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Unformatted text preview: Lecture 7: Propositional logic Prof. Julia Hockenmaier juliahmr@illinois.edu http://cs.illinois.edu/fa11/cs440 CS440/ECE448: Intro to ArtiFcial Intelligence Thursday s key concepts Combining CSP search and inference: Ordering variables (minimum remaining value, degree heuristics) Ordering values (forward checking, MAC) Global constraints: Constraint hypergraph; auxiliary variables Continuous domains: bounds consistency 2 CS440/ECE448: Intro AI Path consistency and arc consistency X is arc consistent with respect to Y if for every value of X there exists some value of Y such that C(X,Y) is satisFed. X and Y are path consistent with respect to Z if for every pair of values of X and Y that satisfy C(X, Y), there exists some value of Z such that C(X,Z) and C(Y,Z) is satisFed. 3 CS440/ECE448: Intro AI Global (nary) constraints: Constraint Hypergraph T U W R O TWO + TWO = FOUR C 1000 C 100 C 10 CS440/ECE448: Intro AI 4 Propositional logic Propositional logic Syntax: What is the language of wellformed formulas of propositional logic? Semantics: What is the interpretation of a wellformed formula in propositional logic? Inference rules and algorithms: How can we reason with propositional logic? Syntax: the building blocks Variables: p  q  r  Constants: (true) , (false) Unary connectives: (negation) Binary connectives: (conjunction) (disjunction) ! (implication) Syntax: wellformed formulas WFF ! Atomic  Complex Atomic ! Constant  Variable WFF ! Atomic  (Complex) Complex ! WFF  WFF WFF  WFF WFF  WFF ! WFF Semantics: truth values The interpretation " v of a wellformed formula " under a model v is a truth value: " v {true, false}. A model (=valuation) v is a complete* assignment of truth values to variables: v(p) = true v(q) = false, *each variable is either true or false With n variables, there are 2 n different models Models of " ( M( " ) ): set of models where " is true Interpretation !...
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This note was uploaded on 10/13/2011 for the course CS 440 taught by Professor Levinson,s during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Levinson,S

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