammar<br />
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分类: 语法<br />
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| || im || Dani || '''haya''' || ba-bayit || maχa ɾ || '''hayinu''' || mevakRim || oto<br />
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Category:Semantics<br />
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分类: 语义学<br />
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Category:Belief revision<br />
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类别: 信念修正<br />
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| || if || Dani || be.'''pst'''.3sm || in-home || tomorrow || be.'''pst'''.1pl || visit.ptc.pl || he.acc<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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Category:Linguistic modality<br />
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类别: 情态<br />
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<small>This page was moved from [[wikipedia:en:Counterfactual conditional]]. Its edit history can be viewed at [[反事实/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22716反事实2021-05-30T16:17:08Z<p>Wei:/* Examples */</p>
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{{Short description|Conditionals that discuss what would have been if things were otherwise}}<br />
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{{Redirect|Counterfactual}}<br />
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'''Counterfactual conditionals''' (also ''subjunctive'' or ''X-marked'') are [[conditional sentence]]s which discuss what would have been true under different circumstances, e.g. <!-- this is example is from Iatridou (2000), ex (47c) on p. 244 --> "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with [[indicative conditionals|indicatives]], which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of [[Counterfactual conditional#Fake tense|fake tense morphology]], which some languages use in combination with other kinds of [[Morphology (linguistics)|morphology]] including [[Counterfactual conditional#Fake aspect|aspect]] and [[Counterfactual conditional#mood|mood]].<br />
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反事实条件句(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的条件句。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
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Counterfactuals are one of the most studied phenomena in [[philosophical logic]], [[formal semantics (natural language)|formal semantics]], and [[philosophy of language]]. They were first discussed as a problem for the [[material conditional]] analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic [[possible world]] approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as [[causal model]]s and [[dynamic semantics]]. Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是微不足道的真实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==Overview==<br />
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=== Examples ===<br />
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The difference between [[indicative conditional|indicative]] and counterfactual conditionals can be illustrated by the following [[minimal pair]]:<br />
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指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
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# '''Indicative Conditional''': If it ''is'' raining right now, then Sally ''is'' inside. <br />
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# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
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# '''Simple Past Counterfactual''': If it ''was raining'' <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally ''would be'' inside.<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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# '''一般过去时的反事实''':如果现在正在下雨,那么Sally就会在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "is" in both the "if" clause and the "then" clause. As a result, it conveys that the speaker is agnostic about whether it is raining. The counterfactual example uses the [[fake tense]] form "was" in the "if" clause and the [[modal verb|modal]] "would" in the "then" clause. As a result, it conveys that the speaker does not believe that it is raining.<br />
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这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
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English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the [[pluperfect|past perfect]] counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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# '''Past Perfect Counterfactual''': If it ''had been raining'' yesterday, then Sally ''would have been'' inside.<br />
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# '''过去完成时的反事实''':如果昨天下了雨,那么Sally就会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<br />
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另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<br />
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# '''Irrealis Counterfactual''': If it ''were raining'' right now, then Sally ''would be'' inside.<br />
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# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
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Past perfect and irrealis counterfactuals can undergo ''conditional inversion'':<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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# Were it raining, Sally would be inside.<br />
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# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
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# Had it rained, Sally would be inside.<br />
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# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
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=== Terminology ===<br />
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<!——鉴于术语上的巨大但往往是细微的差异,本节必须经过仔细的编辑。在点击“发布更改”之前,请考虑结果文本是否有助于读者理解这些术语是如何使用的。如果结果文本读起来像是“热狗是三明治的辩论吗?”删除所有字符提示后,请不要点击”发布更改”。特别是,请确保(1)明确区分事实主张和术语定义(2)记住,不同的来源可以以不同的方式使用单一术语(3)对术语的每个术语或用法进行不偏不倚的框架性解释。--><br />
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The term ''counterfactual conditional'' is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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The term counterfactual conditional is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<br />
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反事实条件这个术语被广泛地用作上面所显示的各种句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,经典的例子被称为“ Anderson 格”,它具有反事实条件的典型语法形式,但是并没有表明它的先行词是假的或者不可能的。<br />
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# '''Anderson Case''': If the patient had taken arsenic, he would have blue spots.<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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Anderson Case: If the patient had taken arsenic, he would have blue spots.<br />
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安德森病例: 如果病人服用了砒霜,他会长出蓝色斑点。<br />
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Such conditionals are also widely referred to as ''subjunctive conditionals'', though this term is likewise acknowledged as a misnomer even by those who use it.<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref> Many languages do not have a morphological [[subjunctive]] (e.g. [[Danish grammar|Danish]] and [[Dutch grammar|Dutch]]) and many that do have it don’t use it for this sort of conditional (e.g. [[French grammar|French]], [[Swahili grammar|Swahili]], all [[Indo-Aryan languages]] that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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Such conditionals are also widely referred to as subjunctive conditionals, though this term is likewise acknowledged as a misnomer even by those who use it. Many languages do not have a morphological subjunctive (e.g. Danish and Dutch) and many that do have it don’t use it for this sort of conditional (e.g. French, Swahili, all Indo-Aryan languages that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<br />
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这种条件句也被广泛地称为虚拟条件句,尽管这个术语同样被使用者认为是用词不当。许多语言都没有形态虚拟语气。丹麦语和荷兰语)和许多有这个词的人不用它来表示这种条件句(例如:。法语,斯瓦希里语,所有的印度-雅利安语支都有虚拟语气)。此外,对于这样的条件句使用虚拟语气的语言,只有在具有特定的过去虚拟形式的情况下才会使用虚拟语气。因此,虚拟标记既不是必要的,也不足以成为这类条件句的成员。<br />
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The terms ''counterfactual'' and ''subjunctive'' have sometimes been repurposed for more specific uses. For instance, the term "counterfactual" is sometimes applied to conditionals that express a contrary-to-fact meaning, regardless of their grammatical structure.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" /> Along similar lines, the term "subjunctive" is sometimes used to refer to conditionals that bear fake past or irrealis marking, regardless of the meaning they convey.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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Recently the term X-Marked has been proposed as a replacement, evoking the extra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as O-Marked conditionals, reflecting their ordinary marking.<br />
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最近术语 x 标记已被提议作为替代,唤起额外的标记,这些条件承担。采用这一术语的人将指示性条件句称为 o 标记条件句,反映了他们的普通标记。<br />
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Recently the term ''X-Marked'' has been proposed as a replacement, evoking the ''ex''tra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as ''O-Marked'' conditionals, reflecting their ''o''rdinary marking.<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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The ''antecedent'' of a conditional is sometimes referred to as its ''"if"-clause'' or ''protasis''. The ''consequent'' of a conditional is sometimes referred to as a ''"then"''-clause or as an apodosis.<br />
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==Logic and semantics==<br />
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According to the material conditional analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated. <br />
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根据实质条件的分析,自然语言条件句---- 形式为如果 p 那么 q 的陈述---- 只要其先行词 p 为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是真空的。古德曼用下面的一对来说明这一点,在这个背景下,我们知道正在讨论的那块黄油并没有被加热。<br />
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If that piece of butter had been heated to 150º, it would have melted.<br />
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如果那块黄油被加热到150度,它就会融化。<br />
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Counterfactuals were first discussed by [[Nelson Goodman]] as a problem for the [[material conditional]] used in [[classical logic]]. Because of these problems, early work such as that of [[W.V. Quine]] held that counterfactuals aren't strictly logical, and do not make true or false claims about the world. However, in the 1970s, [[David Lewis (philosopher)|David Lewis]] showed that these problems are surmountable given an appropriate logical framework. Work since then in [[formal semantics (linguistics)|formal semantics]], [[philosophical logic]], [[philosophy of language]], and [[cognitive science]] has built on Lewis's insight, taking it in a variety of different directions.<ref name="Counterfactuals">{{cite encyclopedia |last1=Starr |first1=Will |editor-last1=Zalta |editor-first1=Edward N.|encyclopedia=The Stanford Encyclopedia of Philosophy|title=Counterfactuals|year=2019 |url=https://plato.stanford.edu/archives/fall2019/entries/counterfactuals}}</ref><br />
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If that piece of butter had been heated to 150º, it would not have melted.<br />
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如果那块黄油被加热到150度,它就不会融化。<br />
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===Classic puzzles===<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<br />
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更一般地说,这些例子表明反事实并不是真理功能的。换句话说,知道先行词和结果是否真实并不足以确定反事实本身是否真实。<br />
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====The problem of counterfactuals====<br />
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If Caesar had been in command in Korea, he would have used the atom bomb.<br />
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如果凯撒当时在朝鲜指挥,他会使用原子弹。<br />
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If Caesar had been in command in Korea, he would have used catapults.<br />
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如果凯撒在朝鲜指挥,他会使用投石器。<br />
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According to the [[material conditional]] analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated.<ref name="jstor.org">Goodman, N., "[https://www.jstor.org/stable/2019988 The Problem of Counterfactual Conditionals]", ''The Journal of Philosophy'', Vol. 44, No. 5, (27 February 1947), pp. 113–28.</ref> <br />
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# If that piece of butter had been heated to 150º, it would have melted.<br />
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# If that piece of butter had been heated to 150º, it would not have melted.<br />
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Counterfactuals are non-monotonic in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by Sobel sequences such as the following:<br />
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反事实是非单调的,因为它们的真值可以通过在其先行词中添加额外的材料而改变。这一事实可以通过 Sobel 序列得到说明,例如:<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<ref name="Counterfactuals"/><br />
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If Hannah had drunk coffee, she would be happy.<br />
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如果汉娜喝了咖啡,她会很高兴的。<br />
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====Context dependence and vagueness====<br />
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If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
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如果汉娜喝了咖啡,咖啡里加了汽油,她会伤心的。<br />
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If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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如果汉娜喝了咖啡,咖啡里加了汽油,而汉娜是个喝汽油的机器人,她会很高兴的。<br />
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Counterfactuals are ''context dependent'' and ''[[vague]]''. For example, either of the following statements can be reasonably held true, though not at the same time:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
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One way of formalizing this fact is to say that the principle of Antecedent Strengthening should not hold for any connective > intended as a formalization of natural language conditionals.<br />
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形式化这一事实的一种方法是说,先行强化原则不适用于任何连接词,它是自然语言条件句的形式化。<br />
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# If [[Julius Caesar|Caesar]] had been in command in Korea, he would have [[Korean War#US threat of atomic warfare|used the atom bomb]].<br />
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# If Caesar had been in command in Korea, he would have used catapults.<br />
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====Non-monotonicity====<br />
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Counterfactuals are ''non-monotonic'' in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by ''[[Jordan Howard Sobel|Sobel sequences]]'' such as the following:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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The most common logical accounts of counterfactuals are couched in the possible world semantics. Broadly speaking, these approaches have in common that they treat a counterfactual A > B as true if B holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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反事实的最常见的逻辑解释是可能世界语义学。一般来说,这些方法的共同点是,如果 b 持有一些可能的世界集合,其中 a 是真实的,那么它们就把反事实的 a > b 当作真实的。它们主要在如何识别相关的 a 世界集方面有所不同。<br />
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# If Hannah had drunk coffee, she would be happy.<br />
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David Lewis's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.<br />
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大卫 · 刘易斯多变的严格条件被认为是哲学中的经典分析。安吉利卡 · 克拉策提出的前提语义学是语言学中的一个标准。然而,市场上有许多可能的世界方法,包括最初被 Lewis 摒弃的严格条件分析的动态变体。<br />
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# If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
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# If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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One way of formalizing this fact is to say that the principle of ''Antecedent Strengthening'' should '''not''' hold for any connective > intended as a formalization of natural language conditionals.<br />
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The strict conditional analysis treats natural language counterfactuals as being equivalent to the modal logic formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as material implication. This approach was first proposed in 1912 by C.I. Lewis as part of his axiomatic approach to modal logic.<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式。在这个公式中,Box 表示必要性,right tarrow </math > 被理解为实质条件。这种方法最早是在1912年由 c.i. 提出的。刘易斯的公理化方法的一部分,模态逻辑。<br />
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* '''Antecedent Strengthening''': <math> P > Q \models (P \land R) > Q </math><br />
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=== Possible worlds accounts ===<br />
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The most common logical accounts of counterfactuals are couched in the [[possible world semantics]]. Broadly speaking, these approaches have in common that they treat a counterfactual ''A'' > ''B'' as true if ''B'' holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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In the belief revision framework, counterfactuals are treated using a formal implementation of the Ramsey test. In these systems, a counterfactual A > B holds if and only if the addition of A to the current body of knowledge has B as a consequence. This condition relates counterfactual conditionals to belief revision, as the evaluation of A > B can be done by first revising the current knowledge with A and then checking whether B is true in what results. Revising is easy when A is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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在信念修正框架中,我们使用 Ramsey 测试的一个正式实现来处理反事实问题。在这些系统中,一个反事实的 a > b 成立当且仅当 a 加入到当前的知识体系中的结果是 b。这个条件将反事实条件与信念修正联系起来,因为 a > b 的评估可以通过首先用 a 修正当前的知识,然后检查 b 在什么结果中是否为真来完成。当 a 与当前的信念一致时,复习就容易了,否则就很难了。每个信念修正的语义都可以用于条件语句的求值。反过来,每一种条件求值方法都可以看作是一种执行修正的方法。<br />
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[[David Lewis (philosopher)|David Lewis]]'s ''variably strict conditional'' is considered the classic analysis within philosophy. The closely related ''premise semantics'' proposed by [[Angelika Kratzer]] is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including [[dynamic semantics|dynamic]] variants of the ''strict conditional'' analysis originally dismissed by Lewis.<br />
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====Strict conditional====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of propositional formulae, considering the maximal sets of these formulae that are consistent with A, and adding A to each. The rationale is that each of these maximal sets represents a possible state of belief in which A is true that is as similar as possible to the original one. The conditional statement A > B therefore holds if and only if B is true in all such sets.<br />
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Ginsberg (1986)提出了条件句的语义假设,假设当前的信念构成一组命题公式,考虑这些公式的最大集与 a 相一致,并在每个公式中加入 a。其基本原理是,这些最大集合中的每一个都代表了一种可能的信念状态,其中 a 为真,且尽可能与原始信念相似。因此,If判断语句集 a > b 成立的充要条件是 b 在所有这样的集合中都为真。<br />
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The [[strict conditional]] analysis treats natural language counterfactuals as being equivalent to the [[modal logic]] formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as [[material conditional|material implication]]. This approach was first proposed in 1912 by [[C.I. Lewis]] as part of his [[Axiomatic system|axiomatic approach]] to modal logic.<ref name="Counterfactuals"/> In modern [[relational semantics]], this means that the strict conditional is true at ''w'' iff the corresponding material conditional is true throughout the worlds accessible from ''w''. More formally:<br />
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* Given a model <math>M = \langle W,R,V \rangle</math>, we have that <math> M,w \models \Box(P \rightarrow Q) </math> iff <math>M, v \models P \rightarrow Q </math> for all <math>v</math> such that <math>Rwv</math><br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual morphemes, while others recruit morphemes which otherwise express tense, aspect, mood, or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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语言使用不同的策略来表达反事实。一些语素有专门的反事实语素,而另一些语素则表示时态、方面、语气或者它们的组合。自2000年代初以来,语言学家、语言哲学家和哲学逻辑学家对这种语法标记的本质进行了大量的研究,并且一直是一个活跃的研究领域。<br />
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Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.<br />
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The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.<br />
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This fact led to widespread abandonment of the strict conditional, in particular in favor of Lewis's [[counterfactual conditional#Variably strict conditional|variably strict analysis]]. However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued that ''Sobel sequences'' don't demand a ''non-monotonic'' logic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as the sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. Warmbrōd's idea was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality.<br />
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In many languages, counterfactuality is marked by past tense morphology. Since these uses of the past tense do not convey their typical temporal meaning, they are called fake past or fake tense. English is one language which uses fake past to mark counterfactuality, as shown in the following minimal pair. In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<br />
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在许多语言中,反事实性以过去时态形态学为标志。由于过去时的这些用法没有传达其典型的时间意义,所以它们被称为假过去时或假过去时。英语是一种使用虚假过去来标记反事实性的语言,如下面的最小对所示。在陈述句中,粗体词是现在时态的形式。在反事实的例子中,两个词都采用过去时态。过去时的这种用法不可能有普通的时间意义,因为它可以和副词“明天”一起使用,而不会产生矛盾。<br />
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Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of [[dynamic semantics]], and given a number of linguistic arguments in favor. One argument is that conditional antecedents license [[Polarity item#Determination of licensing contexts|negative polarity items]], which are thought to be licensed only by monotonic operators.<br />
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Indicative: If Natalia leaves tomorrow, she will arrive on time.<br />
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如果娜塔莉亚明天离开,她会准时到达。<br />
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# If Hannah had drunk any coffee, she would be happy.<br />
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Counterfactual: If Natalia left tomorrow, she would arrive on time.<br />
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反事实: 如果娜塔莉亚明天离开,她会准时到达。<br />
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Another argument in favor of the strict conditional comes from [[Irene Heim|Irene Heim's]] observation that Sobel Sequences are generally [[Felicity (pragmatics)|infelicitous]] (i.e. sound strange) in reverse.<br />
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Modern Hebrew is another language where counterfactuality is marked with a fake past morpheme:<br />
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现代希伯来语是另一种用假的过去语素标记反事实性的语言:<br />
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# If Hannah had drunk coffee with gasoline in it, she would not be happy. But if she had drunk coffee, she would be happy.<br />
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{| <br />
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{|<br />
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| || im || Dani || haya || ba-bayit || maχa ɾ || hayinu || mevakRim || oto<br />
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| || im || Dani || haya || ba-bayit || maχa ɾ || hayinu || mevakRim || oto<br />
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Sarah Moss (2012) and Karen Lewis (2018) have responded to these arguments, showing that a version of the variably strict analysis can account for these patterns, and arguing that such an account is preferable since it can also account for apparent exceptions. As of 2020, this debate continues in the literature, with accounts such as Willer (2019) arguing that a strict conditional account can cover these exceptions as well.<ref name="Counterfactuals"/><br />
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| || if || Dani || be.pst.3sm || in-home || tomorrow || be.pst.1pl || visit.ptc.pl || he.acc<br />
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如果达尼在家里,明天,在家里,在家里,在家里,在家里<br />
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====Variably strict conditional====<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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如果丹妮明天在家,我们就会去看他了<br />
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In the variably strict approach, the semantics of a conditional ''A'' > ''B'' is given by some function on the relative closeness of worlds where A is true and B is true, on the one hand, and worlds where A is true but B is not, on the other.<br />
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Palestinian Arabic is another:<br />
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巴勒斯坦阿拉伯语是另一个例子:<br />
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On Lewis's account, A > C is (a) vacuously true if and only if there are no worlds where A is true (for example, if A is logically or metaphysically impossible); (b) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or (c) false otherwise. Although in Lewis's ''Counterfactuals'' it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did ''not'' intend the metric of 'closeness' to be simply our ordinary notion of [[Similarity (philosophy)#Respective and overall similarity|overall similarity]].<br />
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Example:<br />
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In formal semantics and philosophical logic, fake past is regarded as a puzzle, since it is not obvious why so many unrelated languages would repurpose a tense morpheme to mark counterfactuality. Proposed solutions to this puzzle divide into two camps: past as modal and past as past. These approaches differ in whether or not they take the past tense's core meaning to be about time.<br />
