Negatsiooni

Negatsiooni, commonly translated as negation, is the operation that inverts the truth value of a proposition or denies a predicate. In formal logic and mathematics, negatsiooni is a unary operator that maps a proposition P to ¬P, which is true exactly when P is false. The principle of double negation holds that ¬(¬P) is equivalent to P, and De Morgan's laws describe how negation interacts with conjunction and disjunction: ¬(P ∧ Q) ≡ ¬P ∨ ¬Q and ¬(P ∨ Q) ≡ ¬P ∧ ¬Q.

In natural language, negatsiooni is realized through negative markers such as not, no, or never, as well as through affixes or particles in some languages. The scope of negation determines which portion of a sentence is denied and interacts with tense, aspect, and quantification. Examples: "John did not leave" and "Not all students passed."

Typologically, negatsiooni is encoded in diverse ways. Some languages use sentential negation with a separate word or particle; others employ morphological negation with verb or clitic affixes; some exhibit negative concord, where multiple negative elements reinforce the negation. Many languages allow double negation, while others require one negative element to compute the negation.

In semantics and cognitive science, negatsiooni is a core operator in truth-conditional semantics. Its interaction with quantifiers, modality, and scope is a central topic in linguistic theory. In computer science, the logical NOT operator implements a related form of negation, forming the basis for Boolean logic and conditional statements.