In semantics, a contradiction is 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.
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.
- Gamut, L.T.F. 1991. Logic, language, and meaning. Chicago: Univ. of Chicago Press.