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在形式语义学和哲学逻辑中,虚假的过去被认为是一个谜,因为不明显的是为什么这么多不相关的语言重新使用一个时态语素来标记反事实性。针对这一难题提出的解决办法分为两个阵营: 过去为模式和过去为过去。这些方法的不同之处在于它们是否将过去时的核心意思理解为与时间有关。<br />
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:If he had eaten more at breakfast, he would not have been hungry at 11 am.<br />
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On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where he ate more for breakfast, there is at least one world where he is not hungry at 11 am and which is closer to our world than any world where he ate more for breakfast but is still hungry at 11 am.<br />
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In the past as modal approach, the denotation of the past tense is not fundamentally about time. Rather, it is an underspecified skeleton which can apply either to modal or temporal content. For instance, the particular past as modal proposal of Iatridou (2000), the past tense's core meaning is what's shown schematically below:<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker's account differs from Lewis's most notably in his acceptance of the ''limit'' and ''uniqueness assumptions''. The uniqueness assumption is the thesis that, for any antecedent A, among the possible worlds where A is true, there is a single (''unique'') one that is ''closest'' to the actual world. The limit assumption is the thesis that, for a given antecedent A, if there is a chain of possible worlds where A is true, each closer to the actual world than its predecessor, then the chain has a ''limit'': a possible world where A is true that is closer to the actual worlds than all worlds in the chain. (The uniqueness assumption [[logical consequence|entails]] the limit assumption, but the limit assumption does not entail the uniqueness assumption.) On Stalnaker's account, A > C is non-vacuously true if and only if, at the closest world where A is true, C is true. So, the above example is true just in case at the single, closest world where he ate more breakfast, he does not feel hungry at 11 am. Although it is controversial, Lewis rejected the limit assumption (and therefore the uniqueness assumption) because it rules out the possibility that there might be worlds that get closer and closer to the actual world without limit. For example, there might be an infinite series of worlds, each with a coffee cup a smaller fraction of an inch to the left of its actual position, but none of which is uniquely the closest. (See Lewis 1973: 20.)<br />
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The topic x is not the contextually-provided x<br />
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主题 x 不是上下文提供的 x<br />
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One consequence of Stalnaker's acceptance of the uniqueness assumption is that, if the [[law of excluded middle]] is true, then all instances of the formula (A > C) ∨ (A > ¬C) are true. The law of excluded middle is the thesis that for all propositions p, p ∨ ¬p is true. If the uniqueness assumption is true, then for every antecedent A, there is a uniquely closest world where A is true. If the law of excluded middle is true, any consequent C is either true or false at that world where A is true. So for every counterfactual A > C, either A > C or A > ¬C is true. This is called conditional excluded middle (CEM). Example:<br />
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Depending on how this denotation composes, x can be a time interval or a possible world. When x is a time, the past tense will convey that the sentence is talking about non-current times, i.e. the past. When x is a world, it will convey that the sentence is talking about a potentially non-actual possibility. The latter is what allows for a counterfactual meaning.<br />
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根据这个指称的组成,x 可以是时间间隔,也可以是可能世界。当 x 是时间时,过去时态表示句子指的是非现在时间,也就是说,过去时态指的是非现在时间。过去。当 x 是一个世界时,它将传达出这个句子所指的是一种潜在的不真实的可能性。后者是允许反事实意义的东西。<br />
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:(1) If the fair coin had been flipped, it would have landed heads.<br />
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The past as past approach treats the past tense as having an inherently temporal denotation. On this approach, so-called fake tense isn't actually fake. It differs from "real" tense only in how it takes scope, i.e. which component of the sentence's meaning is shifted to an earlier time. When a sentence has "real" past marking, it discusses something that happened at an earlier time; when a sentence has so-called fake past marking, it discusses possibilities that were accessible at an earlier time but may no longer be.<br />
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过去时作为过去时的方法认为过去时具有内在的时间外延。在这种方法中,所谓的假时态实际上并不是假的。它与“真实”时态的区别仅在于它如何占据范围,即。句子的哪个部分的意思转移到了更早的时间。当一个句子有“真实的”过去标记时,它讨论的是发生在更早的时间的事情; 当一个句子有所谓的“假过去标记”时,它讨论的可能性在更早的时间是可以接受的,但可能不再是。<br />
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:(2) If the fair coin had been flipped, it would have landed tails (i.e. not heads).<br />
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On Stalnaker's analysis, there is a closest world where the fair coin mentioned in (1) and (2) is flipped and at that world either it lands heads or it lands tails. So either (1) is true and (2) is false or (1) is false and (2) true. On Lewis's analysis, however, both (1) and (2) are false, for the worlds where the fair coin lands heads are no more or less close than the worlds where they land tails. For Lewis, "If the coin had been flipped, it would have landed heads or tails" is true, but this does not entail that "If the coin had been flipped, it would have landed heads, or: If the coin had been flipped it would have landed tails."<br />
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=== Other accounts ===<br />
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Fake aspect often accompanies fake tense in languages that mark aspect. In some languages (e.g. Modern Greek, Zulu, and the Romance languages) this fake aspect is imperfective. In other languages (e.g. Palestinian Arabic) it is perfective. However, in other languages including Russian and Polish, counterfactuals can have either perfective or imperfective aspect. In other experiments, participants were asked to read short stories that contained counterfactual conditionals, e.g., ‘If there had been roses in the flower shop then there would have been lilies’. Later in the story, they read sentences corresponding to the presupposed facts, e.g., ‘there were no roses and there were no lilies’. The counterfactual conditional primed them to read the sentence corresponding to the presupposed facts very rapidly; no such priming effect occurred for indicative conditionals. They spent different amounts of time 'updating' a story that contains a counterfactual conditional compared to one that contains factual information and focused on different parts of counterfactual conditionals.<br />
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在标记体的语言中,假体往往伴随着假时态。在某些语言中(例如:。现代希腊语、祖鲁语和罗曼语)这个虚构的部分是不完整的。用其他语言(例如:。巴勒斯坦阿拉伯语)这是完美的。然而,在包括俄语和波兰语在内的其他语言中,反事实可以是完成体或非完整体。在其他实验中,参与者被要求阅读包含反事实条件的短篇小说,例如,如果花店里有玫瑰,那么就会有百合花。在故事的后半部分,他们阅读与预设事实相对应的句子,例如,没有玫瑰,也没有百合。反事实条件让他们非常快速地阅读与预设事实相对应的句子; 指示性条件句则没有这样的启动效应。他们花了不同数量的时间更新一个包含反事实条件的故事,而不是一个包含事实信息的故事,并且关注不同部分的反事实条件句。<br />
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====Causal models====<br />
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Experiments have compared the inferences people make from counterfactual conditionals and indicative conditionals. Given a counterfactual conditional, e.g., 'If there had been a circle on the blackboard then there would have been a triangle', and the subsequent information 'in fact there was no triangle', participants make the modus tollens inference 'there was no circle' more often than they do from an indicative conditional. Given the counterfactual conditional and the subsequent information 'in fact there was a circle', participants make the modus ponens inference as often as they do from an indicative conditional. See counterfactual thinking.<br />
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实验比较了人们从反事实条件句和指示性条件句中得出的推论。给定一个反事实条件,例如,如果黑板上有一个圆,那么就会有一个三角形,并且随后的信息事实上没有三角形,参与者做这种推断的频率比他们从一个直陈条件推断的频率更高。考虑到反事实条件和随后的信息‘事实上存在一个循环’,参与者做这种推理的频率和他们从直陈条件推理的频率一样高。参见反事实思维。<br />
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{{Further|Causal model#Counterfactuals}}<br />
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{{Expand section|date=September 2020}}<br />
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Byrne argues that people construct mental representations that encompass two possibilities when they understand, and reason from, a counterfactual conditional, e.g., 'if Oswald had not shot Kennedy, then someone else would have'. They envisage the conjecture 'Oswald did not shoot Kennedy and someone else did' and they also think about the presupposed facts 'Oswald did shoot Kennedy and someone else did not'. According to the mental model theory of reasoning, they construct mental models of the alternative possibilities.<br />
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认为人们构建的心理表征包括两种可能性,一种是他们理解的反事实条件,另一种是推理,例如,如果 Oswald 没有射杀 Kennedy,那么其他人也会射杀 Kennedy。他们猜想肯尼迪不是奥斯瓦尔德杀的,而是别人杀的,他们还想到了预先假定的事实奥斯瓦尔德确实杀了肯尼迪,而别人没有。根据心理模型推理理论,他们构建了可选择可能性的心理模型。<br />
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The ''causal models framework'' analyzes counterfactuals in terms of systems of [[structural equation model|structural equations]]. In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence "''Y'' would be ''y'' had ''X'' been ''x''" (formally, ''X = x'' > ''Y = y'' ) is defined as the assertion: If we replace the equation currently determining ''X'' with a constant ''X = x'', and solve the set of equations for variable ''Y'', the solution obtained will be ''Y = y''. This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators. This approach was developed by [[Judea Pearl]] (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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====Belief revision====<br />
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{{Further|Belief revision#The Ramsey test}}<br />
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In the [[belief revision]] framework, counterfactuals are treated using a formal implementation of the ''Ramsey test''. In these systems, a counterfactual ''A'' > ''B'' holds if and only if the addition of ''A'' to the current body of knowledge has ''B'' as a consequence. This condition relates counterfactual conditionals to [[belief revision]], as the evaluation of ''A'' > ''B'' can be done by first revising the current knowledge with ''A'' and then checking whether ''B'' is true in what results. Revising is easy when ''A'' is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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====Ginsberg====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of [[propositional formula]]e, considering the maximal sets of these formulae that are consistent with ''A'', and adding ''A'' to each. The rationale is that each of these maximal sets represents a possible state of belief in which ''A'' is true that is as similar as possible to the original one. The conditional statement ''A'' > ''B'' therefore holds if and only if ''B'' is true in all such sets.<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref><br />
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== The grammar of counterfactuality ==<br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual [[morphemes]], while others recruit morphemes which otherwise express [[grammatical tense|tense]], [[grammatical aspect|aspect]], [[grammatical mood|mood]], or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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=== Fake tense ===<br />
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==== Description ====<br />
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In many languages, counterfactuality is marked by [[past tense]] morphology.<ref name = "palmer">{{cite book |last=Palmer |first=Frank Robert |date=1986 |title=Mood and modality |publisher= Cambridge University Press}}</ref> Since these uses of the past tense do not convey their typical temporal meaning, they are called ''fake past'' or ''fake tense''.<ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref> English is one language which uses fake past to mark counterfactuality, as shown in the following [[minimal pair]].<ref>English fake past is sometimes erroneously referred to as "subjunctive", even though it is not the [[English subjunctive|subjunctive mood]].</ref> In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<ref name = palmer /><ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref><br />
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# Indicative: If Natalia '''leaves''' tomorrow, she '''will''' arrive on time.<br />
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# Counterfactual: If Natalia '''left''' tomorrow, she '''would''' arrive on time.<br />
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[[Hebrew language|Modern Hebrew]] is another language where counterfactuality is marked with a fake past morpheme:<ref name="karawani">{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><br />
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Category:Conditionals in linguistics<br />
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范畴: 语言学中的条件句<br />
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Category:Grammar<br />
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分类: 语法<br />
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| || im || Dani || '''haya''' || ba-bayit || maχa ɾ || '''hayinu''' || mevakRim || oto<br />
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Category:Semantics<br />
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分类: 语义学<br />
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Category:Belief revision<br />
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类别: 信念修正<br />
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| || if || Dani || be.'''pst'''.3sm || in-home || tomorrow || be.'''pst'''.1pl || visit.ptc.pl || he.acc<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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Category:Linguistic modality<br />
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类别: 情态<br />
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<small>This page was moved from [[wikipedia:en:Counterfactual conditional]]. Its edit history can be viewed at [[反事实/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22715反事实2021-05-30T16:13:41Z<p>Wei:/* Examples */</p>
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{{Short description|Conditionals that discuss what would have been if things were otherwise}}<br />
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{{Redirect|Counterfactual}}<br />
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'''Counterfactual conditionals''' (also ''subjunctive'' or ''X-marked'') are [[conditional sentence]]s which discuss what would have been true under different circumstances, e.g. <!-- this is example is from Iatridou (2000), ex (47c) on p. 244 --> "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with [[indicative conditionals|indicatives]], which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of [[Counterfactual conditional#Fake tense|fake tense morphology]], which some languages use in combination with other kinds of [[Morphology (linguistics)|morphology]] including [[Counterfactual conditional#Fake aspect|aspect]] and [[Counterfactual conditional#mood|mood]].<br />
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反事实条件句(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的条件句。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
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Counterfactuals are one of the most studied phenomena in [[philosophical logic]], [[formal semantics (natural language)|formal semantics]], and [[philosophy of language]]. They were first discussed as a problem for the [[material conditional]] analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic [[possible world]] approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as [[causal model]]s and [[dynamic semantics]]. Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是微不足道的真实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==Overview==<br />
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=== Examples ===<br />
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The difference between [[indicative conditional|indicative]] and counterfactual conditionals can be illustrated by the following [[minimal pair]]:<br />
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指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
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# '''Indicative Conditional''': If it ''is'' raining right now, then Sally ''is'' inside. <br />
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# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
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# '''Simple Past Counterfactual''': If it ''was raining'' <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally ''would be'' inside.<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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# '''一般过去时的反事实''':如果现在正在下雨,那么Sally就会在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "is" in both the "if" clause and the "then" clause. As a result, it conveys that the speaker is agnostic about whether it is raining. The counterfactual example uses the [[fake tense]] form "was" in the "if" clause and the [[modal verb|modal]] "would" in the "then" clause. As a result, it conveys that the speaker does not believe that it is raining.<br />
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这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
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English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the [[pluperfect|past perfect]] counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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# '''Past Perfect Counterfactual''': If it ''had been raining'' yesterday, then Sally ''would have been'' inside.<br />
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# '''过去完成时的反事实''':如果昨天下了雨,那么Sally就会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<br />
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另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<br />
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# '''Irrealis Counterfactual''': If it ''were raining'' right now, then Sally ''would be'' inside.<br />
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# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
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Past perfect and irrealis counterfactuals can undergo ''conditional inversion'':<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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# Were it raining, Sally would be inside.<br />
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# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
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# Had it rained, Sally would be inside.<br />
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# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
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=== Terminology ===<br />
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<!——鉴于术语上的巨大但往往是细微的差异,本节必须经过仔细的编辑。在点击“发布更改”之前,请考虑结果文本是否有助于读者理解这些术语是如何使用的。如果结果文本读起来像是“热狗是三明治的辩论吗?”删除所有字符提示后,请不要点击”发布更改”。特别是,请确保(1)明确区分事实主张和术语定义(2)记住,不同的来源可以以不同的方式使用单一术语(3)对术语的每个术语或用法进行不偏不倚的框架性解释。--><br />
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The term ''counterfactual conditional'' is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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The term counterfactual conditional is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<br />
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反事实条件这个术语被广泛地用作上面所显示的各种句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,经典的例子被称为“ Anderson 格”,它具有反事实条件的典型语法形式,但是并没有表明它的先行词是假的或者不可能的。<br />
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# '''Anderson Case''': If the patient had taken arsenic, he would have blue spots.<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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Anderson Case: If the patient had taken arsenic, he would have blue spots.<br />
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安德森病例: 如果病人服用了砒霜,他会长出蓝色斑点。<br />
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Such conditionals are also widely referred to as ''subjunctive conditionals'', though this term is likewise acknowledged as a misnomer even by those who use it.<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref> Many languages do not have a morphological [[subjunctive]] (e.g. [[Danish grammar|Danish]] and [[Dutch grammar|Dutch]]) and many that do have it don’t use it for this sort of conditional (e.g. [[French grammar|French]], [[Swahili grammar|Swahili]], all [[Indo-Aryan languages]] that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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Such conditionals are also widely referred to as subjunctive conditionals, though this term is likewise acknowledged as a misnomer even by those who use it. Many languages do not have a morphological subjunctive (e.g. Danish and Dutch) and many that do have it don’t use it for this sort of conditional (e.g. French, Swahili, all Indo-Aryan languages that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<br />
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这种条件句也被广泛地称为虚拟条件句,尽管这个术语同样被使用者认为是用词不当。许多语言都没有形态虚拟语气。丹麦语和荷兰语)和许多有这个词的人不用它来表示这种条件句(例如:。法语,斯瓦希里语,所有的印度-雅利安语支都有虚拟语气)。此外,对于这样的条件句使用虚拟语气的语言,只有在具有特定的过去虚拟形式的情况下才会使用虚拟语气。因此,虚拟标记既不是必要的,也不足以成为这类条件句的成员。<br />
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The terms ''counterfactual'' and ''subjunctive'' have sometimes been repurposed for more specific uses. For instance, the term "counterfactual" is sometimes applied to conditionals that express a contrary-to-fact meaning, regardless of their grammatical structure.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" /> Along similar lines, the term "subjunctive" is sometimes used to refer to conditionals that bear fake past or irrealis marking, regardless of the meaning they convey.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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Recently the term X-Marked has been proposed as a replacement, evoking the extra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as O-Marked conditionals, reflecting their ordinary marking.<br />
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最近术语 x 标记已被提议作为替代,唤起额外的标记,这些条件承担。采用这一术语的人将指示性条件句称为 o 标记条件句,反映了他们的普通标记。<br />
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Recently the term ''X-Marked'' has been proposed as a replacement, evoking the ''ex''tra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as ''O-Marked'' conditionals, reflecting their ''o''rdinary marking.<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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The ''antecedent'' of a conditional is sometimes referred to as its ''"if"-clause'' or ''protasis''. The ''consequent'' of a conditional is sometimes referred to as a ''"then"''-clause or as an apodosis.<br />
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==Logic and semantics==<br />
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According to the material conditional analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated. <br />
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根据实质条件的分析,自然语言条件句---- 形式为如果 p 那么 q 的陈述---- 只要其先行词 p 为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是真空的。古德曼用下面的一对来说明这一点,在这个背景下,我们知道正在讨论的那块黄油并没有被加热。<br />
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If that piece of butter had been heated to 150º, it would have melted.<br />
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如果那块黄油被加热到150度,它就会融化。<br />
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Counterfactuals were first discussed by [[Nelson Goodman]] as a problem for the [[material conditional]] used in [[classical logic]]. Because of these problems, early work such as that of [[W.V. Quine]] held that counterfactuals aren't strictly logical, and do not make true or false claims about the world. However, in the 1970s, [[David Lewis (philosopher)|David Lewis]] showed that these problems are surmountable given an appropriate logical framework. Work since then in [[formal semantics (linguistics)|formal semantics]], [[philosophical logic]], [[philosophy of language]], and [[cognitive science]] has built on Lewis's insight, taking it in a variety of different directions.<ref name="Counterfactuals">{{cite encyclopedia |last1=Starr |first1=Will |editor-last1=Zalta |editor-first1=Edward N.|encyclopedia=The Stanford Encyclopedia of Philosophy|title=Counterfactuals|year=2019 |url=https://plato.stanford.edu/archives/fall2019/entries/counterfactuals}}</ref><br />
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If that piece of butter had been heated to 150º, it would not have melted.<br />
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如果那块黄油被加热到150度,它就不会融化。<br />
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===Classic puzzles===<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<br />
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更一般地说,这些例子表明反事实并不是真理功能的。换句话说,知道先行词和结果是否真实并不足以确定反事实本身是否真实。<br />
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====The problem of counterfactuals====<br />
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If Caesar had been in command in Korea, he would have used the atom bomb.<br />
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如果凯撒当时在朝鲜指挥,他会使用原子弹。<br />
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If Caesar had been in command in Korea, he would have used catapults.<br />
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如果凯撒在朝鲜指挥,他会使用投石器。<br />
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According to the [[material conditional]] analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated.<ref name="jstor.org">Goodman, N., "[https://www.jstor.org/stable/2019988 The Problem of Counterfactual Conditionals]", ''The Journal of Philosophy'', Vol. 44, No. 5, (27 February 1947), pp. 113–28.</ref> <br />
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# If that piece of butter had been heated to 150º, it would have melted.<br />
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# If that piece of butter had been heated to 150º, it would not have melted.<br />
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Counterfactuals are non-monotonic in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by Sobel sequences such as the following:<br />
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反事实是非单调的,因为它们的真值可以通过在其先行词中添加额外的材料而改变。这一事实可以通过 Sobel 序列得到说明,例如:<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<ref name="Counterfactuals"/><br />
