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Lecture-11-12-First-order Logic

Lecture-11-12-First-order Logic - CS 561 Artificial...

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CS 561: Artificial Intelligence Instructor: Sofus A. Macskassy, [email protected] TAs: Nadeesha Ranashinghe ( [email protected] ) William Yeoh ( [email protected] ) Harris Chiu ( [email protected] ) Lectures: MW 5:00-6:20pm, OHE 122 / DEN Office hours: By appointment Class page: http://www-rcf.usc.edu/~macskass/CS561-Spring2010/ This class will use http://www.uscden.net/ 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. (2nd ed)
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CS561 - Lecture 11-12 - Macskassy - Spring 2010 2 Logistics HW2 Homework #2 was due today You should have submitted it before class on turnitin
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CS561 - Lecture 11-12 - Macskassy - Spring 2010 3 Logistics - MIDTERM Midterm 1 is next week Date: March 1 Location: SGM 124 Time: 5pm 6:20pm DEN Students: should have received an email to set up their exam Covers: All lectures through this week (Ch. 1-8) 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 - Spring 2010 4 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 09-10 - Macskassy - Spring 2010 5 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 09-10 - Macskassy - Spring 2010 6 Review: Propositional logic - Semantics
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CS561 - Lecture 11-12 - Macskassy - Spring 2010 7 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 8 CS561 - Lecture 11-12 - Macskassy - Spring 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),
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