Changes

MyWikiBiz, Author Your Legacy — Friday March 29, 2024
Jump to navigationJump to search
3,915 bytes added ,  14:16, 5 November 2015
update
Line 1: Line 1: −
'''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.
+
<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
   −
The [[truth table]] of '''NOT p''' (also written as '''~p''' or '''&not;p''') is as follows:
+
'''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>
! style="width:20%" | p
+
 
! style="width:20%" | &not;p
+
{| 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>
 
|-
 
|-
| 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>
 
|}
 
|}
 +
 
<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===
{|
+
 
| valign=top |
+
{{col-begin}}
 +
{{col-break}}
 
* [[Exclusive disjunction]]
 
* [[Exclusive disjunction]]
 
* [[Logical conjunction]]
 
* [[Logical conjunction]]
 
* [[Logical disjunction]]
 
* [[Logical disjunction]]
 
* [[Logical equality]]
 
* [[Logical equality]]
| valign=top |
+
{{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===
{|
+
 
| valign=top |
+
{{col-begin}}
 +
{{col-break}}
 
* [[Ampheck]]
 
* [[Ampheck]]
* [[Boolean algebra]]
   
* [[Boolean domain]]
 
* [[Boolean domain]]
 
* [[Boolean function]]
 
* [[Boolean function]]
| valign=top |
+
* [[Boolean-valued function]]
* [[Boolean logic]]
+
* [[Differential logic]]
* [[Laws of Form]]
+
{{col-break}}
* [[Logic gate]]
   
* [[Logical graph]]
 
* [[Logical graph]]
| valign=top |
+
* [[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.
   −
{{aficionados}}<sharethis />
+
* [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:Computer Science]]
 
[[Category:Formal Languages]]
 
[[Category:Formal Languages]]
12,080

edits

Navigation menu