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If Hannah had drunk coffee, she would be happy.<br />
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如果汉娜喝了咖啡,她会很高兴的。<br />
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====Context dependence and vagueness====<br />
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If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
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如果汉娜喝了咖啡,咖啡里加了汽油,她会伤心的。<br />
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If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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如果汉娜喝了咖啡,咖啡里加了汽油,而汉娜是个喝汽油的机器人,她会很高兴的。<br />
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Counterfactuals are ''context dependent'' and ''[[vague]]''. For example, either of the following statements can be reasonably held true, though not at the same time:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
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One way of formalizing this fact is to say that the principle of Antecedent Strengthening should not hold for any connective > intended as a formalization of natural language conditionals.<br />
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形式化这一事实的一种方法是说,先行强化原则不适用于任何连接词,它是自然语言条件句的形式化。<br />
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# If [[Julius Caesar|Caesar]] had been in command in Korea, he would have [[Korean War#US threat of atomic warfare|used the atom bomb]].<br />
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# If Caesar had been in command in Korea, he would have used catapults.<br />
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====Non-monotonicity====<br />
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Counterfactuals are ''non-monotonic'' in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by ''[[Jordan Howard Sobel|Sobel sequences]]'' such as the following:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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The most common logical accounts of counterfactuals are couched in the possible world semantics. Broadly speaking, these approaches have in common that they treat a counterfactual A > B as true if B holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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反事实的最常见的逻辑解释是可能世界语义学。一般来说,这些方法的共同点是,如果 b 持有一些可能的世界集合,其中 a 是真实的,那么它们就把反事实的 a > b 当作真实的。它们主要在如何识别相关的 a 世界集方面有所不同。<br />
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# If Hannah had drunk coffee, she would be happy.<br />
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David Lewis's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.<br />
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大卫 · 刘易斯多变的严格条件被认为是哲学中的经典分析。安吉利卡 · 克拉策提出的前提语义学是语言学中的一个标准。然而,市场上有许多可能的世界方法,包括最初被 Lewis 摒弃的严格条件分析的动态变体。<br />
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# If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
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# If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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One way of formalizing this fact is to say that the principle of ''Antecedent Strengthening'' should '''not''' hold for any connective > intended as a formalization of natural language conditionals.<br />
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The strict conditional analysis treats natural language counterfactuals as being equivalent to the modal logic formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as material implication. This approach was first proposed in 1912 by C.I. Lewis as part of his axiomatic approach to modal logic.<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式。在这个公式中,Box 表示必要性,right tarrow </math > 被理解为实质条件。这种方法最早是在1912年由 c.i. 提出的。刘易斯的公理化方法的一部分,模态逻辑。<br />
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* '''Antecedent Strengthening''': <math> P > Q \models (P \land R) > Q </math><br />
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=== Possible worlds accounts ===<br />
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The most common logical accounts of counterfactuals are couched in the [[possible world semantics]]. Broadly speaking, these approaches have in common that they treat a counterfactual ''A'' > ''B'' as true if ''B'' holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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In the belief revision framework, counterfactuals are treated using a formal implementation of the Ramsey test. In these systems, a counterfactual A > B holds if and only if the addition of A to the current body of knowledge has B as a consequence. This condition relates counterfactual conditionals to belief revision, as the evaluation of A > B can be done by first revising the current knowledge with A and then checking whether B is true in what results. Revising is easy when A is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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在信念修正框架中,我们使用 Ramsey 测试的一个正式实现来处理反事实问题。在这些系统中,一个反事实的 a > b 成立当且仅当 a 加入到当前的知识体系中的结果是 b。这个条件将反事实条件与信念修正联系起来,因为 a > b 的评估可以通过首先用 a 修正当前的知识,然后检查 b 在什么结果中是否为真来完成。当 a 与当前的信念一致时,复习就容易了,否则就很难了。每个信念修正的语义都可以用于条件语句的求值。反过来,每一种条件求值方法都可以看作是一种执行修正的方法。<br />
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[[David Lewis (philosopher)|David Lewis]]'s ''variably strict conditional'' is considered the classic analysis within philosophy. The closely related ''premise semantics'' proposed by [[Angelika Kratzer]] is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including [[dynamic semantics|dynamic]] variants of the ''strict conditional'' analysis originally dismissed by Lewis.<br />
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====Strict conditional====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of propositional formulae, considering the maximal sets of these formulae that are consistent with A, and adding A to each. The rationale is that each of these maximal sets represents a possible state of belief in which A is true that is as similar as possible to the original one. The conditional statement A > B therefore holds if and only if B is true in all such sets.<br />
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Ginsberg (1986)提出了条件句的语义假设,假设当前的信念构成一组命题公式,考虑这些公式的最大集与 a 相一致,并在每个公式中加入 a。其基本原理是,这些最大集合中的每一个都代表了一种可能的信念状态,其中 a 为真,且尽可能与原始信念相似。因此,If判断语句集 a > b 成立的充要条件是 b 在所有这样的集合中都为真。<br />
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The [[strict conditional]] analysis treats natural language counterfactuals as being equivalent to the [[modal logic]] formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as [[material conditional|material implication]]. This approach was first proposed in 1912 by [[C.I. Lewis]] as part of his [[Axiomatic system|axiomatic approach]] to modal logic.<ref name="Counterfactuals"/> In modern [[relational semantics]], this means that the strict conditional is true at ''w'' iff the corresponding material conditional is true throughout the worlds accessible from ''w''. More formally:<br />
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* Given a model <math>M = \langle W,R,V \rangle</math>, we have that <math> M,w \models \Box(P \rightarrow Q) </math> iff <math>M, v \models P \rightarrow Q </math> for all <math>v</math> such that <math>Rwv</math><br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual morphemes, while others recruit morphemes which otherwise express tense, aspect, mood, or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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语言使用不同的策略来表达反事实。一些语素有专门的反事实语素,而另一些语素则表示时态、方面、语气或者它们的组合。自2000年代初以来,语言学家、语言哲学家和哲学逻辑学家对这种语法标记的本质进行了大量的研究,并且一直是一个活跃的研究领域。<br />
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Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.<br />
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The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.<br />
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This fact led to widespread abandonment of the strict conditional, in particular in favor of Lewis's [[counterfactual conditional#Variably strict conditional|variably strict analysis]]. However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued that ''Sobel sequences'' don't demand a ''non-monotonic'' logic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as the sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. Warmbrōd's idea was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality.<br />
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In many languages, counterfactuality is marked by past tense morphology. Since these uses of the past tense do not convey their typical temporal meaning, they are called fake past or fake tense. English is one language which uses fake past to mark counterfactuality, as shown in the following minimal pair. In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<br />
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在许多语言中,反事实性以过去时态形态学为标志。由于过去时的这些用法没有传达其典型的时间意义,所以它们被称为假过去时或假过去时。英语是一种使用虚假过去来标记反事实性的语言,如下面的最小对所示。在陈述句中,粗体词是现在时态的形式。在反事实的例子中,两个词都采用过去时态。过去时的这种用法不可能有普通的时间意义,因为它可以和副词“明天”一起使用,而不会产生矛盾。<br />
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Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of [[dynamic semantics]], and given a number of linguistic arguments in favor. One argument is that conditional antecedents license [[Polarity item#Determination of licensing contexts|negative polarity items]], which are thought to be licensed only by monotonic operators.<br />
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Indicative: If Natalia leaves tomorrow, she will arrive on time.<br />
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如果娜塔莉亚明天离开,她会准时到达。<br />
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# If Hannah had drunk any coffee, she would be happy.<br />
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Counterfactual: If Natalia left tomorrow, she would arrive on time.<br />
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反事实: 如果娜塔莉亚明天离开,她会准时到达。<br />
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Another argument in favor of the strict conditional comes from [[Irene Heim|Irene Heim's]] observation that Sobel Sequences are generally [[Felicity (pragmatics)|infelicitous]] (i.e. sound strange) in reverse.<br />
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Modern Hebrew is another language where counterfactuality is marked with a fake past morpheme:<br />
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现代希伯来语是另一种用假的过去语素标记反事实性的语言:<br />
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# If Hannah had drunk coffee with gasoline in it, she would not be happy. But if she had drunk coffee, she would be happy.<br />
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| || im || Dani || haya || ba-bayit || maχa ɾ || hayinu || mevakRim || oto<br />
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| || im || Dani || haya || ba-bayit || maχa ɾ || hayinu || mevakRim || oto<br />
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Sarah Moss (2012) and Karen Lewis (2018) have responded to these arguments, showing that a version of the variably strict analysis can account for these patterns, and arguing that such an account is preferable since it can also account for apparent exceptions. As of 2020, this debate continues in the literature, with accounts such as Willer (2019) arguing that a strict conditional account can cover these exceptions as well.<ref name="Counterfactuals"/><br />
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| || if || Dani || be.pst.3sm || in-home || tomorrow || be.pst.1pl || visit.ptc.pl || he.acc<br />
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如果达尼在家里,明天,在家里,在家里,在家里,在家里<br />
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====Variably strict conditional====<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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如果丹妮明天在家,我们就会去看他了<br />
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In the variably strict approach, the semantics of a conditional ''A'' > ''B'' is given by some function on the relative closeness of worlds where A is true and B is true, on the one hand, and worlds where A is true but B is not, on the other.<br />
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Palestinian Arabic is another:<br />
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巴勒斯坦阿拉伯语是另一个例子:<br />
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On Lewis's account, A > C is (a) vacuously true if and only if there are no worlds where A is true (for example, if A is logically or metaphysically impossible); (b) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or (c) false otherwise. Although in Lewis's ''Counterfactuals'' it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did ''not'' intend the metric of 'closeness' to be simply our ordinary notion of [[Similarity (philosophy)#Respective and overall similarity|overall similarity]].<br />
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Example:<br />
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In formal semantics and philosophical logic, fake past is regarded as a puzzle, since it is not obvious why so many unrelated languages would repurpose a tense morpheme to mark counterfactuality. Proposed solutions to this puzzle divide into two camps: past as modal and past as past. These approaches differ in whether or not they take the past tense's core meaning to be about time.<br />
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在形式语义学和哲学逻辑中,虚假的过去被认为是一个谜,因为不明显的是为什么这么多不相关的语言重新使用一个时态语素来标记反事实性。针对这一难题提出的解决办法分为两个阵营: 过去为模式和过去为过去。这些方法的不同之处在于它们是否将过去时的核心意思理解为与时间有关。<br />
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:If he had eaten more at breakfast, he would not have been hungry at 11 am.<br />
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On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where he ate more for breakfast, there is at least one world where he is not hungry at 11 am and which is closer to our world than any world where he ate more for breakfast but is still hungry at 11 am.<br />
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In the past as modal approach, the denotation of the past tense is not fundamentally about time. Rather, it is an underspecified skeleton which can apply either to modal or temporal content. For instance, the particular past as modal proposal of Iatridou (2000), the past tense's core meaning is what's shown schematically below:<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker's account differs from Lewis's most notably in his acceptance of the ''limit'' and ''uniqueness assumptions''. The uniqueness assumption is the thesis that, for any antecedent A, among the possible worlds where A is true, there is a single (''unique'') one that is ''closest'' to the actual world. The limit assumption is the thesis that, for a given antecedent A, if there is a chain of possible worlds where A is true, each closer to the actual world than its predecessor, then the chain has a ''limit'': a possible world where A is true that is closer to the actual worlds than all worlds in the chain. (The uniqueness assumption [[logical consequence|entails]] the limit assumption, but the limit assumption does not entail the uniqueness assumption.) On Stalnaker's account, A > C is non-vacuously true if and only if, at the closest world where A is true, C is true. So, the above example is true just in case at the single, closest world where he ate more breakfast, he does not feel hungry at 11 am. Although it is controversial, Lewis rejected the limit assumption (and therefore the uniqueness assumption) because it rules out the possibility that there might be worlds that get closer and closer to the actual world without limit. For example, there might be an infinite series of worlds, each with a coffee cup a smaller fraction of an inch to the left of its actual position, but none of which is uniquely the closest. (See Lewis 1973: 20.)<br />
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The topic x is not the contextually-provided x<br />
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主题 x 不是上下文提供的 x<br />
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One consequence of Stalnaker's acceptance of the uniqueness assumption is that, if the [[law of excluded middle]] is true, then all instances of the formula (A > C) ∨ (A > ¬C) are true. The law of excluded middle is the thesis that for all propositions p, p ∨ ¬p is true. If the uniqueness assumption is true, then for every antecedent A, there is a uniquely closest world where A is true. If the law of excluded middle is true, any consequent C is either true or false at that world where A is true. So for every counterfactual A > C, either A > C or A > ¬C is true. This is called conditional excluded middle (CEM). Example:<br />
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Depending on how this denotation composes, x can be a time interval or a possible world. When x is a time, the past tense will convey that the sentence is talking about non-current times, i.e. the past. When x is a world, it will convey that the sentence is talking about a potentially non-actual possibility. The latter is what allows for a counterfactual meaning.<br />
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根据这个指称的组成,x 可以是时间间隔,也可以是可能世界。当 x 是时间时,过去时态表示句子指的是非现在时间,也就是说,过去时态指的是非现在时间。过去。当 x 是一个世界时,它将传达出这个句子所指的是一种潜在的不真实的可能性。后者是允许反事实意义的东西。<br />
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:(1) If the fair coin had been flipped, it would have landed heads.<br />
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The past as past approach treats the past tense as having an inherently temporal denotation. On this approach, so-called fake tense isn't actually fake. It differs from "real" tense only in how it takes scope, i.e. which component of the sentence's meaning is shifted to an earlier time. When a sentence has "real" past marking, it discusses something that happened at an earlier time; when a sentence has so-called fake past marking, it discusses possibilities that were accessible at an earlier time but may no longer be.<br />
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过去时作为过去时的方法认为过去时具有内在的时间外延。在这种方法中,所谓的假时态实际上并不是假的。它与“真实”时态的区别仅在于它如何占据范围,即。句子的哪个部分的意思转移到了更早的时间。当一个句子有“真实的”过去标记时,它讨论的是发生在更早的时间的事情; 当一个句子有所谓的“假过去标记”时,它讨论的可能性在更早的时间是可以接受的,但可能不再是。<br />
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:(2) If the fair coin had been flipped, it would have landed tails (i.e. not heads).<br />
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On Stalnaker's analysis, there is a closest world where the fair coin mentioned in (1) and (2) is flipped and at that world either it lands heads or it lands tails. So either (1) is true and (2) is false or (1) is false and (2) true. On Lewis's analysis, however, both (1) and (2) are false, for the worlds where the fair coin lands heads are no more or less close than the worlds where they land tails. For Lewis, "If the coin had been flipped, it would have landed heads or tails" is true, but this does not entail that "If the coin had been flipped, it would have landed heads, or: If the coin had been flipped it would have landed tails."<br />
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=== Other accounts ===<br />
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Fake aspect often accompanies fake tense in languages that mark aspect. In some languages (e.g. Modern Greek, Zulu, and the Romance languages) this fake aspect is imperfective. In other languages (e.g. Palestinian Arabic) it is perfective. However, in other languages including Russian and Polish, counterfactuals can have either perfective or imperfective aspect. In other experiments, participants were asked to read short stories that contained counterfactual conditionals, e.g., ‘If there had been roses in the flower shop then there would have been lilies’. Later in the story, they read sentences corresponding to the presupposed facts, e.g., ‘there were no roses and there were no lilies’. The counterfactual conditional primed them to read the sentence corresponding to the presupposed facts very rapidly; no such priming effect occurred for indicative conditionals. They spent different amounts of time 'updating' a story that contains a counterfactual conditional compared to one that contains factual information and focused on different parts of counterfactual conditionals.<br />
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在标记体的语言中,假体往往伴随着假时态。在某些语言中(例如:。现代希腊语、祖鲁语和罗曼语)这个虚构的部分是不完整的。用其他语言(例如:。巴勒斯坦阿拉伯语)这是完美的。然而,在包括俄语和波兰语在内的其他语言中,反事实可以是完成体或非完整体。在其他实验中,参与者被要求阅读包含反事实条件的短篇小说,例如,如果花店里有玫瑰,那么就会有百合花。在故事的后半部分,他们阅读与预设事实相对应的句子,例如,没有玫瑰,也没有百合。反事实条件让他们非常快速地阅读与预设事实相对应的句子; 指示性条件句则没有这样的启动效应。他们花了不同数量的时间更新一个包含反事实条件的故事,而不是一个包含事实信息的故事,并且关注不同部分的反事实条件句。<br />
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====Causal models====<br />
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Experiments have compared the inferences people make from counterfactual conditionals and indicative conditionals. Given a counterfactual conditional, e.g., 'If there had been a circle on the blackboard then there would have been a triangle', and the subsequent information 'in fact there was no triangle', participants make the modus tollens inference 'there was no circle' more often than they do from an indicative conditional. Given the counterfactual conditional and the subsequent information 'in fact there was a circle', participants make the modus ponens inference as often as they do from an indicative conditional. See counterfactual thinking.<br />
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实验比较了人们从反事实条件句和指示性条件句中得出的推论。给定一个反事实条件,例如,如果黑板上有一个圆,那么就会有一个三角形,并且随后的信息事实上没有三角形,参与者做这种推断的频率比他们从一个直陈条件推断的频率更高。考虑到反事实条件和随后的信息‘事实上存在一个循环’,参与者做这种推理的频率和他们从直陈条件推理的频率一样高。参见反事实思维。<br />
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{{Further|Causal model#Counterfactuals}}<br />
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{{Expand section|date=September 2020}}<br />
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Byrne argues that people construct mental representations that encompass two possibilities when they understand, and reason from, a counterfactual conditional, e.g., 'if Oswald had not shot Kennedy, then someone else would have'. They envisage the conjecture 'Oswald did not shoot Kennedy and someone else did' and they also think about the presupposed facts 'Oswald did shoot Kennedy and someone else did not'. According to the mental model theory of reasoning, they construct mental models of the alternative possibilities.<br />
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认为人们构建的心理表征包括两种可能性,一种是他们理解的反事实条件,另一种是推理,例如,如果 Oswald 没有射杀 Kennedy,那么其他人也会射杀 Kennedy。他们猜想肯尼迪不是奥斯瓦尔德杀的,而是别人杀的,他们还想到了预先假定的事实奥斯瓦尔德确实杀了肯尼迪,而别人没有。根据心理模型推理理论,他们构建了可选择可能性的心理模型。<br />
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The ''causal models framework'' analyzes counterfactuals in terms of systems of [[structural equation model|structural equations]]. In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence "''Y'' would be ''y'' had ''X'' been ''x''" (formally, ''X = x'' > ''Y = y'' ) is defined as the assertion: If we replace the equation currently determining ''X'' with a constant ''X = x'', and solve the set of equations for variable ''Y'', the solution obtained will be ''Y = y''. This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators. This approach was developed by [[Judea Pearl]] (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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====Belief revision====<br />
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{{Further|Belief revision#The Ramsey test}}<br />
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{{Expand section|date=September 2020}}<br />
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In the [[belief revision]] framework, counterfactuals are treated using a formal implementation of the ''Ramsey test''. In these systems, a counterfactual ''A'' > ''B'' holds if and only if the addition of ''A'' to the current body of knowledge has ''B'' as a consequence. This condition relates counterfactual conditionals to [[belief revision]], as the evaluation of ''A'' > ''B'' can be done by first revising the current knowledge with ''A'' and then checking whether ''B'' is true in what results. Revising is easy when ''A'' is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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====Ginsberg====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of [[propositional formula]]e, considering the maximal sets of these formulae that are consistent with ''A'', and adding ''A'' to each. The rationale is that each of these maximal sets represents a possible state of belief in which ''A'' is true that is as similar as possible to the original one. The conditional statement ''A'' > ''B'' therefore holds if and only if ''B'' is true in all such sets.<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref><br />
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== The grammar of counterfactuality ==<br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual [[morphemes]], while others recruit morphemes which otherwise express [[grammatical tense|tense]], [[grammatical aspect|aspect]], [[grammatical mood|mood]], or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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=== Fake tense ===<br />
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==== Description ====<br />
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In many languages, counterfactuality is marked by [[past tense]] morphology.<ref name = "palmer">{{cite book |last=Palmer |first=Frank Robert |date=1986 |title=Mood and modality |publisher= Cambridge University Press}}</ref> Since these uses of the past tense do not convey their typical temporal meaning, they are called ''fake past'' or ''fake tense''.<ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref> English is one language which uses fake past to mark counterfactuality, as shown in the following [[minimal pair]].<ref>English fake past is sometimes erroneously referred to as "subjunctive", even though it is not the [[English subjunctive|subjunctive mood]].</ref> In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<ref name = palmer /><ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref><br />
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# Indicative: If Natalia '''leaves''' tomorrow, she '''will''' arrive on time.<br />
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# Counterfactual: If Natalia '''left''' tomorrow, she '''would''' arrive on time.<br />
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[[Hebrew language|Modern Hebrew]] is another language where counterfactuality is marked with a fake past morpheme:<ref name="karawani">{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><br />
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Category:Conditionals in linguistics<br />
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范畴: 语言学中的条件句<br />
