negacje

Negacje, or negation, is the operation of denying or contradicting a proposition, statement, or claim. The term spans logic, linguistics, mathematics, and computer science.

In logic, negation is a unary operator that yields the opposite truth value. Represented by ¬ or not, the negation of a proposition p is ¬p. In classical propositional logic, if p is true then ¬p is false, and if p is false then ¬p is true. Double negation often yields the original statement, ¬(¬p) ≡ p, whereas in intuitionistic logic this equivalence is not generally valid.

In mathematics, negation can mean the additive inverse of a number, denoted −a. It also extends to set theory as the complement relative to a universal set, A^c. De Morgan's laws relate the negation of conjunctions and disjunctions: ¬(P ∧ Q) ≡ ¬P ∨ ¬Q and ¬(P ∨ Q) ≡ ¬P ∧ ¬Q.

In linguistics, negation is a grammatical category used to express denial or opposition to a proposition. In Polish, negation is typically realized by the particle nie (as in nie wiem, “I do not know”), which combines with verbs and other elements to form negative phrases. Negation interacts with mood, aspect, and tense, and there are negative pronouns and particles such as nikt, nic, niczym, and żaden that convey various degrees of negation.

In computing, negation is the NOT operation in programming and digital logic, flipping a boolean value or inverting bits (bitwise NOT). Different languages use symbols such as !, not, or ~ to express this operation, and negation plays a central role in control flow, condition checks, and logical expressions.