Difference between revisions of "Logical negation"

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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]].
  
'''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.
+
'''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.
  
The [[truth table]] of '''NOT p''' (also written as '''~p''' or '''&not;p''') is as follows:
+
The [[truth table]] of <math>\operatorname{NOT}~ p,</math> also written <math>\lnot p,\!</math> appears below:
  
 
<br>
 
<br>
  
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:40%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
|+ '''Logical Negation'''
+
|+ style="height:30px" | <math>\text{Logical Negation}\!</math>
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="width:20%" | p
+
| style="width:50%" | <math>p\!</math>
! style="width:20%" | &not;p
+
| 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:
  
 
<br>
 
<br>
  
{| 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" | <math>\text{Variant Notations}\!</math>
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="text-align:center" | Notation
+
| width="50%" align="center" | <math>\text{Notation}\!</math>
! Vocalization
+
| width="50%" | <math>\text{Vocalization}\!</math>
 
|-
 
|-
| style="text-align:center" | <math>\bar{p}</math>
+
| align="center" | <math>\bar{p}\!</math>
| bar ''p''
+
| <math>p\!</math> bar
 
|-
 
|-
| style="text-align:center" | <math>p'\!</math>
+
| align="center" | <math>\tilde{p}\!</math>
| ''p'' prime,<p> ''p'' complement
+
| <math>p\!</math> tilde
 
|-
 
|-
| style="text-align:center" | <math>!p\!</math>
+
| align="center" | <math>p'\!</math>
| bang ''p''
+
| <math>p\!</math> prime<br> <math>p\!</math> complement
 +
|-
 +
| align="center" | <math>!p\!</math>
 +
| bang <math>p\!</math>
 
|}
 
|}
  
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===Focal nodes===
 
===Focal nodes===
  
{{col-begin}}
 
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* [[Inquiry Live]]
 
* [[Inquiry Live]]
{{col-break}}
 
 
* [[Logic Live]]
 
* [[Logic Live]]
{{col-end}}
 
  
 
===Peer nodes===
 
===Peer nodes===
  
{{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]
 
* [http://p2pfoundation.net/Logical_Negation Logical Negation @ P2P Foundation]
 
* [http://semanticweb.org/wiki/Logical_negation Logical Negation @ SemanticWeb]
 
{{col-end}}
 
  
 
===Logical operators===
 
===Logical operators===
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{{col-break}}
 
{{col-break}}
 
* [[Pragmatic maxim]]
 
* [[Pragmatic maxim]]
* [[Pragmatic theory of truth]]
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* [[Truth theory]]
 
{{col-end}}
 
{{col-end}}
  
 
===Related articles===
 
===Related articles===
  
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Semiotic_Information Jon Awbrey, &ldquo;Semiotic Information&rdquo;]
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{{col-begin}}
 
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{{col-break}}
* [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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* [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/Essays/Prospects_For_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Prospects For Inquiry Driven Systems&rdquo;]
+
* [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/Inquiry_Driven_Systems Jon Awbrey, &ldquo;Inquiry Driven Systems : Inquiry Into Inquiry&rdquo;]
+
* [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://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, &ldquo;Propositional Equation Reasoning Systems&rdquo;]
+
* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
 
+
{{col-break}}
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;]
+
* [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://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&rdquo;]
+
* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
 
+
{{col-end}}
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, &ldquo;Differential Logic and Dynamic Systems&rdquo;]
 
  
 
==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.
  
{{col-begin}}
+
* [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]
 +
* [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://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]
 
{{col-break}}
 
* [http://wikinfo.org/index.php/Logical_negation Logical Negation], [http://wikinfo.org/ Wikinfo]
 
* [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}}
 
 
<br><sharethis />
 
  
 
[[Category:Inquiry]]
 
[[Category:Inquiry]]
 
[[Category:Open Educational Resource]]
 
[[Category:Open Educational Resource]]
 
[[Category:Peer Educational Resource]]
 
[[Category:Peer Educational Resource]]
 +
[[Category:Charles Sanders Peirce]]
 
[[Category:Computer Science]]
 
[[Category:Computer Science]]
 
[[Category:Formal Languages]]
 
[[Category:Formal Languages]]

Latest revision as of 14:16, 5 November 2015

This page belongs to resource collections on Logic and 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.

The truth table of \(\operatorname{NOT}~ p,\) also written \(\lnot p,\!\) appears below:


\(\text{Logical Negation}\!\)
\(p\!\) \(\lnot p\!\)
\(\operatorname{F}\) \(\operatorname{T}\)
\(\operatorname{T}\) \(\operatorname{F}\)


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:


\(\text{Variant Notations}\!\)
\(\text{Notation}\!\) \(\text{Vocalization}\!\)
\(\bar{p}\!\) \(p\!\) bar
\(\tilde{p}\!\) \(p\!\) tilde
\(p'\!\) \(p\!\) prime
\(p\!\) complement
\(!p\!\) bang \(p\!\)


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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.