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Contradiction

SEMANTICS: a sentence which is false under all circumstances, i.e. for every assignment of values to its basic expressions. A sentence of propositional logic is a contradiction when it is false for every possible assignment of truth values to the propositional letters of that sentence. For example, the formula p & Neg p is a contradiction of propositional logic. A sentence of predicate logic is a contradiction when it is false for every possible denotation of the variables and individual and predicate constants that it contains. For example, the formula All(x)[ P(x) & Neg P(x) ] is a contradiction of predicate logic.

LIT.	Gamut, L.T.F. (1991)