Editing Negation (section)

{{short description|Logical operation}}
{{for-multi|negation in linguistics|Affirmation and negation|other uses|Negation (disambiguation)}}
{{Use dmy dates|date=March 2020}}
{{Infobox logical connective
| title        = Negation
| other titles = NOT
| wikifunction = Z10216
| Venn diagram = Venn10.svg
| definition   = <math>\lnot{x}</math>
| truth table  = <math>(01)</math>
| logic gate   = NOT_ANSI.svg
| DNF          = <math>\lnot{x}</math>
| CNF          = <math>\lnot{x}</math>
| Zhegalkin    = <math>1 \oplus x</math>
| 0-preserving = no
| 1-preserving = no
| monotone     = no
| affine       = yes
| self-dual    = yes
}}
{{Logical connectives sidebar}}

In [[logic]], '''negation''', also called the '''logical not''' or '''logical complement''', is an [[operation (mathematics)|operation]] that takes a [[Proposition (mathematics)|proposition]] <math>P</math> to another proposition "not <math>P</math>", written <math>\neg P</math>, <math>\mathord{\sim} P</math>, <math>P^\prime</math><ref>Virtually all Turkish high school math textbooks use p' for negation due to the books handed out by the Ministry of National Education representing it as p'.</ref> or <math>\overline{P}</math>.{{cn|reason=Provide a source for each of the notations, including P'.|date=December 2024}} It is interpreted intuitively as being true when <math>P</math> is false, and false when <math>P</math> is true.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Negation|url=https://mathworld.wolfram.com/Negation.html|access-date=2020-09-02|website=mathworld.wolfram.com|language=en}}</ref><ref>{{Cite web|title=Logic and Mathematical Statements - Worked Examples|url=https://www.math.toronto.edu/preparing-for-calculus/3_logic/we_3_negation.html|access-date=2020-09-02|website=www.math.toronto.edu}}</ref> For example, if <math>P</math> is "Spot runs", then "not <math>P</math>" is "Spot does not run". An operand of a negation is called a '''''negand''''' or '''''negatum'''''.<ref name=":212">{{Cite book |last=Beall |first=Jeffrey C. |title=Logic: the basics |date=2010 |publisher=Routledge |isbn=978-0-203-85155-5 |edition=1. publ |location=London |pages=57 |language=en}}</ref>

Negation is a [[unary operation|unary]] [[logical connective]]. It may furthermore be applied not only to propositions, but also to [[notion (philosophy)|notions]], [[truth value]]s, or [[interpretation (logic)|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 <math>P</math> is the proposition whose proofs are the refutations of <math>P</math>.