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| | ===逻辑=== | | ===逻辑=== |
| | + | 逻辑<ref name="ACM Computing Classification System: Artificial intelligence">"ACM Computing Classification System: Artificial intelligence". ACM. 1998. ~I.2.3 and ~I.2.4. </ref>被用来表示知识和解决问题，还可以应用到其他问题上。例如，satplan 算法就使用逻辑进行规划<ref name="Satplan"/>。另外，归纳逻辑编程是一种学习方法。 |
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| − | [[Logic]]<ref name="Logic"/> is used for knowledge representation and problem solving, but it can be applied to other problems as well. For example, the [[satplan]] algorithm uses logic for [[automated planning and scheduling|planning]]<ref name="Satplan"/> and [[inductive logic programming]] is a method for [[machine learning|learning]].<ref name="Symbolic learning techniques"/>
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| − | 逻辑<ref name="Russell & Norvig 2003"/><ref name="Luger & Stubblefield 2004"/><ref name="Nilsson 1998"/><ref>"ACM Computing Classification System: Artificial intelligence". ACM. 1998. ~I.2.3 and ~I.2.4. </ref>被用来表示知识和解决问题，还可以应用到其他问题上。例如，satplan 算法就使用逻辑进行规划<ref name="Satplan"/>。另外，归纳逻辑编程是一种学习方法。
| + | AI研究中使用了多种不同形式的逻辑。命题逻辑包含诸如“或”和“否”这样的真值函数。一阶逻辑<ref name="ACM Computing Classification System: Artificial intelligence"/>增加了量词和谓词，可以表达关于对象、对象属性和对象之间的关系。模糊集合论给诸如“爱丽丝老了”(或是富有的、高的、饥饿的)这样模糊的表述赋予了一个“真实程度”(介于0到1之间)，这些表述在语言上很模糊，不能完全判定为正确或错误。模糊逻辑在控制系统中得到了成功应用，使专家能够制定模糊规则，比如“如果你正以较快的速度接近终点站，那么就增加列车的制动压力”;这些模糊的规则可以在系统内用数值细化。但是，模糊逻辑无助于扩展知识库，许多AI研究者质疑把模糊逻辑和推理结合起来的有效性。<ref>{{cite journal|last1=Elkan|first1=Charles|title=The paradoxical success of fuzzy logic|journal=IEEE Expert|date=1994|volume=9|issue=4|pages=3–49|doi=10.1109/64.336150|citeseerx=10.1.1.100.8402}}</ref><ref name="Fuzzy logic"/><ref>{{cite news|title=What is 'fuzzy logic'? Are there computers that are inherently fuzzy and do not apply the usual binary logic?|url=https://www.scientificamerican.com/article/what-is-fuzzy-logic-are-t/|accessdate=5 May 2018|work=Scientific American|language=en}}</ref> |
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| − | Several different forms of logic are used in AI research. [[Propositional logic]]<ref name="Propositional logic"/> involves [[truth function]]s such as "or" and "not". [[First-order logic]]<ref name="First-order logic"/> adds [[quantifier (logic)|quantifiers]] and [[predicate (mathematical logic)|predicates]], and can express facts about objects, their properties, and their relations with each other. [[Fuzzy set theory]] assigns a "degree of truth" (between 0 and 1) to vague statements such as "Alice is old" (or rich, or tall, or hungry) that are too linguistically imprecise to be completely true or false. [[Fuzzy logic]] is successfully used in [[control system]]s to allow experts to contribute vague rules such as "if you are close to the destination station and moving fast, increase the train's brake pressure"; these vague rules can then be numerically refined within the system. Fuzzy logic fails to scale well in knowledge bases; many AI researchers question the validity of chaining fuzzy-logic inferences.{{efn|"There exist many different types of uncertainty, vagueness, and ignorance... [We] independently confirm the inadequacy of systems for reasoning about uncertainty that propagates numerical factors according to only to which connectives appear in assertions."<ref>{{cite journal|last1=Elkan|first1=Charles|title=The paradoxical success of fuzzy logic|journal=IEEE Expert|date=1994|volume=9|issue=4|pages=3–49|doi=10.1109/64.336150|citeseerx=10.1.1.100.8402}}</ref>}}<ref name="Fuzzy logic"/><ref>{{cite news|title=What is 'fuzzy logic'? Are there computers that are inherently fuzzy and do not apply the usual binary logic?|url=https://www.scientificamerican.com/article/what-is-fuzzy-logic-are-t/|accessdate=5 May 2018|work=Scientific American|language=en}}</ref>
