Synonyms Predicate calculus ; Predicate logic FOL Definition This entry should be read in conjunction with the companion entry First-Order Logic : Syntax where the terms vocabulary, variable, formula, etc. are defined. To give semantics to first-order sentences, first-order structures (a.k.a. ...
08.First order logic
Complexsentences •Complexsentencesaremadefromatomic sentencesusingconnectives • S,S 1 S 2 ,S 1 S 2 ,S 1 S 2 ,S 1 S 2 , E.g.Sibling(KingJohn,Richard) Sibling(Richard,KingJohn) >(1,2) ≤(1,2) >(1,2) >(1,2) Truthinfirst-orderlogic •Sentencesaretruewithrespecttoamodel...
[?P (P(x)?P(y))]Inference in FOL精品文档All rules of inference for propositional logic apply to first-order logic We just need to reduce FOL sentences to PL sentences by instantiating variables and removing quantifiersReduction of FOL to PLSuppose the KB contains the following:?x King(x)...
First-orderlogic •Whereaspropositionallogicassumestheworldcontainsfacts,•first-orderlogic(likenaturallanguage)assumestheworldcontains –Objects:people,houses,numbers,colors,baseballgames,wars,…–Relations:red,round,prime,brotherof,biggerthan,partof,comesbetween,…–Functions:fatherof,bestfriend,onemorethan,...
Higher-order logicviews the relations and functions referred to by first-order logic as objects in themselves. Higher-order logic is strictly more expressive than first-order logic, some sentences of higher-order logic cannot be expressed by any finite number of first-order logic sentences. ...
Connective -> ⇒ | ⋀ | ⋁ | ⇔ // used to construct complex sentences Quantifier -> ∀ | ∃ Constant -> A | X1 | John | … Variable -> a | x | s Predicate -> Before | HasColor | Raining | … Function -> Mother | LeftLegof | … ...
What is first-order logic crucial to? FOL is a system of formal logic that provides a way to formalizenatural languagesinto a computable/mathematical format. With FOL, problems expressed in English sentences can be represented in a formal manner, which makes it possible to formulate ideas, draw...
First-orderlogic Properties,relations,functions,quantifiers,… Terms,sentences,wffs,axioms,theories,proofs,… Extensionstofirst-orderlogic Logicalagents Reflexagents Representingchange:situationcalculus,frameproblem Preferencesonactions Goal-basedagents REMINDER ...
Firstorder logic cs一阶逻辑政务司司长.swarthmore Propositional and First-Order Logic Chapter 7.4-7.5, 7.7, 8.1─8.3, 8.5 Propositional Logic Propositional logic Logical constants: true, false Propositional symbols: P, Q, S, ... (atomic sentences) Wrapping parentheses: ( … ) Sentences are ...