ITCS 3153 Artificial IntelligenceFirst-order logicWhat do we like about propositional logic?What don’t we like about propositional logic?Natural LanguageBut we borrow representational ideas from natural languageOntologyHigher-order logicAnother characterization of a logicFormal structure of first-order logicFirst-order logic syntaxSlide 12SyntaxAtomic SentencesComplex sentencesQuantifiersUniversal QuantificationSlide 18Existential QuantificationSlide 20Nested QuantifiersCombiningSlide 23EqualityAn ExampleSlide 26The Wumpus WorldSlide 28Wumpus WorldDiagnostic RulesCausal RulesSlide 32ConclusionITCS 3153Artificial IntelligenceLecture 13Lecture 13First-Order LogicFirst-Order LogicChapter 8Chapter 8Lecture 13Lecture 13First-Order LogicFirst-Order LogicChapter 8Chapter 8First-order logicWe saw how propositional logic can create We saw how propositional logic can create intelligent behaviorintelligent behaviorBut propositional logic is a poor representation But propositional logic is a poor representation for complex environmentsfor complex environments•Why?Why?First-order logic is a more expressive and First-order logic is a more expressive and powerful representationpowerful representationWe saw how propositional logic can create We saw how propositional logic can create intelligent behaviorintelligent behaviorBut propositional logic is a poor representation But propositional logic is a poor representation for complex environmentsfor complex environments•Why?Why?First-order logic is a more expressive and First-order logic is a more expressive and powerful representationpowerful representationWhat do we like about propositional logic?It is:It is:•DeclarativeDeclarative–Relationships between variables are describedRelationships between variables are described–A method for propagating relationshipsA method for propagating relationships•ExpressiveExpressive–Can represent partial information using disjunctionCan represent partial information using disjunction•CompositionalCompositional–If If A A means foo and means foo and B B means bar, means bar, A ^ BA ^ B means foo and bar means foo and barIt is:It is:•DeclarativeDeclarative–Relationships between variables are describedRelationships between variables are described–A method for propagating relationshipsA method for propagating relationships•ExpressiveExpressive–Can represent partial information using disjunctionCan represent partial information using disjunction•CompositionalCompositional–If If A A means foo and means foo and B B means bar, means bar, A ^ BA ^ B means foo and bar means foo and barWhat don’t we like about propositional logic?Lacks expressive power to describe the Lacks expressive power to describe the environment conciselyenvironment concisely•Separate rules for every square/square relationship in Separate rules for every square/square relationship in Wumpus worldWumpus worldLacks expressive power to describe the Lacks expressive power to describe the environment conciselyenvironment concisely•Separate rules for every square/square relationship in Separate rules for every square/square relationship in Wumpus worldWumpus worldNatural LanguageEnglish appears to be expressiveEnglish appears to be expressive•Squares adjacent to pits are breezySquares adjacent to pits are breezyBut natural language is a medium of communication, not a But natural language is a medium of communication, not a knowledge representationknowledge representation•Much of the information and logic conveyed by language is dependent on Much of the information and logic conveyed by language is dependent on contextcontext•Information exchange is not well definedInformation exchange is not well defined•Not compositional (combining sentences may mean something different)Not compositional (combining sentences may mean something different)•It is ambiguousIt is ambiguousEnglish appears to be expressiveEnglish appears to be expressive•Squares adjacent to pits are breezySquares adjacent to pits are breezyBut natural language is a medium of communication, not a But natural language is a medium of communication, not a knowledge representationknowledge representation•Much of the information and logic conveyed by language is dependent on Much of the information and logic conveyed by language is dependent on contextcontext•Information exchange is not well definedInformation exchange is not well defined•Not compositional (combining sentences may mean something different)Not compositional (combining sentences may mean something different)•It is ambiguousIt is ambiguousBut we borrow representational ideas from natural languageNatural language syntaxNatural language syntax•Nouns and noun phrases refer to Nouns and noun phrases refer to objectsobjects–People, houses, carsPeople, houses, cars•Verbs and verb phrases refer to Verbs and verb phrases refer to relationshipsrelationships btw objects btw objects–Red, round, nearby, eatenRed, round, nearby, eaten•Some relationships are clearly defined Some relationships are clearly defined functions functions where there is only one where there is only one output for a given inputoutput for a given input–Best friend, first thing, plusBest friend, first thing, plusWe build first order logic around objects and relationsWe build first order logic around objects and relationsNatural language syntaxNatural language syntax•Nouns and noun phrases refer to Nouns and noun phrases refer to objectsobjects–People, houses, carsPeople, houses, cars•Verbs and verb phrases refer to Verbs and verb phrases refer to relationshipsrelationships btw objects btw objects–Red, round, nearby, eatenRed, round, nearby, eaten•Some relationships are clearly defined Some relationships are clearly defined functions functions where there is only one where there is only one output for a given inputoutput for a given input–Best friend, first thing, plusBest friend, first thing, plusWe build first order logic around objects and relationsWe build first order logic around objects and relationsOntology•a “a “specification of a conceptualizationspecification of a conceptualization””•A description of the objects and relationships that can existA description of the objects and relationships that can exist–Propositional logic had only true/false relationshipsPropositional logic had only true/false relationships–First-order logic has many more relationshipsFirst-order logic