Lecture-12-13-First-order_Logic

Lecture-12-13-First-order_Logic - CS 561: Artificial...

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CS 561: Artificial Intelligence Instructor: Sofus A. Macskassy, macskass@usc.edu TA: Harris Chiu ( chichiu@usc.edu ), Wed 2:45-4:45pm, PHE 328 Penny Pan ( beipan@usc.edu ), Fri 10am-noon, PHE 328 Lectures: MW 5:00-6:20pm, ZHS 159 Office hours: By appointment Class page: http://www-bcf.usc.edu/~macskass/CS561/Fall2010/ This class will use https://blackboard.usc.edu/webapps/login/ and class webpage - Up to date information - Lecture notes - Relevant dates, links, etc. Course material: [AIMA] Artificial Intelligence: A Modern Approach, by Stuart Russell and Peter Norvig. (3rd ed)
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CS561 - Lecture 13-14 - Macskassy - Fall 2010 2 Logistics - MIDTERM Midterm 1 is in two weeks Date: October 18 Location: Normal class room Time: Normal time Covers: All lectures through next week (Ch. 1-9) It is open book and open notes You can use the book, lecture slides and your notes Example midterms available from AIMA site http://aima.cs.berkeley.edu/instructors.html
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CS561 - Lecture 11-12 - Macskassy - Fall 2010 3 First-order Logic [AIMA Ch. 8] Why FOL? Syntax and semantics of FOL Fun with sentences Wumpus world in FOL
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CS561 - Lecture 11-12 - Macskassy - Fall 2010 4 Review: Propositional logic - syntax Propositional logic is the simplest logic illustrates basic ideas The proposition symbols P 1 , P 2 etc are sentences If S is a sentence, ¬ S is a sentence (negation) If S 1 and S 2 are sentences, S 1 ^ S 2 is a sentence (conjunction) If S 1 and S 2 are sentences, S 1 _ S 2 is a sentence (disjunction) If S 1 and S 2 are sentences, S 1 ) S 2 is a sentence (implication) If S 1 and S 2 are sentences, S 1 , S 2 is a sentence (biconditional)
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CS561 - Lecture 11-12 - Macskassy - Fall 2010 5 Review: Propositional logic - Semantics
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CS561 - Lecture 11-12 - Macskassy - Fall 2010 6 Review propositional logic [cont’d]
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Why first-order logic? Pros and cons of propositional logic Propositional logic is declarative : pieces of syntax correspond to facts Propositional logic allows partial/disjunctive/negated information (unlike most data structures and databases) Propositional logic is compositional : meaning of B1;1 ^ P1;2 is derived from meaning of B1;1 and of P1;2 Meaning in propositional logic is context-independent (unlike natural language, where meaning depends on context) Propositional logic has very limited expressive power (unlike natural language) E.g., cannot say “pits cause breezes in adjacent squares” except by writing one sentence for each square 7 CS561 - Lecture 11-12 - Macskassy - Fall 2010
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First-order logic (FOL) Whereas propositional logic assumes world contains facts, first-order logic (like natural language) assumes the world contains: Objects : wheel, door, body, engine, seat, car, passenger, driver, people, houses, numbers, theories, Ronald McDonald, colors, baseball games, wars, centuries, … Relations : Inside(car, passenger), Beside(driver, passenger), BrotherOf(person, person), BiggerThan(object, object), Inside(), part
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Lecture-12-13-First-order_Logic - CS 561: Artificial...

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