ikkeP

ikkeP is a notation used in formal logic to denote the negation of a proposition P. Read as "not P," it is functionally equivalent to the standard negation operator ¬P in classical propositional logic. The term arises from the word ikke, meaning "not" in several Scandinavian languages, combined with P to indicate negation of P.

In formal terms, if P is a well-formed formula, ikkeP is a formula whose truth value is the opposite of P under classical semantics: P is true implies ikkeP is false, and P is false implies ikkeP is true. In extended logics, the interpretation of ikkeP may vary if truth values extend beyond true and false, but the core idea remains negation.

Derivation and use: ikkeP is commonly encountered in teaching materials, textbooks, or informal notations where authors prefer a non-Latin character or want to emphasize linguistic roots. It is not an official operator in standard logical systems, and its use is mostly idiosyncratic or stylistic.

Examples: If P denotes "it is raining," ikkeP denotes "it is not raining." In a truth-functional setting, when P is true, ikkeP is false; when P is false, ikkeP is true.

Related concepts: negation, negation as failure, double negation, and various non-classical logics where negation is treated differently. See also: propositional logic, negation, logic notation.