MIT24_241F09_handout14

# 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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