Negation [Lat. Negare ‘To Say That…Not, Deny’]

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Routledge Dictionary of Language and Linguistics

1 In formal logic, logical particles—defined as one-place predicates by the truth tables—that convert the truth value of a proposition p into its opposite truth value (notation: ¬p or ~p); that is, ¬p is true if and only if p is false and vice versa. Tokyo is the capital of Japan is true if and only if Tokyo is not the capital of Japan is false. The term ‘negation’ refers both to the one-place sentence operator it is not the case that or not as well as to the proposition defined thereby. The following (two-value) truth table represents a definition of negation:

Since logical negation is basically sentence negation, the clearest everyday paraphrase for it is it is not the case that p ( presupposition test for negation as a criterion for defining presuppositions).

2 In contrast with logical negation, natural language negation functions not only as sentence negation, but also primarily as clausal or constituent negation: She did not pay (= negation of predication), No one paid anything (= negation of the subject NP), He paid nothing (= negation of the object NP). Here the scope (= semantic coverage) of negation is frequently polysemic or dependent on the placement of negation, on the sentence stress ( stress, prosody) as well as on the linguistic and/or extralinguistic context. Natural language negation may be realized in various ways: (a) lexically with adverbs and adverbial expressions (not, never, by no means), indefinite pronouns (nobody, nothing, none), coordinating conjunctions (neither…nor), sentence equivalents (no), or prepositions (without, besides); (b) morphologically with prefixes (in +exact, un+interested) or suffixes (help+ less); (c) intonationally with contrastive accent (in Jacob is not flying to New York tomorrow the negation can refer to Jacob, flying, New York, or tomorrow depending which elements are stressed); (d) idiomatically by expressions like For all I care, Formally, three types of negation are differentiated: (a) internal (= strong) negation, the basic type of natural language negation (e.g. The King of France is not bald); (b) external (=weak) negation, which corresponds to logical negation (e.g. It’s not the case/it’s not true that p); (c) contrastive (=local) negation, which can also be considered a pragmatic variant of strong negation to the degree that stress and the corresponding modifying clause are relevant to the scope of the negation (e.g. The King of France is not bald, but rather wears glasses). The linguistic description of negation has proven to be a difficult problem in all grammatical models owing to the complex interrelationship of syntactic, prosodic, semantic, and pragmatic aspects.

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3 In unification grammar, the logical complement of a feature structure.

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