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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.

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.

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。

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。

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>.

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>.

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。

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。

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.

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.

Indicative: If Natalia leaves tomorrow, she will arrive on time.

  If Natalia leaves tomorrow, she will arrive on time.

 

 

 

 

 

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.

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.

Modern Hebrew is another language where counterfactuality is marked with a fake past morpheme:

If Hannah had drunk coffee with gasoline in it, she would not be happy. But if she had drunk coffee, she would be happy.

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"/>

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"/>

 

 

 

 

 

====Variably strict conditional====

====Variably strict conditional====