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Category:Grammar<br />
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分类: 语法<br />
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| || im || Dani || '''haya''' || ba-bayit || maχa ɾ || '''hayinu''' || mevakRim || oto<br />
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Category:Semantics<br />
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分类: 语义学<br />
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Category:Belief revision<br />
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类别: 信念修正<br />
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| || if || Dani || be.'''pst'''.3sm || in-home || tomorrow || be.'''pst'''.1pl || visit.ptc.pl || he.acc<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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Category:Linguistic modality<br />
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类别: 情态<br />
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<small>This page was moved from [[wikipedia:en:Counterfactual conditional]]. Its edit history can be viewed at [[反事实/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22714反事实2021-05-30T16:12:55Z<p>Wei:/* Examples */</p>
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{{Short description|Conditionals that discuss what would have been if things were otherwise}}<br />
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{{Redirect|Counterfactual}}<br />
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'''Counterfactual conditionals''' (also ''subjunctive'' or ''X-marked'') are [[conditional sentence]]s which discuss what would have been true under different circumstances, e.g. <!-- this is example is from Iatridou (2000), ex (47c) on p. 244 --> "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with [[indicative conditionals|indicatives]], which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of [[Counterfactual conditional#Fake tense|fake tense morphology]], which some languages use in combination with other kinds of [[Morphology (linguistics)|morphology]] including [[Counterfactual conditional#Fake aspect|aspect]] and [[Counterfactual conditional#mood|mood]].<br />
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反事实条件句(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的条件句。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
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Counterfactuals are one of the most studied phenomena in [[philosophical logic]], [[formal semantics (natural language)|formal semantics]], and [[philosophy of language]]. They were first discussed as a problem for the [[material conditional]] analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic [[possible world]] approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as [[causal model]]s and [[dynamic semantics]]. Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是微不足道的真实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==Overview==<br />
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=== Examples ===<br />
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The difference between [[indicative conditional|indicative]] and counterfactual conditionals can be illustrated by the following [[minimal pair]]:<br />
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指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
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# '''Indicative Conditional''': If it ''is'' raining right now, then Sally ''is'' inside. <br />
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# '''指示条件句''': 如果现在正在下雨,那么Sally 就在里面(If it ''is'' raining right now, then Sally ''is'' inside)。 <br />
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# '''Simple Past Counterfactual''': If it ''was raining'' <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally ''would be'' inside.<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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Simple Past Counterfactual: If it was raining <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally would be inside.<br />
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# '''一般过去时的反事实''':如果现在正在下雨,那么Sally就会在里面(If it was raining right now, then Sally would be inside)。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "is" in both the "if" clause and the "then" clause. As a result, it conveys that the speaker is agnostic about whether it is raining. The counterfactual example uses the [[fake tense]] form "was" in the "if" clause and the [[modal verb|modal]] "would" in the "then" clause. As a result, it conveys that the speaker does not believe that it is raining.<br />
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这些条件句在形式和意义上都不同。指示条件在“如果(if)”和 “那么(then)”两个从句中都使用现在时态is。因此,它传达了这样一种信息:说话人对是否下雨是不可知的。反事实的例句在“如果”从句中使用虚拟时态“was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,说话人并不相信天在下雨。<br />
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English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the [[pluperfect|past perfect]] counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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英语还有其他几种语法形式,其含义有时被包括在反事实的范畴内。其中一个是过去完成时的反事实,在使用过去完成时态时,它与指示词和一般完成时的反事实形成对比:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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# '''Past Perfect Counterfactual''': If it ''had been raining'' yesterday, then Sally ''would have been'' inside.<br />
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# '''过去完成时的反事实''':如果昨天下了雨,那么Sally就会在里面(If it ''had been raining'' yesterday, then Sally ''would have been'' inside)。<br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<br />
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另一种条件句的用法是“were”,一般称为“非现实(irrealis)”或“虚拟(subjunctive)”。<br />
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# '''Irrealis Counterfactual''': If it ''were raining'' right now, then Sally ''would be'' inside.<br />
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# '''非现实反事实(Irrealis Counterfactual)''':如果现在正在下雨,那么Sally应该在里面(If it ''were raining'' right now, then Sally ''would be'' inside)。<br />
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Past perfect and irrealis counterfactuals can undergo ''conditional inversion'':<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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过去完成时和非现实的反事实可以进行条件倒置:<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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# Were it raining, Sally would be inside.<br />
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# 如果下雨的话,Sally就会在里面(Were it raining, Sally would be inside)。<br />
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# Had it rained, Sally would be inside.<br />
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# 那时如果下雨的话,Sally就会在里面(Had it rained, Sally would be inside)。<br />
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=== Terminology ===<br />
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<!-- Given the vast but often subtle differences in terminology, this section has to be edited with a lot of care. Before clicking "publish changes", please consider whether the resulting text will help a reader understand how these terms are used. If the resulting text reads like a "is a hotdog a sandwich debate?" with all the character cues removed, please don't click "publish changes". In particular, please be sure to (1) clearly distinguish factual claims from definitions of terms (2) remember that different sources may use a single term in different ways (3) situate each term or usage of a term by giving a framework-neutral explanation of how it is used.--><br />
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<!-- Given the vast but often subtle differences in terminology, this section has to be edited with a lot of care. Before clicking "publish changes", please consider whether the resulting text will help a reader understand how these terms are used. If the resulting text reads like a "is a hotdog a sandwich debate?" with all the character cues removed, please don't click "publish changes". In particular, please be sure to (1) clearly distinguish factual claims from definitions of terms (2) remember that different sources may use a single term in different ways (3) situate each term or usage of a term by giving a framework-neutral explanation of how it is used.--><br />
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<!——鉴于术语上的巨大但往往是细微的差异,本节必须经过仔细的编辑。在点击“发布更改”之前,请考虑结果文本是否有助于读者理解这些术语是如何使用的。如果结果文本读起来像是“热狗是三明治的辩论吗?”删除所有字符提示后,请不要点击”发布更改”。特别是,请确保(1)明确区分事实主张和术语定义(2)记住,不同的来源可以以不同的方式使用单一术语(3)对术语的每个术语或用法进行不偏不倚的框架性解释。--><br />
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The term ''counterfactual conditional'' is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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The term counterfactual conditional is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<br />
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反事实条件这个术语被广泛地用作上面所显示的各种句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,经典的例子被称为“ Anderson 格”,它具有反事实条件的典型语法形式,但是并没有表明它的先行词是假的或者不可能的。<br />
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# '''Anderson Case''': If the patient had taken arsenic, he would have blue spots.<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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Anderson Case: If the patient had taken arsenic, he would have blue spots.<br />
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安德森病例: 如果病人服用了砒霜,他会长出蓝色斑点。<br />
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Such conditionals are also widely referred to as ''subjunctive conditionals'', though this term is likewise acknowledged as a misnomer even by those who use it.<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref> Many languages do not have a morphological [[subjunctive]] (e.g. [[Danish grammar|Danish]] and [[Dutch grammar|Dutch]]) and many that do have it don’t use it for this sort of conditional (e.g. [[French grammar|French]], [[Swahili grammar|Swahili]], all [[Indo-Aryan languages]] that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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Such conditionals are also widely referred to as subjunctive conditionals, though this term is likewise acknowledged as a misnomer even by those who use it. Many languages do not have a morphological subjunctive (e.g. Danish and Dutch) and many that do have it don’t use it for this sort of conditional (e.g. French, Swahili, all Indo-Aryan languages that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<br />
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这种条件句也被广泛地称为虚拟条件句,尽管这个术语同样被使用者认为是用词不当。许多语言都没有形态虚拟语气。丹麦语和荷兰语)和许多有这个词的人不用它来表示这种条件句(例如:。法语,斯瓦希里语,所有的印度-雅利安语支都有虚拟语气)。此外,对于这样的条件句使用虚拟语气的语言,只有在具有特定的过去虚拟形式的情况下才会使用虚拟语气。因此,虚拟标记既不是必要的,也不足以成为这类条件句的成员。<br />
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The terms ''counterfactual'' and ''subjunctive'' have sometimes been repurposed for more specific uses. For instance, the term "counterfactual" is sometimes applied to conditionals that express a contrary-to-fact meaning, regardless of their grammatical structure.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" /> Along similar lines, the term "subjunctive" is sometimes used to refer to conditionals that bear fake past or irrealis marking, regardless of the meaning they convey.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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Recently the term X-Marked has been proposed as a replacement, evoking the extra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as O-Marked conditionals, reflecting their ordinary marking.<br />
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最近术语 x 标记已被提议作为替代,唤起额外的标记,这些条件承担。采用这一术语的人将指示性条件句称为 o 标记条件句,反映了他们的普通标记。<br />
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Recently the term ''X-Marked'' has been proposed as a replacement, evoking the ''ex''tra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as ''O-Marked'' conditionals, reflecting their ''o''rdinary marking.<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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The ''antecedent'' of a conditional is sometimes referred to as its ''"if"-clause'' or ''protasis''. The ''consequent'' of a conditional is sometimes referred to as a ''"then"''-clause or as an apodosis.<br />
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==Logic and semantics==<br />
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According to the material conditional analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated. <br />
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根据实质条件的分析,自然语言条件句---- 形式为如果 p 那么 q 的陈述---- 只要其先行词 p 为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是真空的。古德曼用下面的一对来说明这一点,在这个背景下,我们知道正在讨论的那块黄油并没有被加热。<br />
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If that piece of butter had been heated to 150º, it would have melted.<br />
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如果那块黄油被加热到150度,它就会融化。<br />
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Counterfactuals were first discussed by [[Nelson Goodman]] as a problem for the [[material conditional]] used in [[classical logic]]. Because of these problems, early work such as that of [[W.V. Quine]] held that counterfactuals aren't strictly logical, and do not make true or false claims about the world. However, in the 1970s, [[David Lewis (philosopher)|David Lewis]] showed that these problems are surmountable given an appropriate logical framework. Work since then in [[formal semantics (linguistics)|formal semantics]], [[philosophical logic]], [[philosophy of language]], and [[cognitive science]] has built on Lewis's insight, taking it in a variety of different directions.<ref name="Counterfactuals">{{cite encyclopedia |last1=Starr |first1=Will |editor-last1=Zalta |editor-first1=Edward N.|encyclopedia=The Stanford Encyclopedia of Philosophy|title=Counterfactuals|year=2019 |url=https://plato.stanford.edu/archives/fall2019/entries/counterfactuals}}</ref><br />
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If that piece of butter had been heated to 150º, it would not have melted.<br />
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如果那块黄油被加热到150度,它就不会融化。<br />
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===Classic puzzles===<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<br />
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更一般地说,这些例子表明反事实并不是真理功能的。换句话说,知道先行词和结果是否真实并不足以确定反事实本身是否真实。<br />
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====The problem of counterfactuals====<br />
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If Caesar had been in command in Korea, he would have used the atom bomb.<br />
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如果凯撒当时在朝鲜指挥,他会使用原子弹。<br />
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If Caesar had been in command in Korea, he would have used catapults.<br />
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如果凯撒在朝鲜指挥,他会使用投石器。<br />
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According to the [[material conditional]] analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated.<ref name="jstor.org">Goodman, N., "[https://www.jstor.org/stable/2019988 The Problem of Counterfactual Conditionals]", ''The Journal of Philosophy'', Vol. 44, No. 5, (27 February 1947), pp. 113–28.</ref> <br />
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# If that piece of butter had been heated to 150º, it would have melted.<br />
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# If that piece of butter had been heated to 150º, it would not have melted.<br />
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Counterfactuals are non-monotonic in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by Sobel sequences such as the following:<br />
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反事实是非单调的,因为它们的真值可以通过在其先行词中添加额外的材料而改变。这一事实可以通过 Sobel 序列得到说明,例如:<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<ref name="Counterfactuals"/><br />
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If Hannah had drunk coffee, she would be happy.<br />
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如果汉娜喝了咖啡,她会很高兴的。<br />
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====Context dependence and vagueness====<br />
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If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
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如果汉娜喝了咖啡,咖啡里加了汽油,她会伤心的。<br />
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If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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如果汉娜喝了咖啡,咖啡里加了汽油,而汉娜是个喝汽油的机器人,她会很高兴的。<br />
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Counterfactuals are ''context dependent'' and ''[[vague]]''. For example, either of the following statements can be reasonably held true, though not at the same time:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
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One way of formalizing this fact is to say that the principle of Antecedent Strengthening should not hold for any connective > intended as a formalization of natural language conditionals.<br />
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形式化这一事实的一种方法是说,先行强化原则不适用于任何连接词,它是自然语言条件句的形式化。<br />
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# If [[Julius Caesar|Caesar]] had been in command in Korea, he would have [[Korean War#US threat of atomic warfare|used the atom bomb]].<br />
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# If Caesar had been in command in Korea, he would have used catapults.<br />
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====Non-monotonicity====<br />
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Counterfactuals are ''non-monotonic'' in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by ''[[Jordan Howard Sobel|Sobel sequences]]'' such as the following:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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The most common logical accounts of counterfactuals are couched in the possible world semantics. Broadly speaking, these approaches have in common that they treat a counterfactual A > B as true if B holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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反事实的最常见的逻辑解释是可能世界语义学。一般来说,这些方法的共同点是,如果 b 持有一些可能的世界集合,其中 a 是真实的,那么它们就把反事实的 a > b 当作真实的。它们主要在如何识别相关的 a 世界集方面有所不同。<br />
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# If Hannah had drunk coffee, she would be happy.<br />
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David Lewis's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.<br />
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大卫 · 刘易斯多变的严格条件被认为是哲学中的经典分析。安吉利卡 · 克拉策提出的前提语义学是语言学中的一个标准。然而,市场上有许多可能的世界方法,包括最初被 Lewis 摒弃的严格条件分析的动态变体。<br />
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# If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
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# If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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One way of formalizing this fact is to say that the principle of ''Antecedent Strengthening'' should '''not''' hold for any connective > intended as a formalization of natural language conditionals.<br />
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The strict conditional analysis treats natural language counterfactuals as being equivalent to the modal logic formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as material implication. This approach was first proposed in 1912 by C.I. Lewis as part of his axiomatic approach to modal logic.<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式。在这个公式中,Box 表示必要性,right tarrow </math > 被理解为实质条件。这种方法最早是在1912年由 c.i. 提出的。刘易斯的公理化方法的一部分,模态逻辑。<br />
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* '''Antecedent Strengthening''': <math> P > Q \models (P \land R) > Q </math><br />
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=== Possible worlds accounts ===<br />
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The most common logical accounts of counterfactuals are couched in the [[possible world semantics]]. Broadly speaking, these approaches have in common that they treat a counterfactual ''A'' > ''B'' as true if ''B'' holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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In the belief revision framework, counterfactuals are treated using a formal implementation of the Ramsey test. In these systems, a counterfactual A > B holds if and only if the addition of A to the current body of knowledge has B as a consequence. This condition relates counterfactual conditionals to belief revision, as the evaluation of A > B can be done by first revising the current knowledge with A and then checking whether B is true in what results. Revising is easy when A is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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在信念修正框架中,我们使用 Ramsey 测试的一个正式实现来处理反事实问题。在这些系统中,一个反事实的 a > b 成立当且仅当 a 加入到当前的知识体系中的结果是 b。这个条件将反事实条件与信念修正联系起来,因为 a > b 的评估可以通过首先用 a 修正当前的知识,然后检查 b 在什么结果中是否为真来完成。当 a 与当前的信念一致时,复习就容易了,否则就很难了。每个信念修正的语义都可以用于条件语句的求值。反过来,每一种条件求值方法都可以看作是一种执行修正的方法。<br />
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[[David Lewis (philosopher)|David Lewis]]'s ''variably strict conditional'' is considered the classic analysis within philosophy. The closely related ''premise semantics'' proposed by [[Angelika Kratzer]] is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including [[dynamic semantics|dynamic]] variants of the ''strict conditional'' analysis originally dismissed by Lewis.<br />
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====Strict conditional====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of propositional formulae, considering the maximal sets of these formulae that are consistent with A, and adding A to each. The rationale is that each of these maximal sets represents a possible state of belief in which A is true that is as similar as possible to the original one. The conditional statement A > B therefore holds if and only if B is true in all such sets.<br />
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Ginsberg (1986)提出了条件句的语义假设,假设当前的信念构成一组命题公式,考虑这些公式的最大集与 a 相一致,并在每个公式中加入 a。其基本原理是,这些最大集合中的每一个都代表了一种可能的信念状态,其中 a 为真,且尽可能与原始信念相似。因此,If判断语句集 a > b 成立的充要条件是 b 在所有这样的集合中都为真。<br />
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The [[strict conditional]] analysis treats natural language counterfactuals as being equivalent to the [[modal logic]] formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as [[material conditional|material implication]]. This approach was first proposed in 1912 by [[C.I. Lewis]] as part of his [[Axiomatic system|axiomatic approach]] to modal logic.<ref name="Counterfactuals"/> In modern [[relational semantics]], this means that the strict conditional is true at ''w'' iff the corresponding material conditional is true throughout the worlds accessible from ''w''. More formally:<br />
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* Given a model <math>M = \langle W,R,V \rangle</math>, we have that <math> M,w \models \Box(P \rightarrow Q) </math> iff <math>M, v \models P \rightarrow Q </math> for all <math>v</math> such that <math>Rwv</math><br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual morphemes, while others recruit morphemes which otherwise express tense, aspect, mood, or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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语言使用不同的策略来表达反事实。一些语素有专门的反事实语素,而另一些语素则表示时态、方面、语气或者它们的组合。自2000年代初以来,语言学家、语言哲学家和哲学逻辑学家对这种语法标记的本质进行了大量的研究,并且一直是一个活跃的研究领域。<br />
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Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.<br />
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The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.<br />
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This fact led to widespread abandonment of the strict conditional, in particular in favor of Lewis's [[counterfactual conditional#Variably strict conditional|variably strict analysis]]. However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued that ''Sobel sequences'' don't demand a ''non-monotonic'' logic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as the sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. Warmbrōd's idea was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality.<br />
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In many languages, counterfactuality is marked by past tense morphology. Since these uses of the past tense do not convey their typical temporal meaning, they are called fake past or fake tense. English is one language which uses fake past to mark counterfactuality, as shown in the following minimal pair. In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<br />
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在许多语言中,反事实性以过去时态形态学为标志。由于过去时的这些用法没有传达其典型的时间意义,所以它们被称为假过去时或假过去时。英语是一种使用虚假过去来标记反事实性的语言,如下面的最小对所示。在陈述句中,粗体词是现在时态的形式。在反事实的例子中,两个词都采用过去时态。过去时的这种用法不可能有普通的时间意义,因为它可以和副词“明天”一起使用,而不会产生矛盾。<br />
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Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of [[dynamic semantics]], and given a number of linguistic arguments in favor. One argument is that conditional antecedents license [[Polarity item#Determination of licensing contexts|negative polarity items]], which are thought to be licensed only by monotonic operators.<br />
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Indicative: If Natalia leaves tomorrow, she will arrive on time.<br />
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如果娜塔莉亚明天离开,她会准时到达。<br />
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# If Hannah had drunk any coffee, she would be happy.<br />
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Counterfactual: If Natalia left tomorrow, she would arrive on time.<br />
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反事实: 如果娜塔莉亚明天离开,她会准时到达。<br />
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Another argument in favor of the strict conditional comes from [[Irene Heim|Irene Heim's]] observation that Sobel Sequences are generally [[Felicity (pragmatics)|infelicitous]] (i.e. sound strange) in reverse.<br />
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Modern Hebrew is another language where counterfactuality is marked with a fake past morpheme:<br />
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现代希伯来语是另一种用假的过去语素标记反事实性的语言:<br />
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# If Hannah had drunk coffee with gasoline in it, she would not be happy. But if she had drunk coffee, she would be happy.<br />
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{| <br />
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| || im || Dani || haya || ba-bayit || maχa ɾ || hayinu || mevakRim || oto<br />
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| || im || Dani || haya || ba-bayit || maχa ɾ || hayinu || mevakRim || oto<br />
