negaation

Negaation is commonly a misspelling of negation, the term used to denote the operation of forming the opposite truth value or meaning. In standard usage, negation is the correct spelling; references to "negaation" typically arise as a typo or when discussing the misspelling itself.

In logic, negation is a unary operator that takes a proposition P and yields ¬P, its opposite truth value. Classical logic treats negation with laws such as double negation: ¬(¬P) = P, and De Morgan's laws: ¬(P ∧ Q) ≡ (¬P) ∨ (¬Q) and ¬(P ∨ Q) ≡ (¬P) ∧ (¬Q). Negation interacts with other connectives to form complex truth-functional expressions.

In linguistics, negation refers to the grammatical process of denying or contradicting a proposition. It employs negative particles (such as not or no), affixes, or specific syntactic constructions. Negation can affect tense, aspect, and polarity, and languages differ in how negation scopes across clauses and in phenomena like negative concord and polarity sensitivity.

In mathematics and computer science, negation functions as a fundamental logical operator in formal systems. In programming languages, boolean negation is typically written as not or !, and it controls decisions in conditionals, loops, and boolean expressions. In predicate logic, negation applies to statements with quantifiers, producing equivalents that influence proof strategies and model theory.

Etymology traces negation to Latin negatio, from negare meaning to deny or refuse. See also negation, double negation, and De Morgan's laws.