Chapters 3 & 4: The Boolean Connectives and the Logic of Boolean Connectives

truth functional connectives
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Terms in this set (19)
tautologyA sentence that is logically true in virtue of its truth-functional structure. A tautology is a sentence that comes out true under every row of its truth table Any tautology is logically necessary. Not all logically necessary claims are tautologies.A sentence S is TT-necessary if and only ifthe truth table for S is T in EVERY row under its main connective.A sentence S is TT-possible if and only ifthe truth table for S is T in at least ONE row under its truth tablelogicallly equivalent sentencessentences that have the same truth value in every possible circumstance. sentences have the same truth conditions, since the conditions under which they came out true and false are identical.tautologically equivalentlogically equivalent sentences whose equivalence is due to the meaning of the truth functional connectives they contain. to check of TE, if two sentences on a joint truth table have main connective columns which are completely identical, then the sentences are TE.tautological vs logical equivalenceAll tautologically equivalent sentences are logically equivalent. However, logically equivalent sentences are NOT always tautologically equivalent:logical consequencea sentence, S, is a logical consequence of some premises if S is true in every logically possible situation in which the premises sentences are true or equivalently, if there is no possible situation in which the premises are true and the conclusion false.tautological consequenceS is true in every row of the truth table that makes the premise sentences true. "all we care about is the rows in which P is true. For each row in which P is true, reference the value of Q in that row, and if it is false, we know that Q is not a tautological consequence f P."A connective is truth-functional if and only ifthe truth value of a complex sentence-formed by using the connective - is a function of the truth values of the solo sentences.