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Sarah Moss (2012) and Karen Lewis (2018) have responded to these arguments, showing that a version of the variably strict analysis can account for these patterns, and arguing that such an account is preferable since it can also account for apparent exceptions. As of 2020, this debate continues in the literature, with accounts such as Willer (2019) arguing that a strict conditional account can cover these exceptions as well.<ref name="Counterfactuals"/><br />
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| || if || Dani || be.pst.3sm || in-home || tomorrow || be.pst.1pl || visit.ptc.pl || he.acc<br />
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如果达尼在家里,明天,在家里,在家里,在家里,在家里<br />
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====Variably strict conditional====<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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如果丹妮明天在家,我们就会去看他了<br />
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In the variably strict approach, the semantics of a conditional ''A'' > ''B'' is given by some function on the relative closeness of worlds where A is true and B is true, on the one hand, and worlds where A is true but B is not, on the other.<br />
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Palestinian Arabic is another:<br />
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巴勒斯坦阿拉伯语是另一个例子:<br />
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On Lewis's account, A > C is (a) vacuously true if and only if there are no worlds where A is true (for example, if A is logically or metaphysically impossible); (b) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or (c) false otherwise. Although in Lewis's ''Counterfactuals'' it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did ''not'' intend the metric of 'closeness' to be simply our ordinary notion of [[Similarity (philosophy)#Respective and overall similarity|overall similarity]].<br />
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Example:<br />
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In formal semantics and philosophical logic, fake past is regarded as a puzzle, since it is not obvious why so many unrelated languages would repurpose a tense morpheme to mark counterfactuality. Proposed solutions to this puzzle divide into two camps: past as modal and past as past. These approaches differ in whether or not they take the past tense's core meaning to be about time.<br />
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在形式语义学和哲学逻辑中,虚假的过去被认为是一个谜,因为不明显的是为什么这么多不相关的语言重新使用一个时态语素来标记反事实性。针对这一难题提出的解决办法分为两个阵营: 过去为模式和过去为过去。这些方法的不同之处在于它们是否将过去时的核心意思理解为与时间有关。<br />
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:If he had eaten more at breakfast, he would not have been hungry at 11 am.<br />
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On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where he ate more for breakfast, there is at least one world where he is not hungry at 11 am and which is closer to our world than any world where he ate more for breakfast but is still hungry at 11 am.<br />
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In the past as modal approach, the denotation of the past tense is not fundamentally about time. Rather, it is an underspecified skeleton which can apply either to modal or temporal content. For instance, the particular past as modal proposal of Iatridou (2000), the past tense's core meaning is what's shown schematically below:<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker's account differs from Lewis's most notably in his acceptance of the ''limit'' and ''uniqueness assumptions''. The uniqueness assumption is the thesis that, for any antecedent A, among the possible worlds where A is true, there is a single (''unique'') one that is ''closest'' to the actual world. The limit assumption is the thesis that, for a given antecedent A, if there is a chain of possible worlds where A is true, each closer to the actual world than its predecessor, then the chain has a ''limit'': a possible world where A is true that is closer to the actual worlds than all worlds in the chain. (The uniqueness assumption [[logical consequence|entails]] the limit assumption, but the limit assumption does not entail the uniqueness assumption.) On Stalnaker's account, A > C is non-vacuously true if and only if, at the closest world where A is true, C is true. So, the above example is true just in case at the single, closest world where he ate more breakfast, he does not feel hungry at 11 am. Although it is controversial, Lewis rejected the limit assumption (and therefore the uniqueness assumption) because it rules out the possibility that there might be worlds that get closer and closer to the actual world without limit. For example, there might be an infinite series of worlds, each with a coffee cup a smaller fraction of an inch to the left of its actual position, but none of which is uniquely the closest. (See Lewis 1973: 20.)<br />
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The topic x is not the contextually-provided x<br />
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主题 x 不是上下文提供的 x<br />
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One consequence of Stalnaker's acceptance of the uniqueness assumption is that, if the [[law of excluded middle]] is true, then all instances of the formula (A > C) ∨ (A > ¬C) are true. The law of excluded middle is the thesis that for all propositions p, p ∨ ¬p is true. If the uniqueness assumption is true, then for every antecedent A, there is a uniquely closest world where A is true. If the law of excluded middle is true, any consequent C is either true or false at that world where A is true. So for every counterfactual A > C, either A > C or A > ¬C is true. This is called conditional excluded middle (CEM). Example:<br />
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Depending on how this denotation composes, x can be a time interval or a possible world. When x is a time, the past tense will convey that the sentence is talking about non-current times, i.e. the past. When x is a world, it will convey that the sentence is talking about a potentially non-actual possibility. The latter is what allows for a counterfactual meaning.<br />
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根据这个指称的组成,x 可以是时间间隔,也可以是可能世界。当 x 是时间时,过去时态表示句子指的是非现在时间,也就是说,过去时态指的是非现在时间。过去。当 x 是一个世界时,它将传达出这个句子所指的是一种潜在的不真实的可能性。后者是允许反事实意义的东西。<br />
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:(1) If the fair coin had been flipped, it would have landed heads.<br />
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The past as past approach treats the past tense as having an inherently temporal denotation. On this approach, so-called fake tense isn't actually fake. It differs from "real" tense only in how it takes scope, i.e. which component of the sentence's meaning is shifted to an earlier time. When a sentence has "real" past marking, it discusses something that happened at an earlier time; when a sentence has so-called fake past marking, it discusses possibilities that were accessible at an earlier time but may no longer be.<br />
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过去时作为过去时的方法认为过去时具有内在的时间外延。在这种方法中,所谓的假时态实际上并不是假的。它与“真实”时态的区别仅在于它如何占据范围,即。句子的哪个部分的意思转移到了更早的时间。当一个句子有“真实的”过去标记时,它讨论的是发生在更早的时间的事情; 当一个句子有所谓的“假过去标记”时,它讨论的可能性在更早的时间是可以接受的,但可能不再是。<br />
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:(2) If the fair coin had been flipped, it would have landed tails (i.e. not heads).<br />
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On Stalnaker's analysis, there is a closest world where the fair coin mentioned in (1) and (2) is flipped and at that world either it lands heads or it lands tails. So either (1) is true and (2) is false or (1) is false and (2) true. On Lewis's analysis, however, both (1) and (2) are false, for the worlds where the fair coin lands heads are no more or less close than the worlds where they land tails. For Lewis, "If the coin had been flipped, it would have landed heads or tails" is true, but this does not entail that "If the coin had been flipped, it would have landed heads, or: If the coin had been flipped it would have landed tails."<br />
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=== Other accounts ===<br />
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Fake aspect often accompanies fake tense in languages that mark aspect. In some languages (e.g. Modern Greek, Zulu, and the Romance languages) this fake aspect is imperfective. In other languages (e.g. Palestinian Arabic) it is perfective. However, in other languages including Russian and Polish, counterfactuals can have either perfective or imperfective aspect. In other experiments, participants were asked to read short stories that contained counterfactual conditionals, e.g., ‘If there had been roses in the flower shop then there would have been lilies’. Later in the story, they read sentences corresponding to the presupposed facts, e.g., ‘there were no roses and there were no lilies’. The counterfactual conditional primed them to read the sentence corresponding to the presupposed facts very rapidly; no such priming effect occurred for indicative conditionals. They spent different amounts of time 'updating' a story that contains a counterfactual conditional compared to one that contains factual information and focused on different parts of counterfactual conditionals.<br />
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在标记体的语言中,假体往往伴随着假时态。在某些语言中(例如:。现代希腊语、祖鲁语和罗曼语)这个虚构的部分是不完整的。用其他语言(例如:。巴勒斯坦阿拉伯语)这是完美的。然而,在包括俄语和波兰语在内的其他语言中,反事实可以是完成体或非完整体。在其他实验中,参与者被要求阅读包含反事实条件的短篇小说,例如,如果花店里有玫瑰,那么就会有百合花。在故事的后半部分,他们阅读与预设事实相对应的句子,例如,没有玫瑰,也没有百合。反事实条件让他们非常快速地阅读与预设事实相对应的句子; 指示性条件句则没有这样的启动效应。他们花了不同数量的时间更新一个包含反事实条件的故事,而不是一个包含事实信息的故事,并且关注不同部分的反事实条件句。<br />
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====Causal models====<br />
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Experiments have compared the inferences people make from counterfactual conditionals and indicative conditionals. Given a counterfactual conditional, e.g., 'If there had been a circle on the blackboard then there would have been a triangle', and the subsequent information 'in fact there was no triangle', participants make the modus tollens inference 'there was no circle' more often than they do from an indicative conditional. Given the counterfactual conditional and the subsequent information 'in fact there was a circle', participants make the modus ponens inference as often as they do from an indicative conditional. See counterfactual thinking.<br />
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实验比较了人们从反事实条件句和指示性条件句中得出的推论。给定一个反事实条件,例如,如果黑板上有一个圆,那么就会有一个三角形,并且随后的信息事实上没有三角形,参与者做这种推断的频率比他们从一个直陈条件推断的频率更高。考虑到反事实条件和随后的信息‘事实上存在一个循环’,参与者做这种推理的频率和他们从直陈条件推理的频率一样高。参见反事实思维。<br />
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{{Further|Causal model#Counterfactuals}}<br />
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{{Expand section|date=September 2020}}<br />
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Byrne argues that people construct mental representations that encompass two possibilities when they understand, and reason from, a counterfactual conditional, e.g., 'if Oswald had not shot Kennedy, then someone else would have'. They envisage the conjecture 'Oswald did not shoot Kennedy and someone else did' and they also think about the presupposed facts 'Oswald did shoot Kennedy and someone else did not'. According to the mental model theory of reasoning, they construct mental models of the alternative possibilities.<br />
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认为人们构建的心理表征包括两种可能性,一种是他们理解的反事实条件,另一种是推理,例如,如果 Oswald 没有射杀 Kennedy,那么其他人也会射杀 Kennedy。他们猜想肯尼迪不是奥斯瓦尔德杀的,而是别人杀的,他们还想到了预先假定的事实奥斯瓦尔德确实杀了肯尼迪,而别人没有。根据心理模型推理理论,他们构建了可选择可能性的心理模型。<br />
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The ''causal models framework'' analyzes counterfactuals in terms of systems of [[structural equation model|structural equations]]. In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence "''Y'' would be ''y'' had ''X'' been ''x''" (formally, ''X = x'' > ''Y = y'' ) is defined as the assertion: If we replace the equation currently determining ''X'' with a constant ''X = x'', and solve the set of equations for variable ''Y'', the solution obtained will be ''Y = y''. This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators. This approach was developed by [[Judea Pearl]] (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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====Belief revision====<br />
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{{Further|Belief revision#The Ramsey test}}<br />
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{{Expand section|date=September 2020}}<br />
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In the [[belief revision]] framework, counterfactuals are treated using a formal implementation of the ''Ramsey test''. In these systems, a counterfactual ''A'' > ''B'' holds if and only if the addition of ''A'' to the current body of knowledge has ''B'' as a consequence. This condition relates counterfactual conditionals to [[belief revision]], as the evaluation of ''A'' > ''B'' can be done by first revising the current knowledge with ''A'' and then checking whether ''B'' is true in what results. Revising is easy when ''A'' is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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====Ginsberg====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of [[propositional formula]]e, considering the maximal sets of these formulae that are consistent with ''A'', and adding ''A'' to each. The rationale is that each of these maximal sets represents a possible state of belief in which ''A'' is true that is as similar as possible to the original one. The conditional statement ''A'' > ''B'' therefore holds if and only if ''B'' is true in all such sets.<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref><br />
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== The grammar of counterfactuality ==<br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual [[morphemes]], while others recruit morphemes which otherwise express [[grammatical tense|tense]], [[grammatical aspect|aspect]], [[grammatical mood|mood]], or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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=== Fake tense ===<br />
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==== Description ====<br />
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In many languages, counterfactuality is marked by [[past tense]] morphology.<ref name = "palmer">{{cite book |last=Palmer |first=Frank Robert |date=1986 |title=Mood and modality |publisher= Cambridge University Press}}</ref> Since these uses of the past tense do not convey their typical temporal meaning, they are called ''fake past'' or ''fake tense''.<ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref> English is one language which uses fake past to mark counterfactuality, as shown in the following [[minimal pair]].<ref>English fake past is sometimes erroneously referred to as "subjunctive", even though it is not the [[English subjunctive|subjunctive mood]].</ref> In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<ref name = palmer /><ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref><br />
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# Indicative: If Natalia '''leaves''' tomorrow, she '''will''' arrive on time.<br />
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# Counterfactual: If Natalia '''left''' tomorrow, she '''would''' arrive on time.<br />
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[[Hebrew language|Modern Hebrew]] is another language where counterfactuality is marked with a fake past morpheme:<ref name="karawani">{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><br />
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Category:Conditionals in linguistics<br />
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范畴: 语言学中的条件句<br />
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:: {| <br />
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Category:Grammar<br />
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分类: 语法<br />
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| || im || Dani || '''haya''' || ba-bayit || maχa ɾ || '''hayinu''' || mevakRim || oto<br />
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Category:Semantics<br />
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分类: 语义学<br />
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Category:Belief revision<br />
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类别: 信念修正<br />
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| || if || Dani || be.'''pst'''.3sm || in-home || tomorrow || be.'''pst'''.1pl || visit.ptc.pl || he.acc<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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Category:Linguistic modality<br />
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类别: 情态<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Counterfactual conditional]]. Its edit history can be viewed at [[反事实/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22713反事实2021-05-30T15:58:26Z<p>Wei:</p>
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{{Short description|Conditionals that discuss what would have been if things were otherwise}}<br />
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{{Redirect|Counterfactual}}<br />
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'''Counterfactual conditionals''' (also ''subjunctive'' or ''X-marked'') are [[conditional sentence]]s which discuss what would have been true under different circumstances, e.g. <!-- this is example is from Iatridou (2000), ex (47c) on p. 244 --> "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with [[indicative conditionals|indicatives]], which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of [[Counterfactual conditional#Fake tense|fake tense morphology]], which some languages use in combination with other kinds of [[Morphology (linguistics)|morphology]] including [[Counterfactual conditional#Fake aspect|aspect]] and [[Counterfactual conditional#mood|mood]].<br />
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反事实条件句(虚拟条件或X标记的)是用来讨论在不同情况下什么为真的的条件句。例如:如果彼得相信鬼魂的存在,他就会害怕来到这里。反事实句与指示句形成对比,后者一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚拟时态语法,这种虚拟时态语法与时态和语态等其他语法结合使用。<br />
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Counterfactuals are one of the most studied phenomena in [[philosophical logic]], [[formal semantics (natural language)|formal semantics]], and [[philosophy of language]]. They were first discussed as a problem for the [[material conditional]] analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic [[possible world]] approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as [[causal model]]s and [[dynamic semantics]]. Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是微不足道的真实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学、心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==Overview==<br />
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=== Examples ===<br />
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The difference between [[indicative conditional|indicative]] and counterfactual conditionals can be illustrated by the following [[minimal pair]]:<br />
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指示条件句和反事实条件句之间的区别可以用下面的简单例子来说明:<br />
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# '''Indicative Conditional''': If it ''is'' raining right now, then Sally ''is'' inside. <br />
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# ''指示条件句''': 如果现在正在下雨,那么Sally 就在里面。 <br />
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# '''Simple Past Counterfactual''': If it ''was raining'' <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally ''would be'' inside.<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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Simple Past Counterfactual: If it was raining <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally would be inside.<br />
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# ''简单过去反事实''':如果现在正在下雨,那么Sally就会在里面。<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "is" in both the "if" clause and the "then" clause. As a result, it conveys that the speaker is agnostic about whether it is raining. The counterfactual example uses the [[fake tense]] form "was" in the "if" clause and the [[modal verb|modal]] "would" in the "then" clause. As a result, it conveys that the speaker does not believe that it is raining.<br />
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These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "is" in both the "if" clause and the "then" clause. As a result, it conveys that the speaker is agnostic about whether it is raining. The counterfactual example uses the fake tense form "was" in the "if" clause and the modal "would" in the "then" clause. As a result, it conveys that the speaker does not believe that it is raining.<br />
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这些条件句在形式和意义上都不同。直陈条件在 if 和 then 两个从句中都使用现在时态形式 is。因此,它传达了这样一种信息: 演讲者对是否下雨是不可知的。反事实例句在“如果”句中使用假的时态“ was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,演讲者并不相信天在下雨。<br />
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English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the [[pluperfect|past perfect]] counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the past perfect counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:<br />
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英语还有其他几种语法形式,它们的意思有时被包括在反事实的范畴内。一个是过去完美反事实,它在使用过去完美形态时,与标志词和简单的过去反事实形成对比:<br />
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# '''Past Perfect Counterfactual''': If it ''had been raining'' yesterday, then Sally ''would have been'' inside.<br />
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Past Perfect Counterfactual: If it had been raining yesterday, then Sally would have been inside.<br />
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过去完美反事实: 如果昨天一直在下雨,那么萨莉应该在里面。<br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<br />
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另一种条件用法是“ were”,一般称为“ irrealis”或“ subjunctive”。<br />
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# '''Irrealis Counterfactual''': If it ''were raining'' right now, then Sally ''would be'' inside.<br />
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Irrealis Counterfactual: If it were raining right now, then Sally would be inside.<br />
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非现实: 如果现在正在下雨,那么萨利应该在里面。<br />
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Past perfect and irrealis counterfactuals can undergo ''conditional inversion'':<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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Past perfect and irrealis counterfactuals can undergo conditional inversion:<br />
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过去完成式和非现实式反事实可以经历条件反转:<br />
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# Were it raining, Sally would be inside.<br />
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Were it raining, Sally would be inside.<br />
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如果下雨的话,萨利就会在里面。<br />
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# Had it rained, Sally would be inside.<br />
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Had it rained, Sally would be inside.<br />
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如果下雨的话,萨莉就会在里面。<br />
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=== Terminology ===<br />
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<!-- Given the vast but often subtle differences in terminology, this section has to be edited with a lot of care. Before clicking "publish changes", please consider whether the resulting text will help a reader understand how these terms are used. If the resulting text reads like a "is a hotdog a sandwich debate?" with all the character cues removed, please don't click "publish changes". In particular, please be sure to (1) clearly distinguish factual claims from definitions of terms (2) remember that different sources may use a single term in different ways (3) situate each term or usage of a term by giving a framework-neutral explanation of how it is used.--><br />
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<!——鉴于术语上的巨大但往往是细微的差异,本节必须经过仔细的编辑。在点击“发布更改”之前,请考虑结果文本是否有助于读者理解这些术语是如何使用的。如果结果文本读起来像是“热狗是三明治的辩论吗?”删除所有字符提示后,请不要点击”发布更改”。特别是,请确保(1)明确区分事实主张和术语定义(2)记住,不同的来源可以以不同的方式使用单一术语(3)对术语的每个术语或用法进行不偏不倚的框架性解释。--><br />
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The term ''counterfactual conditional'' is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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The term counterfactual conditional is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<br />
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反事实条件这个术语被广泛地用作上面所显示的各种句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,经典的例子被称为“ Anderson 格”,它具有反事实条件的典型语法形式,但是并没有表明它的先行词是假的或者不可能的。<br />
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# '''Anderson Case''': If the patient had taken arsenic, he would have blue spots.<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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Anderson Case: If the patient had taken arsenic, he would have blue spots.<br />
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安德森病例: 如果病人服用了砒霜,他会长出蓝色斑点。<br />
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Such conditionals are also widely referred to as ''subjunctive conditionals'', though this term is likewise acknowledged as a misnomer even by those who use it.<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref> Many languages do not have a morphological [[subjunctive]] (e.g. [[Danish grammar|Danish]] and [[Dutch grammar|Dutch]]) and many that do have it don’t use it for this sort of conditional (e.g. [[French grammar|French]], [[Swahili grammar|Swahili]], all [[Indo-Aryan languages]] that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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Such conditionals are also widely referred to as subjunctive conditionals, though this term is likewise acknowledged as a misnomer even by those who use it. Many languages do not have a morphological subjunctive (e.g. Danish and Dutch) and many that do have it don’t use it for this sort of conditional (e.g. French, Swahili, all Indo-Aryan languages that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<br />
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这种条件句也被广泛地称为虚拟条件句,尽管这个术语同样被使用者认为是用词不当。许多语言都没有形态虚拟语气。丹麦语和荷兰语)和许多有这个词的人不用它来表示这种条件句(例如:。法语,斯瓦希里语,所有的印度-雅利安语支都有虚拟语气)。此外,对于这样的条件句使用虚拟语气的语言,只有在具有特定的过去虚拟形式的情况下才会使用虚拟语气。因此,虚拟标记既不是必要的,也不足以成为这类条件句的成员。<br />
