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Definition [ edit ] 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.
Ways in which this constituent negation is realized depends on the grammar of the language in question. English generally places not before the negated element, as in "I witnessed not a debate, but a war." There are also negating affixes, such as the English prefixes non-, un-, in-, etc. Such elements are called privatives.
It can be made to hold for all real numbers by extending the definition of negation to include zero and negative numbers. Specifically: The negation of 0 is 0, and; The negation of a negative number is the corresponding positive number. For example, the negation of −3 is +3. In general,
[1] [2] The definition mostly appears in proof theory (of classical logic), e.g. in conjunctive normal form and the method of resolution. Literals can be divided into two types: [2] A positive literal is just an atom (e.g., ). A negative literal is the negation of an atom (e.g., ).
In Boolean logic, logical NOR, [1] non-disjunction, or joint denial [1] is a truth-functional operator which produces a result that is the negation of logical or.That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both p and q are false.
Korean verbs can be negated by the negative verbs 않다 anta and 못하다 mothada or by the negative adverbs 안 an and 못 mot. The copula 이다 ida has a corresponding negative copula 아니다 anida. (anida is an independent word like anta and mothada, unlike ida which cannot stand on its own and must be attached to a noun.)
Do-support (sometimes referred to as do-insertion or periphrastic do), in English grammar, is the use of the auxiliary verb do (or one of its inflected forms e.g. does), to form negated clauses and constructions which require subject–auxiliary inversion, such as questions.
In propositional logic, the double negation of a statement states that "it is not the case that the statement is not true". In classical logic, every statement is logically equivalent to its double negation, but this is not true in intuitionistic logic; this can be expressed by the formula A ≡ ~(~A) where the sign ≡ expresses logical equivalence and the sign ~ expresses negation.