Line 1: |
Line 1: |
| <font size="3">☞</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. | | <font size="3">☞</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. |
| | | |
− | '''Logical equality''' is an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''true'' if and only if both operands are false or both operands are true. | + | '''Logical equality''' is an operation on two logical values, typically the values of two propositions, that produces a value of ''true'' if and only if both operands are false or both operands are true. |
| | | |
− | The [[truth table]] of '''p EQ q''' (also written as '''p = q''', '''p ↔ q''', or '''p ≡ q''') is as follows: | + | The [[truth table]] of <math>p ~\operatorname{EQ}~ q,</math> also written <math>p = q,\!</math> <math>p \Leftrightarrow q,\!</math> or <math>p \equiv q,\!</math> appears below: |
| | | |
| <br> | | <br> |
| | | |
− | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:45%" | + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%" |
− | |+ '''Logical Equality''' | + | |+ style="height:30px" | <math>\text{Logical Equality}\!</math> |
− | |- style="background:#e6e6ff" | + | |- style="height:40px; background:#f0f0ff" |
− | ! style="width:15%" | p
| + | | style="width:33%" | <math>p\!</math> |
− | ! style="width:15%" | q
| + | | style="width:33%" | <math>q\!</math> |
− | ! style="width:15%" | p = q
| + | | style="width:33%" | <math>p = q\!</math> |
| |- | | |- |
− | | F || F || T | + | | <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math> |
| |- | | |- |
− | | F || T || F | + | | <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math> |
| |- | | |- |
− | | T || F || F | + | | <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math> |
| |- | | |- |
− | | T || T || T | + | | <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math> |
| |} | | |} |
| | | |
Line 29: |
Line 29: |
| ===Focal nodes=== | | ===Focal nodes=== |
| | | |
− | {{col-begin}}
| |
− | {{col-break}}
| |
| * [[Inquiry Live]] | | * [[Inquiry Live]] |
− | {{col-break}}
| |
| * [[Logic Live]] | | * [[Logic Live]] |
− | {{col-end}}
| |
| | | |
| ===Peer nodes=== | | ===Peer nodes=== |
| | | |
− | {{col-begin}}
| + | * [http://intersci.ss.uci.edu/wiki/index.php/Logical_equality Logical Equality @ InterSciWiki] |
− | {{col-break}}
| |
| * [http://mywikibiz.com/Logical_equality Logical Equality @ MyWikiBiz] | | * [http://mywikibiz.com/Logical_equality Logical Equality @ MyWikiBiz] |
− | * [http://mathweb.org/wiki/Logical_equality Logical Equality @ MathWeb Wiki] | + | * [http://ref.subwiki.org/wiki/Logical_equality Logical Equality @ Subject Wikis] |
− | * [http://netknowledge.org/wiki/Logical_equality Logical Equality @ NetKnowledge]
| + | * [http://en.wikiversity.org/wiki/Logical_equality Logical Equality @ Wikiversity] |
− | {{col-break}}
| + | * [http://beta.wikiversity.org/wiki/Logical_equality Logical Equality @ Wikiversity Beta] |
− | * [http://wiki.oercommons.org/mediawiki/index.php/Logical_equality Logical Equality @ OER Commons] | |
− | * [http://p2pfoundation.net/Logical_Equality Logical Equality @ P2P Foundation] | |
− | * [http://semanticweb.org/wiki/Logical_equality Logical Equality @ SemanticWeb]
| |
− | {{col-end}}
| |
| | | |
| ===Logical operators=== | | ===Logical operators=== |
Line 121: |
Line 112: |
| {{col-break}} | | {{col-break}} |
| * [[Pragmatic maxim]] | | * [[Pragmatic maxim]] |
− | * [[Pragmatic theory of truth]] | + | * [[Truth theory]] |
| {{col-end}} | | {{col-end}} |
| | | |
| ===Related articles=== | | ===Related articles=== |
| | | |
− | * [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Semiotic_Information Jon Awbrey, “Semiotic Information”] | + | {{col-begin}} |
− | | + | {{col-break}} |
− | * [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, “Introduction To Inquiry Driven Systems”] | + | * [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, “Prospects For Inquiry Driven Systems”] | + | * [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, “Inquiry Driven Systems : Inquiry Into Inquiry”] | + | * [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, “Propositional Equation Reasoning Systems”] | + | * [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, “Differential Logic : Introduction”] | + | * [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, “Differential Propositional Calculus”] | + | * [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, “Differential Logic and Dynamic Systems”] | |
| | | |
| ==Document history== | | ==Document history== |
Line 146: |
Line 136: |
| 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_equality Logical Equality], [http://intersci.ss.uci.edu/ InterSciWiki] |
− | {{col-break}}
| |
| * [http://mywikibiz.com/Logical_equality Logical Equality], [http://mywikibiz.com/ MyWikiBiz] | | * [http://mywikibiz.com/Logical_equality Logical Equality], [http://mywikibiz.com/ MyWikiBiz] |
| + | * [http://wikinfo.org/w/index.php/Logical_equality Logical Equality], [http://wikinfo.org/w/ Wikinfo] |
| + | * [http://en.wikiversity.org/wiki/Logical_equality Logical Equality], [http://en.wikiversity.org/ Wikiversity] |
| * [http://beta.wikiversity.org/wiki/Logical_equality Logical Equality], [http://beta.wikiversity.org/ Wikiversity Beta] | | * [http://beta.wikiversity.org/wiki/Logical_equality Logical Equality], [http://beta.wikiversity.org/ Wikiversity Beta] |
− | * [http://getwiki.net/-Logical_Equality Logical Equality], [http://getwiki.net/ GetWiki]
| |
− | {{col-break}}
| |
− | * [http://wikinfo.org/index.php/Logical_equality Logical Equality], [http://wikinfo.org/ Wikinfo]
| |
− | * [http://textop.org/wiki/index.php?title=Logical_equality Logical Equality], [http://textop.org/wiki/ Textop Wiki]
| |
| * [http://en.wikipedia.org/w/index.php?title=Logical_equality&oldid=77110577 Logical Equality], [http://en.wikipedia.org/ Wikipedia] | | * [http://en.wikipedia.org/w/index.php?title=Logical_equality&oldid=77110577 Logical Equality], [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]] |