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Unformatted text preview: l ). According to the completeness theorem, Tautologies are a subset of Provable Formulas. Completeness Theorem: If S, then S. If for all valuations v, if v*(S i )=T for all i , then v*(S)=T. Note: To prove completeness theorem, use contrapositive. Consider a conditional statement P Q. The statement ~Q ~P is the contrapositive. We want to show // S //= S. Lemma: If // S, then U {~S } is consistent. Def. A set of sentences is consistent if there exist a valuation v such that v*(S i )=T for all S i . GOAL: TO assume // S. Construct v such that v*(R)=T for all R //= S....
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This note was uploaded on 04/07/2008 for the course PHILOSOPHY 407 taught by Professor Dean during the Spring '08 term at Rutgers.
 Spring '08
 Dean

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