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Unformatted text preview: CS 245 Spring 2010 Shai BenDavid Lectures 56 1 So far, we have been discussing only the syntax aspect of propositional logic. We are now turning to the semantics, or meaning of the logic. Next Task : Associate a meaning with propositional formulas. A propositional formula α will be interpreted as a function from {T, F} n to {T, F}, where ‘n’ is the number of letters (we’ll call them “propositional variables”) in α. Let v denote a vector in {T, F} n v = (T, T, F, …, T) } Given a propositional formula α we wish to define what is α(v) for every such v. p The Basic Truth Tables q (p V q) ‘or’ (p Λ q) ‘and’ (p q) `ifthen’ (¬p) ‘not’ T T T T T F T F T F F F F T T F T T F F F F T T The table tries to associate with each connective a meaning which is as close as possible to it intuitive meaning in a natural language. Note that with (p q), the truth table semantics deviates considerably from the natural language meaning. For example, the implication (p q) for the statements below is TRUE according to truth table, but not true in English. Example: p – “I woke up at 5am this morning” q – “I am 6 feet tall” (both statements are False, and the truth table evaluates (p q) as True whenever p is False)....
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 Spring '10
 Mr.Lushman
 Logic, natural language, propositional formula, Shai BenDavid Lectures

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