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The terms ''counterfactual'' and ''subjunctive'' have sometimes been repurposed for more specific uses. For instance, the term "counterfactual" is sometimes applied to conditionals that express a contrary-to-fact meaning, regardless of their grammatical structure.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" /> Along similar lines, the term "subjunctive" is sometimes used to refer to conditionals that bear fake past or irrealis marking, regardless of the meaning they convey.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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Recently the term X-Marked has been proposed as a replacement, evoking the extra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as O-Marked conditionals, reflecting their ordinary marking.<br />
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最近术语 x 标记已被提议作为替代,唤起额外的标记,这些条件承担。采用这一术语的人将指示性条件句称为 o 标记条件句,反映了他们的普通标记。<br />
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Recently the term ''X-Marked'' has been proposed as a replacement, evoking the ''ex''tra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as ''O-Marked'' conditionals, reflecting their ''o''rdinary marking.<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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The ''antecedent'' of a conditional is sometimes referred to as its ''"if"-clause'' or ''protasis''. The ''consequent'' of a conditional is sometimes referred to as a ''"then"''-clause or as an apodosis.<br />
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==Logic and semantics==<br />
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According to the material conditional analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated. <br />
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根据实质条件的分析,自然语言条件句---- 形式为如果 p 那么 q 的陈述---- 只要其先行词 p 为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是真空的。古德曼用下面的一对来说明这一点,在这个背景下,我们知道正在讨论的那块黄油并没有被加热。<br />
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If that piece of butter had been heated to 150º, it would have melted.<br />
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如果那块黄油被加热到150度,它就会融化。<br />
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Counterfactuals were first discussed by [[Nelson Goodman]] as a problem for the [[material conditional]] used in [[classical logic]]. Because of these problems, early work such as that of [[W.V. Quine]] held that counterfactuals aren't strictly logical, and do not make true or false claims about the world. However, in the 1970s, [[David Lewis (philosopher)|David Lewis]] showed that these problems are surmountable given an appropriate logical framework. Work since then in [[formal semantics (linguistics)|formal semantics]], [[philosophical logic]], [[philosophy of language]], and [[cognitive science]] has built on Lewis's insight, taking it in a variety of different directions.<ref name="Counterfactuals">{{cite encyclopedia |last1=Starr |first1=Will |editor-last1=Zalta |editor-first1=Edward N.|encyclopedia=The Stanford Encyclopedia of Philosophy|title=Counterfactuals|year=2019 |url=https://plato.stanford.edu/archives/fall2019/entries/counterfactuals}}</ref><br />
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If that piece of butter had been heated to 150º, it would not have melted.<br />
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如果那块黄油被加热到150度,它就不会融化。<br />
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===Classic puzzles===<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<br />
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更一般地说,这些例子表明反事实并不是真理功能的。换句话说,知道先行词和结果是否真实并不足以确定反事实本身是否真实。<br />
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====The problem of counterfactuals====<br />
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If Caesar had been in command in Korea, he would have used the atom bomb.<br />
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如果凯撒当时在朝鲜指挥,他会使用原子弹。<br />
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If Caesar had been in command in Korea, he would have used catapults.<br />
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如果凯撒在朝鲜指挥,他会使用投石器。<br />
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According to the [[material conditional]] analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated.<ref name="jstor.org">Goodman, N., "[https://www.jstor.org/stable/2019988 The Problem of Counterfactual Conditionals]", ''The Journal of Philosophy'', Vol. 44, No. 5, (27 February 1947), pp. 113–28.</ref> <br />
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# If that piece of butter had been heated to 150º, it would have melted.<br />
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# If that piece of butter had been heated to 150º, it would not have melted.<br />
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Counterfactuals are non-monotonic in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by Sobel sequences such as the following:<br />
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反事实是非单调的,因为它们的真值可以通过在其先行词中添加额外的材料而改变。这一事实可以通过 Sobel 序列得到说明,例如:<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<ref name="Counterfactuals"/><br />
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If Hannah had drunk coffee, she would be happy.<br />
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如果汉娜喝了咖啡,她会很高兴的。<br />
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====Context dependence and vagueness====<br />
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If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
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如果汉娜喝了咖啡,咖啡里加了汽油,她会伤心的。<br />
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If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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如果汉娜喝了咖啡,咖啡里加了汽油,而汉娜是个喝汽油的机器人,她会很高兴的。<br />
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Counterfactuals are ''context dependent'' and ''[[vague]]''. For example, either of the following statements can be reasonably held true, though not at the same time:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
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One way of formalizing this fact is to say that the principle of Antecedent Strengthening should not hold for any connective > intended as a formalization of natural language conditionals.<br />
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形式化这一事实的一种方法是说,先行强化原则不适用于任何连接词,它是自然语言条件句的形式化。<br />
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# If [[Julius Caesar|Caesar]] had been in command in Korea, he would have [[Korean War#US threat of atomic warfare|used the atom bomb]].<br />
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# If Caesar had been in command in Korea, he would have used catapults.<br />
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====Non-monotonicity====<br />
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Counterfactuals are ''non-monotonic'' in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by ''[[Jordan Howard Sobel|Sobel sequences]]'' such as the following:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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The most common logical accounts of counterfactuals are couched in the possible world semantics. Broadly speaking, these approaches have in common that they treat a counterfactual A > B as true if B holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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反事实的最常见的逻辑解释是可能世界语义学。一般来说,这些方法的共同点是,如果 b 持有一些可能的世界集合,其中 a 是真实的,那么它们就把反事实的 a > b 当作真实的。它们主要在如何识别相关的 a 世界集方面有所不同。<br />
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# If Hannah had drunk coffee, she would be happy.<br />
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David Lewis's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.<br />
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大卫 · 刘易斯多变的严格条件被认为是哲学中的经典分析。安吉利卡 · 克拉策提出的前提语义学是语言学中的一个标准。然而,市场上有许多可能的世界方法,包括最初被 Lewis 摒弃的严格条件分析的动态变体。<br />
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# If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
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# If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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One way of formalizing this fact is to say that the principle of ''Antecedent Strengthening'' should '''not''' hold for any connective > intended as a formalization of natural language conditionals.<br />
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The strict conditional analysis treats natural language counterfactuals as being equivalent to the modal logic formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as material implication. This approach was first proposed in 1912 by C.I. Lewis as part of his axiomatic approach to modal logic.<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式。在这个公式中,Box 表示必要性,right tarrow </math > 被理解为实质条件。这种方法最早是在1912年由 c.i. 提出的。刘易斯的公理化方法的一部分,模态逻辑。<br />
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* '''Antecedent Strengthening''': <math> P > Q \models (P \land R) > Q </math><br />
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=== Possible worlds accounts ===<br />
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The most common logical accounts of counterfactuals are couched in the [[possible world semantics]]. Broadly speaking, these approaches have in common that they treat a counterfactual ''A'' > ''B'' as true if ''B'' holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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In the belief revision framework, counterfactuals are treated using a formal implementation of the Ramsey test. In these systems, a counterfactual A > B holds if and only if the addition of A to the current body of knowledge has B as a consequence. This condition relates counterfactual conditionals to belief revision, as the evaluation of A > B can be done by first revising the current knowledge with A and then checking whether B is true in what results. Revising is easy when A is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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在信念修正框架中,我们使用 Ramsey 测试的一个正式实现来处理反事实问题。在这些系统中,一个反事实的 a > b 成立当且仅当 a 加入到当前的知识体系中的结果是 b。这个条件将反事实条件与信念修正联系起来,因为 a > b 的评估可以通过首先用 a 修正当前的知识,然后检查 b 在什么结果中是否为真来完成。当 a 与当前的信念一致时,复习就容易了,否则就很难了。每个信念修正的语义都可以用于条件语句的求值。反过来,每一种条件求值方法都可以看作是一种执行修正的方法。<br />
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[[David Lewis (philosopher)|David Lewis]]'s ''variably strict conditional'' is considered the classic analysis within philosophy. The closely related ''premise semantics'' proposed by [[Angelika Kratzer]] is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including [[dynamic semantics|dynamic]] variants of the ''strict conditional'' analysis originally dismissed by Lewis.<br />
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====Strict conditional====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of propositional formulae, considering the maximal sets of these formulae that are consistent with A, and adding A to each. The rationale is that each of these maximal sets represents a possible state of belief in which A is true that is as similar as possible to the original one. The conditional statement A > B therefore holds if and only if B is true in all such sets.<br />
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Ginsberg (1986)提出了条件句的语义假设,假设当前的信念构成一组命题公式,考虑这些公式的最大集与 a 相一致,并在每个公式中加入 a。其基本原理是,这些最大集合中的每一个都代表了一种可能的信念状态,其中 a 为真,且尽可能与原始信念相似。因此,If判断语句集 a > b 成立的充要条件是 b 在所有这样的集合中都为真。<br />
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The [[strict conditional]] analysis treats natural language counterfactuals as being equivalent to the [[modal logic]] formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as [[material conditional|material implication]]. This approach was first proposed in 1912 by [[C.I. Lewis]] as part of his [[Axiomatic system|axiomatic approach]] to modal logic.<ref name="Counterfactuals"/> In modern [[relational semantics]], this means that the strict conditional is true at ''w'' iff the corresponding material conditional is true throughout the worlds accessible from ''w''. More formally:<br />
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* Given a model <math>M = \langle W,R,V \rangle</math>, we have that <math> M,w \models \Box(P \rightarrow Q) </math> iff <math>M, v \models P \rightarrow Q </math> for all <math>v</math> such that <math>Rwv</math><br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual morphemes, while others recruit morphemes which otherwise express tense, aspect, mood, or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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语言使用不同的策略来表达反事实。一些语素有专门的反事实语素,而另一些语素则表示时态、方面、语气或者它们的组合。自2000年代初以来,语言学家、语言哲学家和哲学逻辑学家对这种语法标记的本质进行了大量的研究,并且一直是一个活跃的研究领域。<br />
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Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.<br />
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The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.<br />
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This fact led to widespread abandonment of the strict conditional, in particular in favor of Lewis's [[counterfactual conditional#Variably strict conditional|variably strict analysis]]. However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued that ''Sobel sequences'' don't demand a ''non-monotonic'' logic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as the sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. Warmbrōd's idea was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality.<br />
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In many languages, counterfactuality is marked by past tense morphology. Since these uses of the past tense do not convey their typical temporal meaning, they are called fake past or fake tense. English is one language which uses fake past to mark counterfactuality, as shown in the following minimal pair. In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<br />
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在许多语言中,反事实性以过去时态形态学为标志。由于过去时的这些用法没有传达其典型的时间意义,所以它们被称为假过去时或假过去时。英语是一种使用虚假过去来标记反事实性的语言,如下面的最小对所示。在陈述句中,粗体词是现在时态的形式。在反事实的例子中,两个词都采用过去时态。过去时的这种用法不可能有普通的时间意义,因为它可以和副词“明天”一起使用,而不会产生矛盾。<br />
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Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of [[dynamic semantics]], and given a number of linguistic arguments in favor. One argument is that conditional antecedents license [[Polarity item#Determination of licensing contexts|negative polarity items]], which are thought to be licensed only by monotonic operators.<br />
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Indicative: If Natalia leaves tomorrow, she will arrive on time.<br />
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如果娜塔莉亚明天离开,她会准时到达。<br />
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# If Hannah had drunk any coffee, she would be happy.<br />
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Counterfactual: If Natalia left tomorrow, she would arrive on time.<br />
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反事实: 如果娜塔莉亚明天离开,她会准时到达。<br />
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Another argument in favor of the strict conditional comes from [[Irene Heim|Irene Heim's]] observation that Sobel Sequences are generally [[Felicity (pragmatics)|infelicitous]] (i.e. sound strange) in reverse.<br />
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Modern Hebrew is another language where counterfactuality is marked with a fake past morpheme:<br />
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现代希伯来语是另一种用假的过去语素标记反事实性的语言:<br />
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# If Hannah had drunk coffee with gasoline in it, she would not be happy. But if she had drunk coffee, she would be happy.<br />
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{| <br />
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| || im || Dani || haya || ba-bayit || maχa ɾ || hayinu || mevakRim || oto<br />
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| || im || Dani || haya || ba-bayit || maχa ɾ || hayinu || mevakRim || oto<br />
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Sarah Moss (2012) and Karen Lewis (2018) have responded to these arguments, showing that a version of the variably strict analysis can account for these patterns, and arguing that such an account is preferable since it can also account for apparent exceptions. As of 2020, this debate continues in the literature, with accounts such as Willer (2019) arguing that a strict conditional account can cover these exceptions as well.<ref name="Counterfactuals"/><br />
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| || if || Dani || be.pst.3sm || in-home || tomorrow || be.pst.1pl || visit.ptc.pl || he.acc<br />
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如果达尼在家里,明天,在家里,在家里,在家里,在家里<br />
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====Variably strict conditional====<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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如果丹妮明天在家,我们就会去看他了<br />
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In the variably strict approach, the semantics of a conditional ''A'' > ''B'' is given by some function on the relative closeness of worlds where A is true and B is true, on the one hand, and worlds where A is true but B is not, on the other.<br />
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Palestinian Arabic is another:<br />
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巴勒斯坦阿拉伯语是另一个例子:<br />
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On Lewis's account, A > C is (a) vacuously true if and only if there are no worlds where A is true (for example, if A is logically or metaphysically impossible); (b) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or (c) false otherwise. Although in Lewis's ''Counterfactuals'' it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did ''not'' intend the metric of 'closeness' to be simply our ordinary notion of [[Similarity (philosophy)#Respective and overall similarity|overall similarity]].<br />
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Example:<br />
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In formal semantics and philosophical logic, fake past is regarded as a puzzle, since it is not obvious why so many unrelated languages would repurpose a tense morpheme to mark counterfactuality. Proposed solutions to this puzzle divide into two camps: past as modal and past as past. These approaches differ in whether or not they take the past tense's core meaning to be about time.<br />
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在形式语义学和哲学逻辑中,虚假的过去被认为是一个谜,因为不明显的是为什么这么多不相关的语言重新使用一个时态语素来标记反事实性。针对这一难题提出的解决办法分为两个阵营: 过去为模式和过去为过去。这些方法的不同之处在于它们是否将过去时的核心意思理解为与时间有关。<br />
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:If he had eaten more at breakfast, he would not have been hungry at 11 am.<br />
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On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where he ate more for breakfast, there is at least one world where he is not hungry at 11 am and which is closer to our world than any world where he ate more for breakfast but is still hungry at 11 am.<br />
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In the past as modal approach, the denotation of the past tense is not fundamentally about time. Rather, it is an underspecified skeleton which can apply either to modal or temporal content. For instance, the particular past as modal proposal of Iatridou (2000), the past tense's core meaning is what's shown schematically below:<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker's account differs from Lewis's most notably in his acceptance of the ''limit'' and ''uniqueness assumptions''. The uniqueness assumption is the thesis that, for any antecedent A, among the possible worlds where A is true, there is a single (''unique'') one that is ''closest'' to the actual world. The limit assumption is the thesis that, for a given antecedent A, if there is a chain of possible worlds where A is true, each closer to the actual world than its predecessor, then the chain has a ''limit'': a possible world where A is true that is closer to the actual worlds than all worlds in the chain. (The uniqueness assumption [[logical consequence|entails]] the limit assumption, but the limit assumption does not entail the uniqueness assumption.) On Stalnaker's account, A > C is non-vacuously true if and only if, at the closest world where A is true, C is true. So, the above example is true just in case at the single, closest world where he ate more breakfast, he does not feel hungry at 11 am. Although it is controversial, Lewis rejected the limit assumption (and therefore the uniqueness assumption) because it rules out the possibility that there might be worlds that get closer and closer to the actual world without limit. For example, there might be an infinite series of worlds, each with a coffee cup a smaller fraction of an inch to the left of its actual position, but none of which is uniquely the closest. (See Lewis 1973: 20.)<br />
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The topic x is not the contextually-provided x<br />
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主题 x 不是上下文提供的 x<br />
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One consequence of Stalnaker's acceptance of the uniqueness assumption is that, if the [[law of excluded middle]] is true, then all instances of the formula (A > C) ∨ (A > ¬C) are true. The law of excluded middle is the thesis that for all propositions p, p ∨ ¬p is true. If the uniqueness assumption is true, then for every antecedent A, there is a uniquely closest world where A is true. If the law of excluded middle is true, any consequent C is either true or false at that world where A is true. So for every counterfactual A > C, either A > C or A > ¬C is true. This is called conditional excluded middle (CEM). Example:<br />
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Depending on how this denotation composes, x can be a time interval or a possible world. When x is a time, the past tense will convey that the sentence is talking about non-current times, i.e. the past. When x is a world, it will convey that the sentence is talking about a potentially non-actual possibility. The latter is what allows for a counterfactual meaning.<br />
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根据这个指称的组成,x 可以是时间间隔,也可以是可能世界。当 x 是时间时,过去时态表示句子指的是非现在时间,也就是说,过去时态指的是非现在时间。过去。当 x 是一个世界时,它将传达出这个句子所指的是一种潜在的不真实的可能性。后者是允许反事实意义的东西。<br />
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:(1) If the fair coin had been flipped, it would have landed heads.<br />
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The past as past approach treats the past tense as having an inherently temporal denotation. On this approach, so-called fake tense isn't actually fake. It differs from "real" tense only in how it takes scope, i.e. which component of the sentence's meaning is shifted to an earlier time. When a sentence has "real" past marking, it discusses something that happened at an earlier time; when a sentence has so-called fake past marking, it discusses possibilities that were accessible at an earlier time but may no longer be.<br />
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过去时作为过去时的方法认为过去时具有内在的时间外延。在这种方法中,所谓的假时态实际上并不是假的。它与“真实”时态的区别仅在于它如何占据范围,即。句子的哪个部分的意思转移到了更早的时间。当一个句子有“真实的”过去标记时,它讨论的是发生在更早的时间的事情; 当一个句子有所谓的“假过去标记”时,它讨论的可能性在更早的时间是可以接受的,但可能不再是。<br />
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:(2) If the fair coin had been flipped, it would have landed tails (i.e. not heads).<br />
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On Stalnaker's analysis, there is a closest world where the fair coin mentioned in (1) and (2) is flipped and at that world either it lands heads or it lands tails. So either (1) is true and (2) is false or (1) is false and (2) true. On Lewis's analysis, however, both (1) and (2) are false, for the worlds where the fair coin lands heads are no more or less close than the worlds where they land tails. For Lewis, "If the coin had been flipped, it would have landed heads or tails" is true, but this does not entail that "If the coin had been flipped, it would have landed heads, or: If the coin had been flipped it would have landed tails."<br />
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=== Other accounts ===<br />
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Fake aspect often accompanies fake tense in languages that mark aspect. In some languages (e.g. Modern Greek, Zulu, and the Romance languages) this fake aspect is imperfective. In other languages (e.g. Palestinian Arabic) it is perfective. However, in other languages including Russian and Polish, counterfactuals can have either perfective or imperfective aspect. In other experiments, participants were asked to read short stories that contained counterfactual conditionals, e.g., ‘If there had been roses in the flower shop then there would have been lilies’. Later in the story, they read sentences corresponding to the presupposed facts, e.g., ‘there were no roses and there were no lilies’. The counterfactual conditional primed them to read the sentence corresponding to the presupposed facts very rapidly; no such priming effect occurred for indicative conditionals. They spent different amounts of time 'updating' a story that contains a counterfactual conditional compared to one that contains factual information and focused on different parts of counterfactual conditionals.<br />
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在标记体的语言中,假体往往伴随着假时态。在某些语言中(例如:。现代希腊语、祖鲁语和罗曼语)这个虚构的部分是不完整的。用其他语言(例如:。巴勒斯坦阿拉伯语)这是完美的。然而,在包括俄语和波兰语在内的其他语言中,反事实可以是完成体或非完整体。在其他实验中,参与者被要求阅读包含反事实条件的短篇小说,例如,如果花店里有玫瑰,那么就会有百合花。在故事的后半部分,他们阅读与预设事实相对应的句子,例如,没有玫瑰,也没有百合。反事实条件让他们非常快速地阅读与预设事实相对应的句子; 指示性条件句则没有这样的启动效应。他们花了不同数量的时间更新一个包含反事实条件的故事,而不是一个包含事实信息的故事,并且关注不同部分的反事实条件句。<br />
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====Causal models====<br />
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Experiments have compared the inferences people make from counterfactual conditionals and indicative conditionals. Given a counterfactual conditional, e.g., 'If there had been a circle on the blackboard then there would have been a triangle', and the subsequent information 'in fact there was no triangle', participants make the modus tollens inference 'there was no circle' more often than they do from an indicative conditional. Given the counterfactual conditional and the subsequent information 'in fact there was a circle', participants make the modus ponens inference as often as they do from an indicative conditional. See counterfactual thinking.<br />
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实验比较了人们从反事实条件句和指示性条件句中得出的推论。给定一个反事实条件,例如,如果黑板上有一个圆,那么就会有一个三角形,并且随后的信息事实上没有三角形,参与者做这种推断的频率比他们从一个直陈条件推断的频率更高。考虑到反事实条件和随后的信息‘事实上存在一个循环’,参与者做这种推理的频率和他们从直陈条件推理的频率一样高。参见反事实思维。<br />
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{{Further|Causal model#Counterfactuals}}<br />
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{{Expand section|date=September 2020}}<br />
