Lecture04TheoremsAndProofs

Lecture04TheoremsAndProofs - Lecture 4 - CS 2603 Applied...

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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 1 Lecture 4 — CS 2603 Applied Logic for Hardware and Software Truth Inference and the Logical Way
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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 2 ± Inference ( courtesy of Merriam-Webster, www.m-w.com ) ² verb- the act of passing from one proposition, statement, or judgment considered as true to another whose truth is believed to follow from that of the former ² noun– a proposition arrived at by inferring ± Formal Inference (mathematical logic) ² Object Language – notation for stating premises and conclusions 9 WFFs form the object language ² Inference Rules – ways to conclude new WFFs from proven WFFs ² Metalanguage – notation for proofs of theorems ² Formal Inference (Proof) a set of assumptions together with an ordered collection of inference rules applied to reach a conclusion ² Theorem (sequent) – a set of assumptions and a conclusion for which there is a formal inference (that is, a proof) Logical Inference
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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 3 w 1 , w 2 , …, w n w Theorem – a statement that can be proved premises (WFFs) conclusion (WFF) turnstile Theorem Meaning of turnstile : If the premises are true, then there is a path through the rules of inference that leads to the conclusion double turnstile indicates “fact” Fact a semantic entailment (whether provable or not) w 1 , w 2 , …, w n w The o r e m s a p v b l f c t F y u n . T h re single indicates provable fact
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This note was uploaded on 04/08/2008 for the course CS 2603 taught by Professor Rexpage during the Spring '08 term at The University of Oklahoma.

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Lecture04TheoremsAndProofs - Lecture 4 - CS 2603 Applied...

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