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Logical implication (view source)

Revision as of 20:18, 4 November 2015

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==Definition==
 
==Definition==
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The concept of logical implication is associated with an operation on two logical values, typically the values of two propositions, that produces a value of <math>\operatorname{false}</math> just in case the first operand is true and the second operand is false.
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The concept of logical implication is associated with an operation on two logical values, typically the values of two propositions, that produces a value of ''false'' just in case the first operand is true and the second operand is false.
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In the interpretation where <math>0 = \operatorname{false}</math> and <math>1 = \operatorname{true}</math>, the truth table associated with the statement <math>{}^{\backprime\backprime} p ~\text{implies}~ q {}^{\prime\prime},</math> symbolized as <math>{}^{\backprime\backprime} p \Rightarrow q {}^{\prime\prime},</math> is as follows:
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In the interpretation where <math>0 = \operatorname{false}</math> and <math>1 = \operatorname{true}</math>, the truth table associated with the statement <math>{}^{\backprime\backprime} p ~\text{implies}~ q {}^{\prime\prime},</math> symbolized as <math>{}^{\backprime\backprime} p \Rightarrow q {}^{\prime\prime},</math> appears below:
    
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The usage of the terms '''''logical implication''''' and '''''material conditional''''' varies from field to field and even across different contexts of discussion.  One way to minimize the potential confusion is to begin with a focus on the various types of formal objects that are being discussed, of which there are only a few, taking up the variations in language as a secondary matter.
 
The usage of the terms '''''logical implication''''' and '''''material conditional''''' varies from field to field and even across different contexts of discussion.  One way to minimize the potential confusion is to begin with a focus on the various types of formal objects that are being discussed, of which there are only a few, taking up the variations in language as a secondary matter.
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The main formal object under discussion is a logical operation on two logical values, typically the values of two [[proposition]]s, that produces a value of <math>\operatorname{false}</math> just in case the first operand is true and the second operand is false.  By way of a temporary name, the logical operation in question may be written as <math>\operatorname{Cond}(p, q),</math> where <math>p\!</math> and <math>q\!</math> are logical values.  The [[truth table]] associated with this operation is as follows:
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The main formal object under discussion is a logical operation on two logical values, typically the values of two propositions, that produces a value of <math>\operatorname{false}</math> just in case the first operand is true and the second operand is false.  By way of a temporary name, the logical operation in question may be written as <math>\operatorname{Cond}(p, q),</math> where <math>p\!</math> and <math>q\!</math> are logical values.  The [[truth table]] associated with this operation appears below:
    
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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_implication Logical Implication @ InterSciWiki]
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* [http://mywikibiz.com/Logical_implication Logical Implication @ MyWikiBiz]
 
* [http://mywikibiz.com/Logical_implication Logical Implication @ MyWikiBiz]
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* [http://mathweb.org/wiki/Logical_implication Logical Implication @ MathWeb Wiki]
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* [http://ref.subwiki.org/wiki/Logical_implication Logical Implication @ Subject Wikis]
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* [http://netknowledge.org/wiki/Logical_implication Logical Implication @ NetKnowledge]
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* [http://en.wikiversity.org/wiki/Logical_implication Logical Implication @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Logical_implication Logical Implication @ Wikiversity Beta]
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* [http://wiki.oercommons.org/mediawiki/index.php/Logical_implication Logical Implication @ OER Commons]
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* [http://p2pfoundation.net/Logical_Implication Logical Implication @ P2P Foundation]
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* [http://semanticweb.org/wiki/Logical_implication Logical Implication @ SemanticWeb]
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===Logical operators===
 
===Logical operators===
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===Related articles===
 
===Related articles===
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* [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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* [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]
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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/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/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
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{{col-break}}
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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/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/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_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
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{{col-break}}
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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/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://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&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}}
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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;]
      
==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_implication Logical Implication], [http://intersci.ss.uci.edu/ InterSciWiki]
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* [http://mywikibiz.com/Logical_implication Logical Implication], [http://mywikibiz.com/ MyWikiBiz]
 
* [http://mywikibiz.com/Logical_implication Logical Implication], [http://mywikibiz.com/ MyWikiBiz]
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* [http://wikinfo.org/w/index.php/Logical_implication Logical Implication], [http://wikinfo.org/w/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Logical_implication Logical Implication], [http://en.wikiversity.org/ Wikiversity]
 
* [http://beta.wikiversity.org/wiki/Logical_implication Logical Implication], [http://beta.wikiversity.org/ Wikiversity Beta]
 
* [http://beta.wikiversity.org/wiki/Logical_implication Logical Implication], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [http://planetmath.org/encyclopedia/LogicalImplication.html Logical Implication], [http://planetmath.org/ PlanetMath]
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* [http://getwiki.net/-Logical_Implication Logical Implication], [http://getwiki.net/ GetWiki]
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* [http://wikinfo.org/index.php/Logical_implication Logical Implication], [http://wikinfo.org/ Wikinfo]
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* [http://textop.org/wiki/index.php?title=Logical_implication Logical Implication], [http://textop.org/wiki/ Textop Wiki]
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* [http://en.wikipedia.org/w/index.php?title=Logical_implication&oldid=77109738 Logical Implication], [http://en.wikipedia.org/ Wikipedia]
 
* [http://en.wikipedia.org/w/index.php?title=Logical_implication&oldid=77109738 Logical Implication], [http://en.wikipedia.org/ Wikipedia]
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<br><sharethis />
      
[[Category:Inquiry]]
 
[[Category:Inquiry]]
Jon Awbrey
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