This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CS245  Winter 2010, Lecture 13 Shai BenDavid We are getting close to completing the picture of relationship between syn tactic and semantic notions. In the last lecture we proved that the consistency of a set of propositions is equivalent to its satisfiability. We have also seen that provability entails logical implication. Namely, if then  = . This is the Soundness theorem. The last remaining component is the Completeness theorem, which is the reverse of the soundness theorem. Theorem 1 (The Completeness Theorem) For every set of propositions and every proposition , if  = then . Proof Let us prove the equivalent contrapositive statement: If 6 then 6 = . Recall Lemma ?? from the previous lecture. That lemma states that for every set of propositions and every proposition , if 6 then { ( ) } is consistent....
View
Full
Document
This note was uploaded on 02/11/2010 for the course ART AFM101 taught by Professor Mr.lushman during the Spring '10 term at University of Toronto Toronto.
 Spring '10
 Mr.Lushman

Click to edit the document details