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:
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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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==Syllabus==
 
==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===
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* [[Boolean function]]
 
* [[Boolean function]]
 
* [[Boolean-valued function]]
 
* [[Boolean-valued function]]
 +
* [[Differential logic]]
 
{{col-break}}
 
{{col-break}}
 
* [[Logical graph]]
 
* [[Logical graph]]
* [[Logical matrix]]
 
 
* [[Minimal negation operator]]
 
* [[Minimal negation operator]]
 +
* [[Multigrade operator]]
 +
* [[Parametric operator]]
 
* [[Peirce's law]]
 
* [[Peirce's law]]
 
{{col-break}}
 
{{col-break}}
 
* [[Propositional calculus]]
 
* [[Propositional calculus]]
 +
* [[Sole sufficient operator]]
 
* [[Truth table]]
 
* [[Truth table]]
 
* [[Universe of discourse]]
 
* [[Universe of discourse]]
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{{col-end}}
 
{{col-end}}
  
==Document history==
+
===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}}
  
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.
+
===Related articles===
  
 
{{col-begin}}
 
{{col-begin}}
 
{{col-break}}
 
{{col-break}}
* [http://mywikibiz.com/Logical_negation Logical Negation], [http://mywikibiz.com/ MyWikiBiz]
+
* [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language]
* [http://beta.wikiversity.org/wiki/Logical_negation Logical Negation], [http://beta.wikiversity.org/ Wikiversity Beta]
+
* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
* [http://getwiki.net/-Logical_negation Logical Negation], [http://getwiki.net/ GetWiki]
+
* [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}}
 
{{col-break}}
* [http://wikinfo.org/index.php/Logical_negation Logical Negation], [http://wikinfo.org/ Wikinfo]
+
* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]
* [http://textop.org/wiki/index.php?title=Logical_negation Logical Negation], [http://textop.org/wiki/ Textop Wiki]
+
* [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
* [http://en.wikipedia.org/w/index.php?title=Negation&oldid=77111608 Logical Negation], [http://en.wikipedia.org/ Wikipedia]
+
* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
 
{{col-end}}
 
{{col-end}}
  
<br><sharethis />
+
==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: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 \(p\!\)


Syllabus

Focal nodes

Peer nodes

Logical operators

Template:Col-breakTemplate:Col-breakTemplate:Col-end

Related topics

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-end

Relational concepts

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-end

Information, Inquiry

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-end

Related articles

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate: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.