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cs440-lec21-resolution - Artificial Intelligence Lecture#21...

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Artificial Intelligence Lecture #21: Resolution Theorem Proving UIUC CS 440 / ECE 448 Professor: Eyal Amir Spring Semester 2008
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SAT via Generate and Test If we have a truth table of KB, then we can check that KB satisfiable by looking at it. Problem: n propositional symbols 2 n rows in truth table Checking interpretation I takes time O(|KB|) Generating table is expensive: O(2 n |KB|) time Observation: SAT requires us to look only for one model
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Clausal Form Every formula can be reformulated into an equivalent CNF formula (conjunction of clauses). Examples (using De Morgan Laws): ) ( ) ( b a b a ¬ ) ( b b ) ( a b ¬ ) ( b a ) ( a a ¬
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Clausal Form Every formula can be reformulated into an equivalent CNF formula (conjunction of clauses). Examples: 2 _ _ 1 _ 90 _ _ 1 _ _ t door face t cl turn t door face ¬ 2 _ _ 1 _ 90 _ _ 1 _ _ t door face t cl turn t door face ¬ ¬ ¬
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Clausal Form Every formula can be reformulated into an equivalent CNF formula (conjunction of clauses). Examples: ¬ 2 _ _ 2 _ _ t door face t corridor at 1 _ _ 1 _ _ t fwd move t door face 2 _ _ 1 _ _ 1 _ _ 2 _ _ 1 _ _ 1 _ _ t door face t
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