# Negation

•  this article includes a list of references, but its sources remain unclear because it has insufficient inline citations. please help to improve this article by introducing more precise citations. (march 2013) (learn how and when to remove this template message)

negation
not
definition
truth table
logic gate
normal forms
disjunctive
conjunctive
zhegalkin polynomial
post's lattices
0-preservingno
1-preservingno
monotoneno
affineyes

in logic, negation, also called the logical complement, is an operation that takes a proposition to another proposition "not ", written , which is interpreted intuitively as being true when is false, and false when is true. negation is thus a unary (single-argument) logical connective. it may be applied as an operation on notions, 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 is the proposition whose proofs are the refutations of .

• definition
• notation
• properties
• rules of inference
• programming
• kripke semantics
• references

## For negation in linguistics, see Affirmation and negation. For other uses, see Negation (disambiguation). This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (March 2013) (Learn how and when to remove this template message) NegationNOTDefinition${\displaystyle {\overline {x}}}$Truth table${\displaystyle (10)}$Logic gateNormal formsDisjunctive${\displaystyle {\overline {x}}}$Conjunctive${\displaystyle {\overline {x}}}$Zhegalkin polynomial${\displaystyle 1\oplus x}$Post's lattices0-preservingno1-preservingnoMonotonenoAffineyesvt In logic, negation, also called the logical complement, is an operation that takes a proposition ${\displaystyle P}$ to another proposition "not ${\displaystyle P}$", written ${\displaystyle \neg P}$, which is interpreted intuitively as being true when ${\displaystyle P}$ is false, and false when ${\displaystyle P}$ is true. Negation is thus a unary (single-argument) logical connective. It may be applied as an operation on notions, 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 ${\displaystyle P}$ is the proposition whose proofs are the refutations of ${\displaystyle P}$. Contents 1 Definition 2 Notation 3 Properties 3.1 Double negation 3.2 Distributivity 3.3 Linearity 3.4 Self dual 3.5 Negations of quantifiers 4 Rules of inference 5 Programming 6 Kripke semantics 7 See also 8 References 9 Further reading 10 External links

Other Languages
العربية: نفي (رياضيات)
български: Отрицание
čeština: Negace
dansk: Negation
Deutsch: Negation
eesti: Eitus
emiliàn e rumagnòl: Negasiòun (matemàtica)
Esperanto: Logika neo
فارسی: نقیض
हिन्दी: निषेध (तर्क)
hrvatski: Negacija
Bahasa Indonesia: Negasi
қазақша: Терістеу
Latina: Negatio
magyar: Negáció
македонски: Негација
Bahasa Melayu: Negasi
Nederlands: Logische negatie

norsk: Negasjon
Piemontèis: Negassion
polski: Negacja
português: Negação
русский: Отрицание
shqip: Negacioni
Simple English: Logical negation
slovenčina: Negácia (logika)
slovenščina: Negacija
српски / srpski: Логичка негација
srpskohrvatski / српскохрватски: Logička negacija
svenska: Negation
ไทย: นิเสธ
тоҷикӣ: Инкор
українська: Заперечення