Transcript Thursday
Logical Reasoning II Lecture 4-2 January 28th, 1999 CS250 Lecture 4-2 CS250: Intro to AI/Lisp Building a Logic • Syntax – Rules for building expressions • Semantics – Assigns meaning to sentences • Proof theory – Rules for deducing entailments of sentences Lecture 4-2 CS250: Intro to AI/Lisp Sentences • Valid sentences are tautologies -- they are always true – Either there is a blood-curdling scream from the soon-to-be deceased wumpus, or there is not a scream from the wumpus • Satisfiable sentences could be true – If there’s some interpretation in some world in which the sentence is true Lecture 4-2 CS250: Intro to AI/Lisp Propositional Logic • Symbols stand for propositions • Propositions can be combined with Boolean operators • Example S1 is “The wumpus is dead” S2 is “The arrow hit the wumpus” S1 S2 Lecture 4-2 CS250: Intro to AI/Lisp First-Order Logic • World consists of objects and predicates on objects • Get to keep Boolean operators • Add quantifiers • Example “The wumpus is dead” could be Dead(wumpus) “All wumpi are dead” could be x Wumpi(x)Dead(x) Lecture 4-2 CS250: Intro to AI/Lisp Logics aren’t Afraid of Commitment • Ontological commitment – How do you capture the reality of the world? – Propositional: “Just the facts, ma’am” • Epistemological commitment – Possible states of knowledge – Law of the Excluded Middle – Degree of belief Lecture 4-2 CS250: Intro to AI/Lisp Summary of Commitment Lecture 4-2 CS250: Intro to AI/Lisp Models • Models are formal worlds in which truth is evaluated m is a model of if is true in m M() is the set of all models in which is true Lecture 4-2 CS250: Intro to AI/Lisp Inferencing Lecture 4-2 CS250: Intro to AI/Lisp A Representational Straw Man: Propositional Logic • Combine symbols that represent propositions with Boolean operators • No commitments Lecture 4-2 CS250: Intro to AI/Lisp Syntax of Propositional Logic • Sentences of propositional logic can be built from – Logical constants: TRUE, FALSE – Propositional symbols:P, Q – Parentheses are okay too: (PQ) – Logical connectives Lecture 4-2 CS250: Intro to AI/Lisp Linking Propositions • Not, • Equivalence, P is the negation of P • And, (P Q) (P Q) (Q P) • Implication, (P Q) R • Or, (P Q) Lecture 4-2 CS250: Intro to AI/Lisp Semantics Lecture 4-2 CS250: Intro to AI/Lisp Practicing Inferencing Suppose that: =AB KB = (A C) (B C) Does KB entail ? Lecture 4-2 CS250: Intro to AI/Lisp Does KB entail ? Lecture 4-2 CS250: Intro to AI/Lisp The Wumpus World Lecture 4-2 CS250: Intro to AI/Lisp