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| − | AI研究中使用了多种不同形式的逻辑。命题逻辑<ref name="Propositional logic"/>包含诸如“或”和“否”这样的真值函数。一阶逻辑<ref name="First-order logic"/>增加了量词和谓词，可以表达关于对象、对象属性和对象之间的关系。模糊集合论给诸如“爱丽丝老了”(或是富有的、高的、饥饿的)这样模糊的表述赋予了一个“真实程度”(介于0到1之间)，这些表述在语言上很模糊，不能完全判定为正确或错误。模糊逻辑在控制系统中得到了成功应用，使专家能够制定模糊规则，比如“如果你正以较快的速度接近终点站，那么就增加列车的制动压力”;这些模糊的规则可以在系统内用数值细化。但是，模糊逻辑无助于扩展知识库，许多AI研究者质疑把模糊逻辑和推理结合起来的有效性。{{efn|"There exist many different types of uncertainty, vagueness, and ignorance... [We] independently confirm the inadequacy of systems for reasoning about uncertainty that propagates numerical factors according to only to which connectives appear in assertions."<ref>{{cite journal|last1=Elkan|first1=Charles|title=The paradoxical success of fuzzy logic|journal=IEEE Expert|date=1994|volume=9|issue=4|pages=3–49|doi=10.1109/64.336150|citeseerx=10.1.1.100.8402}}</ref>}}<ref name="Fuzzy logic"/><ref>{{cite news|title=What is 'fuzzy logic'? Are there computers that are inherently fuzzy and do not apply the usual binary logic?|url=https://www.scientificamerican.com/article/what-is-fuzzy-logic-are-t/|accessdate=5 May 2018|work=Scientific American|language=en}}</ref>
| + | '''缺省逻辑 Default Logics'''、'''非单调逻辑 Non-monotonic Logics'''、'''限制逻辑 Circumscription'''和'''模态逻辑 Modal Logics'''，都用逻辑形式来解决缺省推理和限定问题。一些逻辑扩展被用于处理特定的知识领域，例如:'''描述逻辑 Description Logics''' 、情景演算、事件演算、'''流态演算 Fluent Calculus'''（用于表示事件和时间）、因果演算、信念演算(信念修正)<ref>"The Belief Calculus and Uncertain Reasoning", Yen-Teh Hsia</ref>、和模态逻辑。人们也设计了对多主体系统中出现的矛盾或不一致陈述进行建模的逻辑，如次协调逻辑。 |
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| − | [[Default logic]]s, [[non-monotonic logic]]s and [[circumscription (logic)|circumscription]]<ref name="Default reasoning and non-monotonic logic"/> are forms of logic designed to help with default reasoning and the [[qualification problem]]. Several extensions of logic have been designed to handle specific domains of [[knowledge representation|knowledge]], such as: [[description logic]]s;<ref name="Representing categories and relations"/> [[situation calculus]], [[event calculus]] and [[fluent calculus]] (for representing events and time);<ref name="Representing time"/> [[Causality#Causal calculus|causal calculus]];<ref name="Representing causation"/> [[Belief revision|belief calculus (belief revision)]];<ref>"The Belief Calculus and Uncertain Reasoning", Yen-Teh Hsia</ref> and [[modal logic]]s.<ref name="Representing knowledge about knowledge"/> Logics to model contradictory or inconsistent statements arising in multi-agent systems have also been designed, such as [[paraconsistent logic]]s.
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| − | '''缺省逻辑 Default Logics'''、'''非单调逻辑 Non-monotonic Logics'''、'''限制逻辑 Circumscription'''和'''模态逻辑 Modal Logics'''<ref name="Default reasoning and non-monotonic logic"/>，都用逻辑形式来解决缺省推理和限定问题。一些逻辑扩展被用于处理特定的知识领域，例如:'''描述逻辑 Description Logics'''<ref name="Representing categories and relations"/> 、情景演算、事件演算、'''流态演算 Fluent Calculus'''（用于表示事件和时间）<ref name="Representing time"/>、因果演算<ref name="Representing causation"/>、信念演算(信念修正)<ref>"The Belief Calculus and Uncertain Reasoning", Yen-Teh Hsia</ref>、和模态逻辑<ref name="Representing knowledge about knowledge"/>。人们也设计了对多主体系统中出现的矛盾或不一致陈述进行建模的逻辑，如次协调逻辑。
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| | ===不确定推理的概率方法=== | | ===不确定推理的概率方法=== |