truth tables-1 - Symbolic Logic: Sentential/Propositional...

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Symbolic Logic: Sentential/Propositional System I. Foundation Simple/Atomic Proposition: A proposition that cannot be reduced to other propositions and/or does not contain a logical operator. Example : The cat sat on the mat. Compound/Complex/Molecular Proposition: A proposition that can be reduced to other propositions and/or does contain a logical operator. Examples : The cat sat on the mat and the dog barked. The cat did not sit on the mat. Logical operator/connective/relation : A word in ordinary language that has implications for the truth or falsity of propositions and which is symbolized for logical manipulation. II. The Grammar of the System a. Logical Operators/Connectives/Relations (truth-functional) Ordinary Language Name Symbol And Conjunction Not Negation ~ (Either ). ..Or Inclusive Disjunction v 'If . .. Then' or 'Implies' Material Conditional Material Implication General Inference Rule -> 'If and only If' ( Iff ) Material Equivalence Bi-Conditional General Replacement Rule <-> b. Prepositional Symbols 1. Constants: Symbols that can stand for only one proposition in a field of discourse. Cannot be used to state rules. Capital Letters A--Z Generally the letter used suggests the proposition, but doesn't have to. Example: The cat sat on the mat and the dog barked.: C & D or equally well P 2. Variables: Symbols that can stand for a range of propositions with the same basic pattern of operators (either major or minor). They must be used to state rules . Small letters p, q, r, s, t, u, v, w. For example: Any conjunction is represented by "p q." The letters are supposed to represent an order: p is the first proposition, q is the next different proposition in the field of discourse, r is the next different proposition etc. . The small letters x, y, z are reserved as
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symbols for quantifiers. Do not indiscriminately translate propositions into the variable symbols. c. Rules of Parentheses
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This note was uploaded on 04/07/2008 for the course PHIL 205 taught by Professor Apostol during the Spring '08 term at Northern Illinois University.

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truth tables-1 - Symbolic Logic: Sentential/Propositional...

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