In logic and mathematics, negation, also called logical complement, is a unary logical connective. It is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is true when that proposition is false, and vice versa. 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. In Kripke semantics where the semantic values of formulae are sets of possible worlds, negation is set-theoretic complementation.

Read more about NegationDefinition, Notation, Rules of Inference, Programming

Other articles related to "negation":

Self-refuting Idea - Variations - In Logic
... For example, the negation of a proposition can be proved by showing that the proposition infers its own negation ... by (1) showing that a proof would infer the negation of the proposition or by (2) showing a proof would infer that the negation of the proposition can be proved ...
Making Do With A Single Logical Quality
... from denial is typically now done through the theory of negation ... logicians, making a denial is essentially reducible to affirming a negation ... trend may go back to Frege although his notation for negation is ambiguous between asserting a negation and denying ...
... are a race of beings created for the CrossGen comic Negation ... The Lawbringers are the twisted, mis-shapen gods of the Negation universe and have abilities on par with the beautiful, perfectly formed First, those ... The Lawgivers were created when Charon, the mad god of the Negation universe, somehow expelled from himself all his rage and madness ...
Negation - Programming
... As in mathematics, negation is used in computer science to construct logical statements ... Perl, etc.) provide more than one operator for negation ... few languages like PL/I and Ratfor use ¬ for negation ...
Stevens Negation
... "Negation" is a poem from Wallace Stevens's first book of poetry, Harmonium ... Negation Hi! The creator too is blind, Struggling toward his harmonious whole, Rejecting intermediate parts, Horrors and falsities and wrongs Incapable master of all force, Too vague ... It was extracted as "Negation" for inclusion in the second edition of Harmonium ...

Famous quotes containing the word negation:

    Friendship, according to Proust, is the negation of that irremediable solitude to which every human being is condemned.
    Samuel Beckett (1906–1989)

    Michelangelo said to Pope Julius II, “Self negation is noble, self-culture is beneficent, self-possession is manly, but to the truly great and inspiring soul they are poor and tame compared to self-abuse.” Mr. Brown, here, in one of his latest and most graceful poems refers to it in an eloquent line which is destined to live to the end of time—”None know it but to love it, None name it but to praise.”
    Mark Twain [Samuel Langhorne Clemens] (1835–1910)

    We make a mistake forsaking England and moving out into the periphery of life. After all, Taormina, Ceylon, Africa, America—as far as we go, they are only the negation of what we ourselves stand for and are: and we’re rather like Jonahs running away from the place we belong.
    —D.H. (David Herbert)