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]].
  
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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 <math>\operatorname{NOT}~ p,</math> also written <math>\lnot p,\!</math> 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%"
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|+ '''Logical Negation'''
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|+ style="height:30px" | <math>\text{Logical Negation}\!</math>
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|- style="background:#e6e6ff"
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|- style="height:40px; background:#f0f0ff"
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! style="width:20%" | p
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| style="width:50%" | <math>p\!</math>
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! style="width:20%" | &not;p
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| style="width:50%" | <math>\lnot p\!</math>
 
|-
 
|-
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| F || T
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| <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
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| T || F
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| <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
 
|}
 
|}
  
 
<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 <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>
  
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; width:40%"
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{| align="center" border="1" cellpadding="8" cellspacing="0" width="45%"
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|+ '''Variant Notations'''
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|+ style="height:30px" | <math>\text{Variant Notations}\!</math>
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|- style="background:#e6e6ff"
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|- style="height:40px; background:#f0f0ff"
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! style="text-align:center" | Notation
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| width="50%" align="center" | <math>\text{Notation}\!</math>
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! Vocalization
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| width="50%" | <math>\text{Vocalization}\!</math>
 
|-
 
|-
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| style="text-align:center" | <math>\bar{p}</math>
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| align="center" | <math>\bar{p}\!</math>
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| bar ''p''
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| <math>p\!</math> bar
 
|-
 
|-
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| style="text-align:center" | <math>p'\!</math>
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| align="center" | <math>\tilde{p}\!</math>
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| ''p'' prime,<p> ''p'' complement
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| <math>p\!</math> tilde
 
|-
 
|-
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| style="text-align:center" | <math>!p\!</math>
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| align="center" | <math>p'\!</math>
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| bang ''p''
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| <math>p\!</math> prime<br> <math>p\!</math> complement
 +
|-
 +
| align="center" | <math>!p\!</math>
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| bang <math>p\!</math>
 
|}
 
|}
  
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===Focal nodes===
 
===Focal nodes===
  
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* [[Inquiry Live]]
 
* [[Inquiry Live]]
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* [[Logic Live]]
 
* [[Logic Live]]
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===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]
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{{col-break}}
 
 
* [http://mywikibiz.com/Logical_negation Logical Negation @ MyWikiBiz]
 
* [http://mywikibiz.com/Logical_negation Logical Negation @ MyWikiBiz]
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* [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]
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* [http://netknowledge.org/wiki/Logical_negation Logical Negation @ NetKnowledge]
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* [http://en.wikiversity.org/wiki/Logical_negation Logical Negation @ Wikiversity]
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{{col-break}}
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* [http://beta.wikiversity.org/wiki/Logical_negation Logical Negation @ Wikiversity Beta]
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* [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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===Logical operators===
 
===Logical operators===
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* [[Inquiry]]
 
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* [[Dynamics of inquiry]]
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* [[Semeiotic]]
 
* [[Logic of information]]
 
* [[Logic of information]]
 
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* [[Pragmatic maxim]]
 
* [[Pragmatic maxim]]
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* [[Pragmatic theory of truth]]
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* [[Truth theory]]
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* [[Semeiotic]]
 
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* [[Semiotic information]]
 
 
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===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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* [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]
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* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
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* [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]
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* [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]
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* [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]
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{{col-break}}
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* [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]
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* [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]
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{{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]
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* [http://getwiki.net/-Logical_negation Logical Negation], [http://getwiki.net/ GetWiki]
 
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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]
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[[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]]

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 \(p\!\)


Syllabus

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Logical operators

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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.

Retrieved from "https://mywikibiz.com/index.php?title=Logical_negation&oldid=466827"