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Byrne argues that people construct mental representations that encompass two possibilities when they understand, and reason from, a counterfactual conditional, e.g., 'if Oswald had not shot Kennedy, then someone else would have'. They envisage the conjecture 'Oswald did not shoot Kennedy and someone else did' and they also think about the presupposed facts 'Oswald did shoot Kennedy and someone else did not'. According to the mental model theory of reasoning, they construct mental models of the alternative possibilities.<br />
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认为人们构建的心理表征包括两种可能性,一种是他们理解的反事实条件,另一种是推理,例如,如果 Oswald 没有射杀 Kennedy,那么其他人也会射杀 Kennedy。他们猜想肯尼迪不是奥斯瓦尔德杀的,而是别人杀的,他们还想到了预先假定的事实奥斯瓦尔德确实杀了肯尼迪,而别人没有。根据心理模型推理理论,他们构建了可选择可能性的心理模型。<br />
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The ''causal models framework'' analyzes counterfactuals in terms of systems of [[structural equation model|structural equations]]. In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence "''Y'' would be ''y'' had ''X'' been ''x''" (formally, ''X = x'' > ''Y = y'' ) is defined as the assertion: If we replace the equation currently determining ''X'' with a constant ''X = x'', and solve the set of equations for variable ''Y'', the solution obtained will be ''Y = y''. This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators. This approach was developed by [[Judea Pearl]] (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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====Belief revision====<br />
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{{Further|Belief revision#The Ramsey test}}<br />
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{{Expand section|date=September 2020}}<br />
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In the [[belief revision]] framework, counterfactuals are treated using a formal implementation of the ''Ramsey test''. In these systems, a counterfactual ''A'' > ''B'' holds if and only if the addition of ''A'' to the current body of knowledge has ''B'' as a consequence. This condition relates counterfactual conditionals to [[belief revision]], as the evaluation of ''A'' > ''B'' can be done by first revising the current knowledge with ''A'' and then checking whether ''B'' is true in what results. Revising is easy when ''A'' is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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====Ginsberg====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of [[propositional formula]]e, considering the maximal sets of these formulae that are consistent with ''A'', and adding ''A'' to each. The rationale is that each of these maximal sets represents a possible state of belief in which ''A'' is true that is as similar as possible to the original one. The conditional statement ''A'' > ''B'' therefore holds if and only if ''B'' is true in all such sets.<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref><br />
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== The grammar of counterfactuality ==<br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual [[morphemes]], while others recruit morphemes which otherwise express [[grammatical tense|tense]], [[grammatical aspect|aspect]], [[grammatical mood|mood]], or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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=== Fake tense ===<br />
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==== Description ====<br />
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In many languages, counterfactuality is marked by [[past tense]] morphology.<ref name = "palmer">{{cite book |last=Palmer |first=Frank Robert |date=1986 |title=Mood and modality |publisher= Cambridge University Press}}</ref> Since these uses of the past tense do not convey their typical temporal meaning, they are called ''fake past'' or ''fake tense''.<ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref> English is one language which uses fake past to mark counterfactuality, as shown in the following [[minimal pair]].<ref>English fake past is sometimes erroneously referred to as "subjunctive", even though it is not the [[English subjunctive|subjunctive mood]].</ref> In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<ref name = palmer /><ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref><br />
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# Indicative: If Natalia '''leaves''' tomorrow, she '''will''' arrive on time.<br />
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# Counterfactual: If Natalia '''left''' tomorrow, she '''would''' arrive on time.<br />
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[[Hebrew language|Modern Hebrew]] is another language where counterfactuality is marked with a fake past morpheme:<ref name="karawani">{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><br />
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Category:Conditionals in linguistics<br />
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范畴: 语言学中的条件句<br />
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Category:Grammar<br />
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分类: 语法<br />
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| || im || Dani || '''haya''' || ba-bayit || maχa ɾ || '''hayinu''' || mevakRim || oto<br />
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Category:Semantics<br />
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分类: 语义学<br />
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Category:Belief revision<br />
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| || if || Dani || be.'''pst'''.3sm || in-home || tomorrow || be.'''pst'''.1pl || visit.ptc.pl || he.acc<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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Category:Linguistic modality<br />
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类别: 情态<br />
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<small>This page was moved from [[wikipedia:en:Counterfactual conditional]]. Its edit history can be viewed at [[反事实/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E5%8F%8D%E4%BA%8B%E5%AE%9E&diff=22702反事实2021-05-30T12:46:05Z<p>Wei:</p>
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{{Short description|Conditionals that discuss what would have been if things were otherwise}}<br />
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{{Redirect|Counterfactual}}<br />
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'''Counterfactual conditionals''' (also ''subjunctive'' or ''X-marked'') are [[conditional sentence]]s which discuss what would have been true under different circumstances, e.g. <!-- this is example is from Iatridou (2000), ex (47c) on p. 244 --> "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with [[indicative conditionals|indicatives]], which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of [[Counterfactual conditional#Fake tense|fake tense morphology]], which some languages use in combination with other kinds of [[Morphology (linguistics)|morphology]] including [[Counterfactual conditional#Fake aspect|aspect]] and [[Counterfactual conditional#mood|mood]].<br />
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反事实条件句(也是虚拟或 x 标记的)是条件句,用来讨论在不同情况下什么是真的,例如:。“如果彼得相信鬼魂的存在,他就会害怕来到这里。”反事实与标记形成对比,标记一般只限于讨论开放的可能性。反事实动词的语法特征是使用虚假的时态形态,这种虚假的时态形态与体、语气等其他形态结合使用。<br />
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Counterfactuals are one of the most studied phenomena in [[philosophical logic]], [[formal semantics (natural language)|formal semantics]], and [[philosophy of language]]. They were first discussed as a problem for the [[material conditional]] analysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classic [[possible world]] approach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such as [[causal model]]s and [[dynamic semantics]]. Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.<br />
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反事实是哲学逻辑、形式语义学和语言哲学中研究最多的现象之一。它们首先作为条件句的实质条件分析的问题被讨论,条件句把它们都当作是微不足道的真实。从20世纪60年代开始,哲学家和语言学家发展出现在经典的可能世界方法,在这种方法中,反事实的真理取决于它在某些可能世界中的后果,而这些可能世界的前因是成立的。最近的形式化分析使用因果模型和动态语义等工具对它们进行了处理。其他研究已经解决了他们的形而上学,心理学和语法基础,同时将一些结果的见解应用到包括历史,市场营销和流行病学领域。<br />
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==Overview==<br />
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=== Examples ===<br />
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The difference between [[indicative conditional|indicative]] and counterfactual conditionals can be illustrated by the following [[minimal pair]]:<br />
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The difference between indicative and counterfactual conditionals can be illustrated by the following minimal pair:<br />
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指示性条件句和反事实条件句之间的区别可以用下面的最小对来说明:<br />
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# '''Indicative Conditional''': If it ''is'' raining right now, then Sally ''is'' inside. <br />
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Indicative Conditional: If it is raining right now, then Sally is inside. <br />
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直陈条件: 如果现在正在下雨,那么 Sally 就在里面。<br />
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# '''Simple Past Counterfactual''': If it ''was raining'' <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally ''would be'' inside.<ref>{{cite journal |last1=von Prince |first1=Kilu |date=2019 |title=Counterfactuality and past |url=https://link.springer.com/content/pdf/10.1007/s10988-019-09259-6.pdf |journal=Linguistics and Philosophy |volume=42 |issue=6|pages=577–615 |doi=10.1007/s10988-019-09259-6 |s2cid=181778834 |doi-access=free }}</ref><ref>{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |page=186 |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><ref name="Linguistic Society of America">{{cite conference |url=https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/27.547 |title=Fake Perfect in X-Marked Conditionals |last1=Schulz |first1=Katrin |date=2017 |publisher=Linguistic Society of America |book-title=Proceedings from Semantics and Linguistic Theory. |pages=547–570 |conference= Semantics and Linguistic Theory.|doi=10.3765/salt.v27i0.4149|doi-access=free }}</ref><ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |isbn=978-0521431460|pages=85–86}}</ref><br />
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Simple Past Counterfactual: If it was raining <!-- See discussion on talk page of "was" vs "were" --> right now, then Sally would be inside.<br />
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简单过去反事实: 如果现在正在下雨,见聊天页面" was" vs" were" -- > ,那么萨莉就会在里面。<br />
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These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "is" in both the "if" clause and the "then" clause. As a result, it conveys that the speaker is agnostic about whether it is raining. The counterfactual example uses the [[fake tense]] form "was" in the "if" clause and the [[modal verb|modal]] "would" in the "then" clause. As a result, it conveys that the speaker does not believe that it is raining.<br />
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These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "is" in both the "if" clause and the "then" clause. As a result, it conveys that the speaker is agnostic about whether it is raining. The counterfactual example uses the fake tense form "was" in the "if" clause and the modal "would" in the "then" clause. As a result, it conveys that the speaker does not believe that it is raining.<br />
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这些条件句在形式和意义上都不同。直陈条件在 if 和 then 两个从句中都使用现在时态形式 is。因此,它传达了这样一种信息: 演讲者对是否下雨是不可知的。反事实例句在“如果”句中使用假的时态“ was”,在“ then”句中使用情态“ would”。因此,它传达的信息是,演讲者并不相信天在下雨。<br />
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English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the [[pluperfect|past perfect]] counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:<ref>{{cite book |last1=Huddleston |first1=Rodney | last2=Pullum |first2=Geoff |date=2002 |title= The Cambridge Grammar of the English Language |publisher=Cambridge University Press |page=150 |isbn=978-0521431460}}</ref><br />
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English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the past perfect counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:<br />
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英语还有其他几种语法形式,它们的意思有时被包括在反事实的范畴内。一个是过去完美反事实,它在使用过去完美形态时,与标志词和简单的过去反事实形成对比:<br />
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# '''Past Perfect Counterfactual''': If it ''had been raining'' yesterday, then Sally ''would have been'' inside.<br />
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Past Perfect Counterfactual: If it had been raining yesterday, then Sally would have been inside.<br />
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过去完美反事实: 如果昨天一直在下雨,那么萨莉应该在里面。<br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<ref>There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.</ref><br />
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Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.<br />
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另一种条件用法是“ were”,一般称为“ irrealis”或“ subjunctive”。<br />
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# '''Irrealis Counterfactual''': If it ''were raining'' right now, then Sally ''would be'' inside.<br />
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Irrealis Counterfactual: If it were raining right now, then Sally would be inside.<br />
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非现实: 如果现在正在下雨,那么萨利应该在里面。<br />
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Past perfect and irrealis counterfactuals can undergo ''conditional inversion'':<ref>{{cite encyclopedia |last1=Bhatt |first=Rajesh|last2=Pancheva|first2=Roumyana |editor-last1=Everaert |editor-first1=Martin | editor-last2=van Riemsdijk |editor-first2=Henk |encyclopedia= |title=The Wiley Blackwell Companion to Syntax |url=https://people.umass.edu/bhatt/papers/bhatt-pancheva-cond.pdf |year=2006 |publisher=Wiley Blackwell |doi=10.1002/9780470996591.ch16}}</ref><br />
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Past perfect and irrealis counterfactuals can undergo conditional inversion:<br />
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过去完成式和非现实式反事实可以经历条件反转:<br />
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# Were it raining, Sally would be inside.<br />
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Were it raining, Sally would be inside.<br />
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如果下雨的话,萨利就会在里面。<br />
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# Had it rained, Sally would be inside.<br />
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Had it rained, Sally would be inside.<br />
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如果下雨的话,萨莉就会在里面。<br />
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=== Terminology ===<br />
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The term ''counterfactual conditional'' is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<ref name = "vonfintel98" >{{cite encyclopedia |last1=von Fintel |first1=Kai |editor-last1=Sauerland |editor-first1=Uli |editor-last2=Percus |editor-first2=Oren |encyclopedia=The Interpretive Tract |title=The Presupposition of Subjunctive Conditionals |year=1998 |publisher=Cambridge University Press |pages=29–44|url=http://web.mit.edu/fintel/fintel-1998-subjunctive.pdf}}</ref><ref name="Conditionals">{{cite encyclopedia |last1=Egré |first1=Paul | last2=Cozic |first2=Mikaël |editor-last1=Aloni |editor-first1=Maria |editor-last2=Dekker |editor-first2=Paul |encyclopedia=Cambridge Handbook of Formal Semantics |title=Conditionals |year=2016 |publisher=Cambridge University Press |isbn=978-1-107-02839-5 |pages=515}}</ref><br />
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The term counterfactual conditional is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely.<br />
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反事实条件这个术语被广泛地用作上面所显示的各种句子的总称。然而,并非所有这类条件句都表达与事实相反的意思。例如,经典的例子被称为“ Anderson 格”,它具有反事实条件的典型语法形式,但是并没有表明它的先行词是假的或者不可能的。<br />
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# '''Anderson Case''': If the patient had taken arsenic, he would have blue spots.<ref>{{cite journal |last1=Anderson |first1=Alan |date=1951 |title=A Note on Subjunctive and Counterfactual Conditionals |journal=Analysis |volume=12 |issue = 2|pages=35–38|doi=10.1093/analys/12.2.35 }}</ref><br />
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Anderson Case: If the patient had taken arsenic, he would have blue spots.<br />
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安德森病例: 如果病人服用了砒霜,他会长出蓝色斑点。<br />
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Such conditionals are also widely referred to as ''subjunctive conditionals'', though this term is likewise acknowledged as a misnomer even by those who use it.<ref>See for instance [https://pdfs.semanticscholar.org/e68d/612d7a93c98956e7314e0d131d90244c31f2.pdf Ippolito (2002)]: "Because ''subjunctive'' and ''indicative'' are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, [http://web.mit.edu/fintel/fintel-2011-hsk-conditionals.pdf von Fintel (2011)] "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it."</ref> Many languages do not have a morphological [[subjunctive]] (e.g. [[Danish grammar|Danish]] and [[Dutch grammar|Dutch]]) and many that do have it don’t use it for this sort of conditional (e.g. [[French grammar|French]], [[Swahili grammar|Swahili]], all [[Indo-Aryan languages]] that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<ref>{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref>{{cite journal |last1= Kaufmann |first1= Stefan |s2cid= 60598513 |date=2005 |title=Conditional predictions |journal= Linguistics and Philosophy |volume=28 |issue = 2|doi= 10.1007/s10988-005-3731-9 |at=183-184}}</ref><ref name="Conditionals"/><br />
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Such conditionals are also widely referred to as subjunctive conditionals, though this term is likewise acknowledged as a misnomer even by those who use it. Many languages do not have a morphological subjunctive (e.g. Danish and Dutch) and many that do have it don’t use it for this sort of conditional (e.g. French, Swahili, all Indo-Aryan languages that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.<br />
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这种条件句也被广泛地称为虚拟条件句,尽管这个术语同样被使用者认为是用词不当。许多语言都没有形态虚拟语气。丹麦语和荷兰语)和许多有这个词的人不用它来表示这种条件句(例如:。法语,斯瓦希里语,所有的印度-雅利安语支都有虚拟语气)。此外,对于这样的条件句使用虚拟语气的语言,只有在具有特定的过去虚拟形式的情况下才会使用虚拟语气。因此,虚拟标记既不是必要的,也不足以成为这类条件句的成员。<br />
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The terms ''counterfactual'' and ''subjunctive'' have sometimes been repurposed for more specific uses. For instance, the term "counterfactual" is sometimes applied to conditionals that express a contrary-to-fact meaning, regardless of their grammatical structure.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref name = "vonfintel98" /> Along similar lines, the term "subjunctive" is sometimes used to refer to conditionals that bear fake past or irrealis marking, regardless of the meaning they convey.<ref name = "lewis73" >{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><ref>{{cite journal |last1=Khoo |first1=Justin |date=2015 |title=On Indicative and Subjunctive Conditionals |url=https://quod.lib.umich.edu/cgi/p/pod/dod-idx/on-indicative-and-subjunctive-conditionals.pdf?c=phimp;idno=3521354.0015.032;format=pdf |journal=Philosophers' Imprint |volume=15 |issue=32}}</ref><br />
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Recently the term X-Marked has been proposed as a replacement, evoking the extra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as O-Marked conditionals, reflecting their ordinary marking.<br />
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最近术语 x 标记已被提议作为替代,唤起额外的标记,这些条件承担。采用这一术语的人将指示性条件句称为 o 标记条件句,反映了他们的普通标记。<br />
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Recently the term ''X-Marked'' has been proposed as a replacement, evoking the ''ex''tra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as ''O-Marked'' conditionals, reflecting their ''o''rdinary marking.<ref>von Fintel, Kai; Iatridou, Sabine. [http://web.mit.edu/fintel/fintel-iatridou-2019-x-slides.pdf Prolegomena to a theory of X-marking ] Unpublished lecture slides.</ref><ref>von Fintel, Kai; Iatridou, Sabine. [https://web.mit.edu/fintel/ks-x-phlip-slides.pdf X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality ] Unpublished lecture slides.</ref><ref name="Linguistic Society of America"/><br />
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The ''antecedent'' of a conditional is sometimes referred to as its ''"if"-clause'' or ''protasis''. The ''consequent'' of a conditional is sometimes referred to as a ''"then"''-clause or as an apodosis.<br />
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==Logic and semantics==<br />
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According to the material conditional analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated. <br />
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根据实质条件的分析,自然语言条件句---- 形式为如果 p 那么 q 的陈述---- 只要其先行词 p 为假就是真。由于反事实条件句是那些前置假设的条件句,这种分析会错误地预测所有反事实条件句都是真空的。古德曼用下面的一对来说明这一点,在这个背景下,我们知道正在讨论的那块黄油并没有被加热。<br />
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If that piece of butter had been heated to 150º, it would have melted.<br />
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如果那块黄油被加热到150度,它就会融化。<br />
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Counterfactuals were first discussed by [[Nelson Goodman]] as a problem for the [[material conditional]] used in [[classical logic]]. Because of these problems, early work such as that of [[W.V. Quine]] held that counterfactuals aren't strictly logical, and do not make true or false claims about the world. However, in the 1970s, [[David Lewis (philosopher)|David Lewis]] showed that these problems are surmountable given an appropriate logical framework. Work since then in [[formal semantics (linguistics)|formal semantics]], [[philosophical logic]], [[philosophy of language]], and [[cognitive science]] has built on Lewis's insight, taking it in a variety of different directions.<ref name="Counterfactuals">{{cite encyclopedia |last1=Starr |first1=Will |editor-last1=Zalta |editor-first1=Edward N.|encyclopedia=The Stanford Encyclopedia of Philosophy|title=Counterfactuals|year=2019 |url=https://plato.stanford.edu/archives/fall2019/entries/counterfactuals}}</ref><br />
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If that piece of butter had been heated to 150º, it would not have melted.<br />
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如果那块黄油被加热到150度,它就不会融化。<br />
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===Classic puzzles===<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<br />
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更一般地说,这些例子表明反事实并不是真理功能的。换句话说,知道先行词和结果是否真实并不足以确定反事实本身是否真实。<br />
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====The problem of counterfactuals====<br />
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If Caesar had been in command in Korea, he would have used the atom bomb.<br />
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如果凯撒当时在朝鲜指挥,他会使用原子弹。<br />
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If Caesar had been in command in Korea, he would have used catapults.<br />
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如果凯撒在朝鲜指挥,他会使用投石器。<br />
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According to the [[material conditional]] analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated.<ref name="jstor.org">Goodman, N., "[https://www.jstor.org/stable/2019988 The Problem of Counterfactual Conditionals]", ''The Journal of Philosophy'', Vol. 44, No. 5, (27 February 1947), pp. 113–28.</ref> <br />
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# If that piece of butter had been heated to 150º, it would have melted.<br />
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# If that piece of butter had been heated to 150º, it would not have melted.<br />
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Counterfactuals are non-monotonic in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by Sobel sequences such as the following:<br />
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反事实是非单调的,因为它们的真值可以通过在其先行词中添加额外的材料而改变。这一事实可以通过 Sobel 序列得到说明,例如:<br />
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More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.<ref name="Counterfactuals"/><br />
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If Hannah had drunk coffee, she would be happy.<br />
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如果汉娜喝了咖啡,她会很高兴的。<br />
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====Context dependence and vagueness====<br />
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If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
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如果汉娜喝了咖啡,咖啡里加了汽油,她会伤心的。<br />
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If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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如果汉娜喝了咖啡,咖啡里加了汽油,而汉娜是个喝汽油的机器人,她会很高兴的。<br />
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Counterfactuals are ''context dependent'' and ''[[vague]]''. For example, either of the following statements can be reasonably held true, though not at the same time:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref><br />
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One way of formalizing this fact is to say that the principle of Antecedent Strengthening should not hold for any connective > intended as a formalization of natural language conditionals.<br />
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形式化这一事实的一种方法是说,先行强化原则不适用于任何连接词,它是自然语言条件句的形式化。<br />
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# If [[Julius Caesar|Caesar]] had been in command in Korea, he would have [[Korean War#US threat of atomic warfare|used the atom bomb]].<br />
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# If Caesar had been in command in Korea, he would have used catapults.<br />
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====Non-monotonicity====<br />
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Counterfactuals are ''non-monotonic'' in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by ''[[Jordan Howard Sobel|Sobel sequences]]'' such as the following:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref><br />
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The most common logical accounts of counterfactuals are couched in the possible world semantics. Broadly speaking, these approaches have in common that they treat a counterfactual A > B as true if B holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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反事实的最常见的逻辑解释是可能世界语义学。一般来说,这些方法的共同点是,如果 b 持有一些可能的世界集合,其中 a 是真实的,那么它们就把反事实的 a > b 当作真实的。它们主要在如何识别相关的 a 世界集方面有所不同。<br />
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# If Hannah had drunk coffee, she would be happy.<br />
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David Lewis's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.<br />
