Negation

In logic, negation, also called logical complement, is an operation that takes a proposition p to another proposition "not p", written ¬p, which is interpreted intuitively as being true when p is false and false when p is true. Negation is thus a unary (single-argument) logical connective. It may be applied as an operation on propositions, truth values, or semantic values more generally. In classical logic, negation is normally identified with the truth function that takes truth to falsity and vice versa. In intuitionistic logic, according to the Brouwer–Heyting–Kolmogorov interpretation, the negation of a proposition p is the proposition whose proofs are the refutations of p.

Definition

No agreement exists as to the possibility of defining negation, as to its logical status, function, and meaning, as to its field of applicability..., and as to the interpretation of the negative judgment, (F.H. Heinemann 1944).

Classical negation is an operation on one logical value, typically the value of a proposition, that produces a value of true when its operand is false and a value of false when its operand is true. So, if statement A is true, then ¬A (pronounced "not A") would therefore be false; and conversely, if ¬A is true, then A would be false.

Affirmative and negative

In linguistics and grammar, affirmative and negative are terms of opposite meaning which may be applied to statements, verb phrases, clauses, and some other utterances. Essentially an affirmative (positive) form is used to express the validity or truth of a basic assertion, while a negative form expresses its falsity. Examples are the sentences "Jane is here" and "Jane is not here"; the first is affirmative, while the second is negative.

The grammatical category associated with affirmative and negative is called polarity. This means that a sentence, verb phrase, etc. may be said to have either affirmative or negative polarity (its polarity may be either affirmative or negative). Affirmative is generally the unmarked polarity; the negative is marked by a negating word or particle such as the English not, German nicht, Swedish inte, and so on, which reverses the meaning of the predicate. The process of converting affirmative to negative is called negation – the grammatical rules for negation vary from language to language, and a given language may have more than one way of producing negations.

Negation (disambiguation)

Negation is a connective in logic and an operation computing that maps true to false and false to true. It may also refer to:

Mathematics

See also