# Changes

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<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].

<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
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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.
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'''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.
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The [[truth table]] of '''NOT p''' (also written as '''~p''' or '''&not;p''') is as follows:
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The [[truth table]] of $\operatorname{NOT}~ p,$ also written $\lnot p,\!$ appears below:

<br>

<br>
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:40%"
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
|+ '''Logical Negation'''
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|+ style="height:30px" | $\text{Logical Negation}\!$
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="width:20%" | p
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| style="width:50%" | $p\!$
! style="width:20%" | &not;p
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| style="width:50%" | $\lnot p\!$

|-

|-
| F || T
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| $\operatorname{F}$ || $\operatorname{T}$

|-

|-
| T || F
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| $\operatorname{T}$ || $\operatorname{F}$

|}

|}

<br>

<br>
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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:
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The negation of a proposition $p\!$ may be found notated in various ways in various contexts of application, often merely for typographical convenience.  Among these variants are the following:

<br>

<br>
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; width:40%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" width="45%"
|+ '''Variant Notations'''
+
|+ style="height:30px" | $\text{Variant Notations}\!$
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="text-align:center" | Notation
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| width="50%" align="center" | $\text{Notation}\!$
! Vocalization
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| width="50%" | $\text{Vocalization}\!$

|-

|-
| style="text-align:center" | $\bar{p}$
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| align="center" | $\bar{p}\!$
| bar ''p''
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| $p\!$ bar

|-

|-
| style="text-align:center" | $p'\!$
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| align="center" | $\tilde{p}\!$
| ''p'' prime,<p> ''p'' complement
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| p\!</math> tilde |- |- | style="text-align:center" | [itex]!p\!
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| align="center" | $p'\!$
| bang ''p''
+
| $p\!$ prime<br> $p\!$ complement
+
|-
+
| align="center" | $!p\!$
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| bang $p\!$

|}

|}
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===Focal nodes===

===Focal nodes===
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{{col-break}}

* [[Inquiry Live]]

* [[Inquiry Live]]
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* [[Logic Live]]

* [[Logic Live]]
{{col-end}}

===Peer nodes===

===Peer nodes===
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{{col-begin}}
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* [http://intersci.ss.uci.edu/wiki/index.php/Logical_negation Logical Negation @ InterSciWiki]
{{col-break}}

* [http://mywikibiz.com/Logical_negation Logical Negation @ MyWikiBiz]

* [http://mywikibiz.com/Logical_negation Logical Negation @ MyWikiBiz]
* [http://mathweb.org/wiki/Logical_negation Logical Negation @ MathWeb Wiki]
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* [http://ref.subwiki.org/wiki/Logical_negation Logical Negation @ Subject Wikis]
* [http://netknowledge.org/wiki/Logical_negation Logical Negation @ NetKnowledge]
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* [http://en.wikiversity.org/wiki/Logical_negation Logical Negation @ Wikiversity]
{{col-break}}
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* [http://beta.wikiversity.org/wiki/Logical_negation Logical Negation @ Wikiversity Beta]
* [http://wiki.oercommons.org/mediawiki/index.php/Logical_negation Logical Negation @ OER Commons]
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* [http://p2pfoundation.net/Logical_Negation Logical Negation @ P2P Foundation]
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* [http://semanticweb.org/wiki/Logical_negation Logical Negation @ SemanticWeb]
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{{col-end}}

===Logical operators===

===Logical operators===
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{{col-break}}

{{col-break}}

* [[Inquiry]]

* [[Inquiry]]
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* [[Dynamics of inquiry]]
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{{col-break}}
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* [[Semeiotic]]

* [[Logic of information]]

* [[Logic of information]]

{{col-break}}

{{col-break}}
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{{col-break}}

* [[Pragmatic maxim]]

* [[Pragmatic maxim]]
* [[Pragmatic theory of truth]]
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* [[Truth theory]]
{{col-break}}
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* [[Semeiotic]]
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* [[Semiotic information]]

{{col-end}}

{{col-end}}

===Related articles===

===Related articles===
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Introduction To Inquiry Driven Systems&rdquo;]
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{{col-begin}}

+
{{col-break}}
* [http://mywikibiz.com/Directory:Jon_Awbrey/Essays/Prospects_For_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Prospects For Inquiry Driven Systems&rdquo;]
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* [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://mywikibiz.com/Directory:Jon_Awbrey/Papers/Inquiry_Driven_Systems Jon Awbrey, &ldquo;Inquiry Driven Systems : Inquiry Into Inquiry&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]

+
{{col-break}}
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, &ldquo;Propositional Equation Reasoning Systems&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction]

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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus]
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]

+
{{col-break}}
* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]

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* [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, &ldquo;Differential Logic and Dynamic Systems&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
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{{col-end}}

==Document history==

==Document history==
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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.

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.
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{{col-begin}}
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* [http://intersci.ss.uci.edu/wiki/index.php/Logical_negation Logical Negation], [http://intersci.ss.uci.edu/ InterSciWiki]
{{col-break}}

* [http://mywikibiz.com/Logical_negation Logical Negation], [http://mywikibiz.com/ MyWikiBiz]

* [http://mywikibiz.com/Logical_negation Logical Negation], [http://mywikibiz.com/ MyWikiBiz]
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* [http://wikinfo.org/w/index.php/Logical_negation Logical Negation], [http://wikinfo.org/w/ Wikinfo]
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* [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://beta.wikiversity.org/wiki/Logical_negation Logical Negation], [http://beta.wikiversity.org/ Wikiversity Beta]
* [http://getwiki.net/-Logical_negation Logical Negation], [http://getwiki.net/ GetWiki]
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{{col-break}}
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* [http://wikinfo.org/index.php/Logical_negation Logical Negation], [http://wikinfo.org/ Wikinfo]
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* [http://textop.org/wiki/index.php?title=Logical_negation Logical Negation], [http://textop.org/wiki/ Textop Wiki]

* [http://en.wikipedia.org/w/index.php?title=Logical_negation&oldid=77111608 Logical Negation], [http://en.wikipedia.org/ Wikipedia]

* [http://en.wikipedia.org/w/index.php?title=Logical_negation&oldid=77111608 Logical Negation], [http://en.wikipedia.org/ Wikipedia]
{{col-end}}
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<br><sharethis />

[[Category:Inquiry]]

[[Category:Inquiry]]

[[Category:Open Educational Resource]]

[[Category:Open Educational Resource]]

[[Category:Peer Educational Resource]]

[[Category:Peer Educational Resource]]
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[[Category:Charles Sanders Peirce]]

[[Category:Computer Science]]

[[Category:Computer Science]]

[[Category:Formal Languages]]

[[Category:Formal Languages]]
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