MIT24_241F09_handout14 - Logic I Fall 2009 Session 14...

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Unformatted text preview: Logic I Fall 2009 Session 14 Handout The vocabulary of PL The symbols in the language PL, the basic building blocks, are: Sentence letters of PL : A, B, C 3 , . . . Predicates of PL : A , B , C 2 , . . . Individual terms of PL : Individual constants of PL and variables of PL * Individual constants of PL : a, b 4 , c 2 , . . . , v * Variables of PL : w, x, y 3 , z 1 , . . . Quantifiers of PL : ( x ), ( z 2 ), ( x ), . . . And, of course, parentheses and the truth-functional connectives from SL. Essentials of PL syntax Sentence : An expression P is a sentence of PL iff P is a formula of PL and no variable occurs free in P . Formula : An expression is a formula of PL iff it can be formed by (possibly repeated) applications of the following rules: 1. Every atomic formula of PL is a formula of PL. 2. If P is a formula of PL, so is P . 3. If P and Q are formulas of PL, so are ( P & Q ), ( P Q ), ( P Q ), and ( P Q )....
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MIT24_241F09_handout14 - Logic I Fall 2009 Session 14...

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