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−'''Logical negation''' is an [[logical operation|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.+The [[truth table]] of '''NOT p''' (also written as '''~p''' or '''¬p''') is as follows:+
−! style="width:20%" | p+
−! style="width:20%" | ¬p+
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−| valign=top |+| valign=top |+|}+
−| valign=top |+* [[Boolean algebra]]
| valign=top |+* [[Logic gate]]
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<font size="3">☞</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
−'''Logical 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.
−{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:40%"
+The [[truth table]] of <math>\operatorname{NOT}~ p,</math> also written <math>\lnot p,\!</math> appears below:
−|+ '''Logical Negation'''
+|- style="background:paleturquoise"
+<br>
−{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
+|+ style="height:30px" | <math>\text{Logical Negation}\!</math>
+|- style="height:40px; background:#f0f0ff"
+| style="width:50%" | <math>p\!</math>
+| style="width:50%" | <math>\lnot p\!</math>
|-
|-
−| F || T
+| <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
|-
|-
−| T || F
+| <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
|}
|}
+
<br>
<br>
−The logical negation of a proposition '''p''' is notated in different ways in various contexts of discussion and fields of application. Among these variants are the following:
+The negation of a proposition <math>p\!</math> may be found notated in various ways in various contexts of application, often merely for typographical convenience. Among these variants are the following:
−{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; width:40%"
+<br>
−|+ '''Variant Notations'''
+|- style="background:paleturquoise"
+{| align="center" border="1" cellpadding="8" cellspacing="0" width="45%"
−! style="text-align:center" | Notation
+|+ style="height:30px" | <math>\text{Variant Notations}\!</math>
−! Vocalization
+|- style="height:40px; background:#f0f0ff"
+| width="50%" align="center" | <math>\text{Notation}\!</math>
+| width="50%" | <math>\text{Vocalization}\!</math>
+|-
+| align="center" | <math>\bar{p}\!</math>
+| <math>p\!</math> bar
|-
|-
−| style="text-align:center" | <math>\bar{p}</math>
+| align="center" | <math>\tilde{p}\!</math>
−| bar ''p''
+| <math>p\!</math> tilde
|-
|-
−| style="text-align:center" | <math>p'\!</math>
+| align="center" | <math>p'\!</math>
−| ''p'' prime,<p> ''p'' complement
+| <math>p\!</math> prime<br> <math>p\!</math> complement
|-
|-
−| style="text-align:center" | <math>!p\!</math>
+| align="center" | <math>!p\!</math>
−| bang ''p''
+| bang <math>p\!</math>
|}
|}
+
<br>
<br>
−==See also==
+==Syllabus==
+===Focal nodes===
+* [[Inquiry Live]]
+* [[Logic Live]]
+===Peer nodes===
+* [http://intersci.ss.uci.edu/wiki/index.php/Logical_negation Logical Negation @ InterSciWiki]
+* [http://mywikibiz.com/Logical_negation Logical Negation @ MyWikiBiz]
+* [http://ref.subwiki.org/wiki/Logical_negation Logical Negation @ Subject Wikis]
+* [http://en.wikiversity.org/wiki/Logical_negation Logical Negation @ Wikiversity]
+* [http://beta.wikiversity.org/wiki/Logical_negation Logical Negation @ Wikiversity Beta]
+===Logical operators===
===Logical operators===
−{|
+{{col-begin}}
+{{col-break}}
* [[Exclusive disjunction]]
* [[Exclusive disjunction]]
* [[Logical conjunction]]
* [[Logical conjunction]]
* [[Logical disjunction]]
* [[Logical disjunction]]
* [[Logical equality]]
* [[Logical equality]]
−{{col-break}}
* [[Logical implication]]
* [[Logical implication]]
* [[Logical NAND]]
* [[Logical NAND]]
* [[Logical NNOR]]
* [[Logical NNOR]]
* [[Logical negation|Negation]]
* [[Logical negation|Negation]]
−{{col-end}}
+===Related topics===
===Related topics===
−{|
+{{col-begin}}
+{{col-break}}
* [[Ampheck]]
* [[Ampheck]]
−* [[Boolean domain]]
* [[Boolean domain]]
* [[Boolean function]]
* [[Boolean function]]
−* [[Boolean-valued function]]
−* [[Boolean logic]]
+* [[Differential logic]]
−* [[Laws of Form]]
+{{col-break}}
−* [[Logical graph]]
* [[Logical graph]]
−* [[Minimal negation operator]]
+* [[Multigrade operator]]
+* [[Parametric operator]]
* [[Peirce's law]]
* [[Peirce's law]]
+{{col-break}}
* [[Propositional calculus]]
* [[Propositional calculus]]
* [[Sole sufficient operator]]
* [[Sole sufficient operator]]
+* [[Truth table]]
+* [[Universe of discourse]]
* [[Zeroth order logic]]
* [[Zeroth order logic]]
−|}
+{{col-end}}
+===Relational concepts===
+{{col-begin}}
+{{col-break}}
+* [[Continuous predicate]]
+* [[Hypostatic abstraction]]
+* [[Logic of relatives]]
+* [[Logical matrix]]
+{{col-break}}
+* [[Relation (mathematics)|Relation]]
+* [[Relation composition]]
+* [[Relation construction]]
+* [[Relation reduction]]
+{{col-break}}
+* [[Relation theory]]
+* [[Relative term]]
+* [[Sign relation]]
+* [[Triadic relation]]
+{{col-end}}
+===Information, Inquiry===
+{{col-begin}}
+{{col-break}}
+* [[Inquiry]]
+* [[Dynamics of inquiry]]
+{{col-break}}
+* [[Semeiotic]]
+* [[Logic of information]]
+{{col-break}}
+* [[Descriptive science]]
+* [[Normative science]]
+{{col-break}}
+* [[Pragmatic maxim]]
+* [[Truth theory]]
+{{col-end}}
+===Related articles===
+{{col-begin}}
+{{col-break}}
+* [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language]
+* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
+* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
+{{col-break}}
+* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction]
+* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus]
+* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
+{{col-break}}
+* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]
+* [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
+* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
+{{col-end}}
+==Document history==
+Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
+* [http://intersci.ss.uci.edu/wiki/index.php/Logical_negation Logical Negation], [http://intersci.ss.uci.edu/ InterSciWiki]
+* [http://mywikibiz.com/Logical_negation Logical Negation], [http://mywikibiz.com/ MyWikiBiz]
+* [http://wikinfo.org/w/index.php/Logical_negation Logical Negation], [http://wikinfo.org/w/ Wikinfo]
+* [http://en.wikiversity.org/wiki/Logical_negation Logical Negation], [http://en.wikiversity.org/ Wikiversity]
+* [http://beta.wikiversity.org/wiki/Logical_negation Logical Negation], [http://beta.wikiversity.org/ Wikiversity Beta]
+* [http://en.wikipedia.org/w/index.php?title=Logical_negation&oldid=77111608 Logical Negation], [http://en.wikipedia.org/ Wikipedia]
+[[Category:Inquiry]]
+[[Category:Open Educational Resource]]
+[[Category:Peer Educational Resource]]
+[[Category:Charles Sanders Peirce]]
+[[Category:Computer Science]]
+[[Category:Formal Languages]]
+[[Category:Formal Sciences]]
+[[Category:Formal Systems]]
+[[Category:Linguistics]]
+[[Category:Logic]]
+[[Category:Mathematics]]
+[[Category:Philosophy]]
+[[Category:Semiotics]]