# Contradiction

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In semantics, a **contradiction** is a sentence which is false under all circumstances, i.e. for every assignment of values to its basic expressions.

### Example

For example, the formula *p & Neg p* is a contradiction of propositional logic.

### Comments

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.

### Link

Utrecht Lexicon of Linguistics

### Reference

- Gamut, L.T.F. 1991.
*Logic, language, and meaning.*Chicago: Univ. of Chicago Press.