L15ResolutionPart1

# L15ResolutionPart1 - Propositional Resolution Part 1 Short...

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Propositional Resolution Part 1 Short Review Professor Anita Wasilewska CSE 352 Artificial Intelligence

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SYNTAX “dictionary” Literal – any propositional VARIABLE a or negation of a variable ¬ a, a VAR, Example - variables: a, b, c, negation of variables: ¬a, ¬b, -d … Positive Literal any variable a VAR Clause – any finite set of literals Example- C1, C2, C3 are clauses where C1 = {a, b} , C2 = {a, ¬ c} , C3 = { a, ¬a, ……,a k }
Syntax “Dictionary” Empty Clause {} – is an empty set i.e. a clause without elements. Finite set of clauses CL = { C1, …., Cn} Example CL = {{a}, { }, { b, ¬a} , {c, ¬ d}}

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Semantics – Interpretation of Clauses Think semantically of a clause C = { a 1 , ……., a n } as disjunction, i.e. C is logically equivalent to a 1 U a 2 U …… U a n a i Literal Formally – a truth assignment v : VAR -> {0, 1} we extended it to set of all CLAUSES CL as follows: v* : CL -> {0, 1} we extend v*(C) = v*(a 1 ) U …. . U v*(a n ) for any clause C in CL , where 0 – False, 1 – True Shorthand : v* = v