Introduction 1.3

Introduction 1.3 - Propositional Logic (review) Alphabet...

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Unformatted text preview: Propositional Logic (review) Alphabet Variables, e.g. p, q, r, ..., p 1 , ..., p, ... Constants: T and (or F) Connectives: or {~, &, #, ->, <-> in some books} Brackets: ( and ) Well-formed-formula (wff) All variables and constants are wffs. If A and B are wffs, then the following are also wffs. Priority of connectives, and rules for removing brackets } , , , , { ) ( ), ( ), ( ), ( ), ( B A B A B A B A A York University- CSE 3401 11 01_Introduction Propositional Logic (cont.) Semantics and truth tables true (1) and false (0) State: possible assignment to variables Tautology A formula A is a tautology if v(A)=1 (true) in all possible states Example: Satisfiable / consistent A formula A is satisfiable iff there is at least one state v where v(A)=1 (true). Examples: A set of formulae X is satisfiable (or consistent) iff there is at least one state v where for every formula A in X, v(A)=1. Example: state v where for every formula A in X, v(A)=1....
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This note was uploaded on 02/14/2012 for the course CSE 3401 taught by Professor Movahedi during the Fall '11 term at York University.

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Introduction 1.3 - Propositional Logic (review) Alphabet...

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