Resolution_Part_1

# Resolution_Part_1 - • To prove G we need to show is...

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Resolution and Refutation York University Department of Computer Science and Engineering York University- CSE 3401- V. Movahedi 1 04_Resolution

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Overview Propositional Logic Resolution Refutation Predicate Logic Substitution Unification Resolution Refutation Search space [ref.: Nilsson- Chap.3] [Prof. Zbigniew Stachniak’s class notes] York University- CSE 3401 2 04_Resolution
Theorems from Logic [from Mathematical Logic, George Tourlakis] Modus Ponens Cut Rule Transitivity of Proof by Contradiction York University- CSE 3401 3 04_Resolution

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Resolution in Logic By A. Robinson (1965) Example: Prove We need to show that the following set is inconsistent: York University- CSE 3401 4 04_Resolution
Resolution in Logic Programming Program P (facts and rules in clause form) Goal G negated and added to program P

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Unformatted text preview: • To prove G, we need to show is inconsistent York University- CSE 3401 5 } { G P q; t :- p. , p:- s. Parent clauses q; t :- s. Resolvent Resolving upon p, being on different sides of :- Complementary literals 04_Resolution Example (1) • Program P={q:-. , p:-q.} • Query :-p. – This is already the negated form of our goal! York University- CSE 3401 6 q:-. p:- q. :-p. :-q. :- empty clause, inconsistency therefore p is satisfiable true 04_Resolution Refutation • When resolution is used to prove inconsistency, it is also called refutation. (refute=disprove) • The above binary tree, showing resolution and resulting in the empty clause, is called a refutation tree. • NOTE: To avoid potential mistakes, DO NOT RESOLVE UPON MORE THAN ONE LITERAL SIMULTANEOUSLY. York University- CSE 3401 7 04_Resolution...
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