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大卫 · 刘易斯多变的严格条件被认为是哲学中的经典分析。安吉利卡 · 克拉策提出的前提语义学是语言学中的一个标准。然而,市场上有许多可能的世界方法,包括最初被 Lewis 摒弃的严格条件分析的动态变体。<br />
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# If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.<br />
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# If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.<br />
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One way of formalizing this fact is to say that the principle of ''Antecedent Strengthening'' should '''not''' hold for any connective > intended as a formalization of natural language conditionals.<br />
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The strict conditional analysis treats natural language counterfactuals as being equivalent to the modal logic formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as material implication. This approach was first proposed in 1912 by C.I. Lewis as part of his axiomatic approach to modal logic.<br />
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严格条件分析将自然语言反事实视为等同于模态逻辑公式。在这个公式中,Box 表示必要性,right tarrow </math > 被理解为实质条件。这种方法最早是在1912年由 c.i. 提出的。刘易斯的公理化方法的一部分,模态逻辑。<br />
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* '''Antecedent Strengthening''': <math> P > Q \models (P \land R) > Q </math><br />
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=== Possible worlds accounts ===<br />
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The most common logical accounts of counterfactuals are couched in the [[possible world semantics]]. Broadly speaking, these approaches have in common that they treat a counterfactual ''A'' > ''B'' as true if ''B'' holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.<br />
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In the belief revision framework, counterfactuals are treated using a formal implementation of the Ramsey test. In these systems, a counterfactual A > B holds if and only if the addition of A to the current body of knowledge has B as a consequence. This condition relates counterfactual conditionals to belief revision, as the evaluation of A > B can be done by first revising the current knowledge with A and then checking whether B is true in what results. Revising is easy when A is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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在信念修正框架中,我们使用 Ramsey 测试的一个正式实现来处理反事实问题。在这些系统中,一个反事实的 a > b 成立当且仅当 a 加入到当前的知识体系中的结果是 b。这个条件将反事实条件与信念修正联系起来,因为 a > b 的评估可以通过首先用 a 修正当前的知识,然后检查 b 在什么结果中是否为真来完成。当 a 与当前的信念一致时,复习就容易了,否则就很难了。每个信念修正的语义都可以用于条件语句的求值。反过来,每一种条件求值方法都可以看作是一种执行修正的方法。<br />
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[[David Lewis (philosopher)|David Lewis]]'s ''variably strict conditional'' is considered the classic analysis within philosophy. The closely related ''premise semantics'' proposed by [[Angelika Kratzer]] is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including [[dynamic semantics|dynamic]] variants of the ''strict conditional'' analysis originally dismissed by Lewis.<br />
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====Strict conditional====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of propositional formulae, considering the maximal sets of these formulae that are consistent with A, and adding A to each. The rationale is that each of these maximal sets represents a possible state of belief in which A is true that is as similar as possible to the original one. The conditional statement A > B therefore holds if and only if B is true in all such sets.<br />
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Ginsberg (1986)提出了条件句的语义假设,假设当前的信念构成一组命题公式,考虑这些公式的最大集与 a 相一致,并在每个公式中加入 a。其基本原理是,这些最大集合中的每一个都代表了一种可能的信念状态,其中 a 为真,且尽可能与原始信念相似。因此,If判断语句集 a > b 成立的充要条件是 b 在所有这样的集合中都为真。<br />
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The [[strict conditional]] analysis treats natural language counterfactuals as being equivalent to the [[modal logic]] formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as [[material conditional|material implication]]. This approach was first proposed in 1912 by [[C.I. Lewis]] as part of his [[Axiomatic system|axiomatic approach]] to modal logic.<ref name="Counterfactuals"/> In modern [[relational semantics]], this means that the strict conditional is true at ''w'' iff the corresponding material conditional is true throughout the worlds accessible from ''w''. More formally:<br />
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* Given a model <math>M = \langle W,R,V \rangle</math>, we have that <math> M,w \models \Box(P \rightarrow Q) </math> iff <math>M, v \models P \rightarrow Q </math> for all <math>v</math> such that <math>Rwv</math><br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual morphemes, while others recruit morphemes which otherwise express tense, aspect, mood, or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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语言使用不同的策略来表达反事实。一些语素有专门的反事实语素,而另一些语素则表示时态、方面、语气或者它们的组合。自2000年代初以来,语言学家、语言哲学家和哲学逻辑学家对这种语法标记的本质进行了大量的研究,并且一直是一个活跃的研究领域。<br />
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Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.<br />
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The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.<br />
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This fact led to widespread abandonment of the strict conditional, in particular in favor of Lewis's [[counterfactual conditional#Variably strict conditional|variably strict analysis]]. However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued that ''Sobel sequences'' don't demand a ''non-monotonic'' logic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as the sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. Warmbrōd's idea was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality.<br />
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In many languages, counterfactuality is marked by past tense morphology. Since these uses of the past tense do not convey their typical temporal meaning, they are called fake past or fake tense. English is one language which uses fake past to mark counterfactuality, as shown in the following minimal pair. In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<br />
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在许多语言中,反事实性以过去时态形态学为标志。由于过去时的这些用法没有传达其典型的时间意义,所以它们被称为假过去时或假过去时。英语是一种使用虚假过去来标记反事实性的语言,如下面的最小对所示。在陈述句中,粗体词是现在时态的形式。在反事实的例子中,两个词都采用过去时态。过去时的这种用法不可能有普通的时间意义,因为它可以和副词“明天”一起使用,而不会产生矛盾。<br />
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Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of [[dynamic semantics]], and given a number of linguistic arguments in favor. One argument is that conditional antecedents license [[Polarity item#Determination of licensing contexts|negative polarity items]], which are thought to be licensed only by monotonic operators.<br />
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Indicative: If Natalia leaves tomorrow, she will arrive on time.<br />
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如果娜塔莉亚明天离开,她会准时到达。<br />
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# If Hannah had drunk any coffee, she would be happy.<br />
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Counterfactual: If Natalia left tomorrow, she would arrive on time.<br />
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反事实: 如果娜塔莉亚明天离开,她会准时到达。<br />
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Another argument in favor of the strict conditional comes from [[Irene Heim|Irene Heim's]] observation that Sobel Sequences are generally [[Felicity (pragmatics)|infelicitous]] (i.e. sound strange) in reverse.<br />
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Modern Hebrew is another language where counterfactuality is marked with a fake past morpheme:<br />
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现代希伯来语是另一种用假的过去语素标记反事实性的语言:<br />
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# If Hannah had drunk coffee with gasoline in it, she would not be happy. But if she had drunk coffee, she would be happy.<br />
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| || im || Dani || haya || ba-bayit || maχa ɾ || hayinu || mevakRim || oto<br />
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| || im || Dani || haya || ba-bayit || maχa ɾ || hayinu || mevakRim || oto<br />
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Sarah Moss (2012) and Karen Lewis (2018) have responded to these arguments, showing that a version of the variably strict analysis can account for these patterns, and arguing that such an account is preferable since it can also account for apparent exceptions. As of 2020, this debate continues in the literature, with accounts such as Willer (2019) arguing that a strict conditional account can cover these exceptions as well.<ref name="Counterfactuals"/><br />
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| || if || Dani || be.pst.3sm || in-home || tomorrow || be.pst.1pl || visit.ptc.pl || he.acc<br />
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如果达尼在家里,明天,在家里,在家里,在家里,在家里<br />
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====Variably strict conditional====<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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如果丹妮明天在家,我们就会去看他了<br />
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In the variably strict approach, the semantics of a conditional ''A'' > ''B'' is given by some function on the relative closeness of worlds where A is true and B is true, on the one hand, and worlds where A is true but B is not, on the other.<br />
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Palestinian Arabic is another:<br />
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巴勒斯坦阿拉伯语是另一个例子:<br />
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On Lewis's account, A > C is (a) vacuously true if and only if there are no worlds where A is true (for example, if A is logically or metaphysically impossible); (b) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or (c) false otherwise. Although in Lewis's ''Counterfactuals'' it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did ''not'' intend the metric of 'closeness' to be simply our ordinary notion of [[Similarity (philosophy)#Respective and overall similarity|overall similarity]].<br />
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Example:<br />
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In formal semantics and philosophical logic, fake past is regarded as a puzzle, since it is not obvious why so many unrelated languages would repurpose a tense morpheme to mark counterfactuality. Proposed solutions to this puzzle divide into two camps: past as modal and past as past. These approaches differ in whether or not they take the past tense's core meaning to be about time.<br />
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在形式语义学和哲学逻辑中,虚假的过去被认为是一个谜,因为不明显的是为什么这么多不相关的语言重新使用一个时态语素来标记反事实性。针对这一难题提出的解决办法分为两个阵营: 过去为模式和过去为过去。这些方法的不同之处在于它们是否将过去时的核心意思理解为与时间有关。<br />
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:If he had eaten more at breakfast, he would not have been hungry at 11 am.<br />
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On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where he ate more for breakfast, there is at least one world where he is not hungry at 11 am and which is closer to our world than any world where he ate more for breakfast but is still hungry at 11 am.<br />
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In the past as modal approach, the denotation of the past tense is not fundamentally about time. Rather, it is an underspecified skeleton which can apply either to modal or temporal content. For instance, the particular past as modal proposal of Iatridou (2000), the past tense's core meaning is what's shown schematically below:<br />
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过去式作为情态动词的方法,过去时的外延从根本上说不是关于时间的。相反,它是一个未指定的框架,既可以应用于模态内容,也可以应用于时态内容。例如,Iatridou (2000)的特殊过去式作为情态提议,过去式的核心含义是下面的图示:<br />
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Stalnaker's account differs from Lewis's most notably in his acceptance of the ''limit'' and ''uniqueness assumptions''. The uniqueness assumption is the thesis that, for any antecedent A, among the possible worlds where A is true, there is a single (''unique'') one that is ''closest'' to the actual world. The limit assumption is the thesis that, for a given antecedent A, if there is a chain of possible worlds where A is true, each closer to the actual world than its predecessor, then the chain has a ''limit'': a possible world where A is true that is closer to the actual worlds than all worlds in the chain. (The uniqueness assumption [[logical consequence|entails]] the limit assumption, but the limit assumption does not entail the uniqueness assumption.) On Stalnaker's account, A > C is non-vacuously true if and only if, at the closest world where A is true, C is true. So, the above example is true just in case at the single, closest world where he ate more breakfast, he does not feel hungry at 11 am. Although it is controversial, Lewis rejected the limit assumption (and therefore the uniqueness assumption) because it rules out the possibility that there might be worlds that get closer and closer to the actual world without limit. For example, there might be an infinite series of worlds, each with a coffee cup a smaller fraction of an inch to the left of its actual position, but none of which is uniquely the closest. (See Lewis 1973: 20.)<br />
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The topic x is not the contextually-provided x<br />
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主题 x 不是上下文提供的 x<br />
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One consequence of Stalnaker's acceptance of the uniqueness assumption is that, if the [[law of excluded middle]] is true, then all instances of the formula (A > C) ∨ (A > ¬C) are true. The law of excluded middle is the thesis that for all propositions p, p ∨ ¬p is true. If the uniqueness assumption is true, then for every antecedent A, there is a uniquely closest world where A is true. If the law of excluded middle is true, any consequent C is either true or false at that world where A is true. So for every counterfactual A > C, either A > C or A > ¬C is true. This is called conditional excluded middle (CEM). Example:<br />
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Depending on how this denotation composes, x can be a time interval or a possible world. When x is a time, the past tense will convey that the sentence is talking about non-current times, i.e. the past. When x is a world, it will convey that the sentence is talking about a potentially non-actual possibility. The latter is what allows for a counterfactual meaning.<br />
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根据这个指称的组成,x 可以是时间间隔,也可以是可能世界。当 x 是时间时,过去时态表示句子指的是非现在时间,也就是说,过去时态指的是非现在时间。过去。当 x 是一个世界时,它将传达出这个句子所指的是一种潜在的不真实的可能性。后者是允许反事实意义的东西。<br />
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:(1) If the fair coin had been flipped, it would have landed heads.<br />
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The past as past approach treats the past tense as having an inherently temporal denotation. On this approach, so-called fake tense isn't actually fake. It differs from "real" tense only in how it takes scope, i.e. which component of the sentence's meaning is shifted to an earlier time. When a sentence has "real" past marking, it discusses something that happened at an earlier time; when a sentence has so-called fake past marking, it discusses possibilities that were accessible at an earlier time but may no longer be.<br />
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过去时作为过去时的方法认为过去时具有内在的时间外延。在这种方法中,所谓的假时态实际上并不是假的。它与“真实”时态的区别仅在于它如何占据范围,即。句子的哪个部分的意思转移到了更早的时间。当一个句子有“真实的”过去标记时,它讨论的是发生在更早的时间的事情; 当一个句子有所谓的“假过去标记”时,它讨论的可能性在更早的时间是可以接受的,但可能不再是。<br />
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:(2) If the fair coin had been flipped, it would have landed tails (i.e. not heads).<br />
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On Stalnaker's analysis, there is a closest world where the fair coin mentioned in (1) and (2) is flipped and at that world either it lands heads or it lands tails. So either (1) is true and (2) is false or (1) is false and (2) true. On Lewis's analysis, however, both (1) and (2) are false, for the worlds where the fair coin lands heads are no more or less close than the worlds where they land tails. For Lewis, "If the coin had been flipped, it would have landed heads or tails" is true, but this does not entail that "If the coin had been flipped, it would have landed heads, or: If the coin had been flipped it would have landed tails."<br />
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=== Other accounts ===<br />
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Fake aspect often accompanies fake tense in languages that mark aspect. In some languages (e.g. Modern Greek, Zulu, and the Romance languages) this fake aspect is imperfective. In other languages (e.g. Palestinian Arabic) it is perfective. However, in other languages including Russian and Polish, counterfactuals can have either perfective or imperfective aspect. In other experiments, participants were asked to read short stories that contained counterfactual conditionals, e.g., ‘If there had been roses in the flower shop then there would have been lilies’. Later in the story, they read sentences corresponding to the presupposed facts, e.g., ‘there were no roses and there were no lilies’. The counterfactual conditional primed them to read the sentence corresponding to the presupposed facts very rapidly; no such priming effect occurred for indicative conditionals. They spent different amounts of time 'updating' a story that contains a counterfactual conditional compared to one that contains factual information and focused on different parts of counterfactual conditionals.<br />
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在标记体的语言中,假体往往伴随着假时态。在某些语言中(例如:。现代希腊语、祖鲁语和罗曼语)这个虚构的部分是不完整的。用其他语言(例如:。巴勒斯坦阿拉伯语)这是完美的。然而,在包括俄语和波兰语在内的其他语言中,反事实可以是完成体或非完整体。在其他实验中,参与者被要求阅读包含反事实条件的短篇小说,例如,如果花店里有玫瑰,那么就会有百合花。在故事的后半部分,他们阅读与预设事实相对应的句子,例如,没有玫瑰,也没有百合。反事实条件让他们非常快速地阅读与预设事实相对应的句子; 指示性条件句则没有这样的启动效应。他们花了不同数量的时间更新一个包含反事实条件的故事,而不是一个包含事实信息的故事,并且关注不同部分的反事实条件句。<br />
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====Causal models====<br />
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Experiments have compared the inferences people make from counterfactual conditionals and indicative conditionals. Given a counterfactual conditional, e.g., 'If there had been a circle on the blackboard then there would have been a triangle', and the subsequent information 'in fact there was no triangle', participants make the modus tollens inference 'there was no circle' more often than they do from an indicative conditional. Given the counterfactual conditional and the subsequent information 'in fact there was a circle', participants make the modus ponens inference as often as they do from an indicative conditional. See counterfactual thinking.<br />
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实验比较了人们从反事实条件句和指示性条件句中得出的推论。给定一个反事实条件,例如,如果黑板上有一个圆,那么就会有一个三角形,并且随后的信息事实上没有三角形,参与者做这种推断的频率比他们从一个直陈条件推断的频率更高。考虑到反事实条件和随后的信息‘事实上存在一个循环’,参与者做这种推理的频率和他们从直陈条件推理的频率一样高。参见反事实思维。<br />
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{{Further|Causal model#Counterfactuals}}<br />
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Byrne argues that people construct mental representations that encompass two possibilities when they understand, and reason from, a counterfactual conditional, e.g., 'if Oswald had not shot Kennedy, then someone else would have'. They envisage the conjecture 'Oswald did not shoot Kennedy and someone else did' and they also think about the presupposed facts 'Oswald did shoot Kennedy and someone else did not'. According to the mental model theory of reasoning, they construct mental models of the alternative possibilities.<br />
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认为人们构建的心理表征包括两种可能性,一种是他们理解的反事实条件,另一种是推理,例如,如果 Oswald 没有射杀 Kennedy,那么其他人也会射杀 Kennedy。他们猜想肯尼迪不是奥斯瓦尔德杀的,而是别人杀的,他们还想到了预先假定的事实奥斯瓦尔德确实杀了肯尼迪,而别人没有。根据心理模型推理理论,他们构建了可选择可能性的心理模型。<br />
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The ''causal models framework'' analyzes counterfactuals in terms of systems of [[structural equation model|structural equations]]. In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence "''Y'' would be ''y'' had ''X'' been ''x''" (formally, ''X = x'' > ''Y = y'' ) is defined as the assertion: If we replace the equation currently determining ''X'' with a constant ''X = x'', and solve the set of equations for variable ''Y'', the solution obtained will be ''Y = y''. This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators. This approach was developed by [[Judea Pearl]] (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.<ref name="Pearl2000">{{Cite book |last=Pearl |first=Judea |title=Causality |publisher=Cambridge University Press |year=2000 }}</ref><br />
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====Belief revision====<br />
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{{Further|Belief revision#The Ramsey test}}<br />
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In the [[belief revision]] framework, counterfactuals are treated using a formal implementation of the ''Ramsey test''. In these systems, a counterfactual ''A'' > ''B'' holds if and only if the addition of ''A'' to the current body of knowledge has ''B'' as a consequence. This condition relates counterfactual conditionals to [[belief revision]], as the evaluation of ''A'' > ''B'' can be done by first revising the current knowledge with ''A'' and then checking whether ''B'' is true in what results. Revising is easy when ''A'' is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.<br />
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====Ginsberg====<br />
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Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of [[propositional formula]]e, considering the maximal sets of these formulae that are consistent with ''A'', and adding ''A'' to each. The rationale is that each of these maximal sets represents a possible state of belief in which ''A'' is true that is as similar as possible to the original one. The conditional statement ''A'' > ''B'' therefore holds if and only if ''B'' is true in all such sets.<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref><br />
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== The grammar of counterfactuality ==<br />
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Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactual [[morphemes]], while others recruit morphemes which otherwise express [[grammatical tense|tense]], [[grammatical aspect|aspect]], [[grammatical mood|mood]], or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.<br />
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=== Fake tense ===<br />
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==== Description ====<br />
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In many languages, counterfactuality is marked by [[past tense]] morphology.<ref name = "palmer">{{cite book |last=Palmer |first=Frank Robert |date=1986 |title=Mood and modality |publisher= Cambridge University Press}}</ref> Since these uses of the past tense do not convey their typical temporal meaning, they are called ''fake past'' or ''fake tense''.<ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref> English is one language which uses fake past to mark counterfactuality, as shown in the following [[minimal pair]].<ref>English fake past is sometimes erroneously referred to as "subjunctive", even though it is not the [[English subjunctive|subjunctive mood]].</ref> In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.<ref name = palmer /><ref name = "ingredients">{{cite journal |last1=Iatridou |first1=Sabine |date=2000 |title=The grammatical ingredients of counterfactuality |journal= Linguistic Inquiry |volume=31 |issue = 2|pages=231–270|doi=10.1162/002438900554352 |s2cid=57570935 |url=http://lingphil.mit.edu/papers/iatridou/counterfactuality.pdf}}</ref><ref name="portner">{{cite book |last=Portner |first=Paul |date=2009 |title=Modality |publisher= Oxford University Press|isbn=978-0199292424}}</ref><ref name = "prolegomena">von Fintel, Kai; Iatridou, Sabine (2020). [https://semanticsarchive.net/Archive/zdjYTJjY/fintel-iatridou-2020-x.pdf Prolegomena to a Theory of X-Marking]. ''Manuscript''.</ref><br />
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# Indicative: If Natalia '''leaves''' tomorrow, she '''will''' arrive on time.<br />
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# Counterfactual: If Natalia '''left''' tomorrow, she '''would''' arrive on time.<br />
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[[Hebrew language|Modern Hebrew]] is another language where counterfactuality is marked with a fake past morpheme:<ref name="karawani">{{cite thesis |last=Karawani |first=Hadil |date=2014 |title=The Real, the Fake, and the Fake Fake in Counterfactual Conditionals, Crosslinguistically |publisher=Universiteit van Amsterdam |url=https://pure.uva.nl/ws/files/1695453/142017_thesis.pdf}}</ref><br />
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Category:Conditionals in linguistics<br />
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范畴: 语言学中的条件句<br />
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:: {| <br />
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Category:Grammar<br />
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分类: 语法<br />
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| || im || Dani || '''haya''' || ba-bayit || maχa ɾ || '''hayinu''' || mevakRim || oto<br />
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Category:Semantics<br />
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分类: 语义学<br />
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|-<br />
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Category:Belief revision<br />
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类别: 信念修正<br />
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| || if || Dani || be.'''pst'''.3sm || in-home || tomorrow || be.'''pst'''.1pl || visit.ptc.pl || he.acc<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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|} 'If Dani had been home tomorrow, we would’ve visited him.'<br />
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Category:Linguistic modality<br />
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类别: 情态<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Counterfactual conditional]]. Its edit history can be viewed at [[反事实/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Weihttps://wiki.swarma.org/index.php?title=%E7%94%A8%E6%88%B7:Wei&diff=22605用户:Wei2021-05-28T08:55:01Z<p>Wei:/* 自我简介 */</p>
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<div>=== 自我简介 ===<br />
* 学校:广东工业大学<br />
* 研究领域:因果发现、因果性学习</div>Wei