AI Spring 2010 Lecture 10

# AI Spring 2010 Lecture 10 - Artificial Intelligence Lecture...

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Click to edit Master subtitle style Artificial Intelligence Lecture 10: First Order Logic (FOL) (Part III: Knowledge & Reasoning, Chapter 8) Spring 2010 Instructor: Paul S. Rosenbloom

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Midterm 1 £ Here, Tuesday, February 16, 12:30-1:50 l Open book and notes but no electronic devices of any sort l Must be your own work l Covers chapters 1-8 except 6 and 4.2 (3rd Ed.) l Course is based on 3rd Ed., but I am not aware of anything on exam that depends on the differences £ Review session today 2-2:50, ZHS 159 22
33 Today’s Lecture £ Why FOL? £ Syntax and semantics of FOL £ Using FOL £ Wumpus world in FOL £ Knowledge engineering in FOL

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44 Pros and Cons of Propositional Logic r It allows partial/disjunctive/negated information l Unlike most data structures and databases J It is compositional o meaning of B1,1 P1,2 derived from meaning of B1,1 and P1,2 o Meaning of sentences is context independent o Unlike natural language and computer programs, where the meaning of a sentence depends on context or usage l It has very limited expressive power l Unlike natural language l E.g., cannot say "pits cause breezes in adjacent squares“ l Except by writing one sentence for each square
55 Assumptions about the World £ Propositional logic assumes the world consists of a set of “black box” facts, which it represents via symbols and combines via connectives £ First-order logic, more like natural language, provides more structured way of representing world l Objects : Things you can talk about l E.g., people, houses, numbers, colors, baseball games, wars l Relations : Relations among objects that can be true or false l E.g., red, round, prime, brother of, bigger than, part of, comes between l Functions : Functions of objects that return unique values l E.g., father of, best friend of, one more than, plus, … l Can be viewed as relation where one argument has at most one value E.g., Father-of(Fred, George) ° Father-of(Fred) = George l FOL represents each of these, plus uses connectives, and more

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66 Example Domain Arithmetic on Natural Numbers £ Objects l Non-negative numbers (0, 1, …) £ Relations l NatNum, =, <, >, … £ Functions l Successor, +, -, x, integer division, remainder, exponentiation,… E.g., >(+(5, 20211), -(5111,777)) ° =(5,+(3,2))
Example Domain English History £ Objects l Richard, John, crown, left legs £ Unary Predicates l Crown, King l King(John) £ Binary Predicates l Brother, OnHead l OnHead(crown, J) £ Functions l LeftLeg(R) = LL1 77

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88 Representational Commitments in Logic £ Ontological Commitment: What kinds of things exist in the world l Propositional: facts that hold or do not hold l First-Order: objects with relations among them that hold or do not hold £ Epistemological Commitment: Form/level of belief * * * Likelihood of truth versus degree of truth
99 Syntax of FOL Basic Elements £ Constants KingJohn, 2, Crown,...

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