Difference between revisions of "Sole sufficient operator"

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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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A '''sole sufficient operator''' or a '''sole sufficient connective''' is an operator that is sufficient by itself to generate all of the operators in a specified class of operators. In [[logic]], it is a logical operator that suffices to generate all of the [[boolean-valued function]]s, <math>f : X \to \mathbb{B} </math>, where <math>X\!</math> is an arbitrary set and where <math>\mathbb{B}</math> is a generic 2-element set, typically <math>\mathbb{B} = \{ 0, 1 \} = \{ false, true \}</math>, in particular, to generate all of the [[finitary boolean function]]s, <math> f : \mathbb{B}^k \to \mathbb{B} </math>.
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A '''sole sufficient operator''' is an operator that is sufficient by itself to generate every operator in a specified class of operators.&nbsp; In the context of [[logic]], it is a logical operator that suffices to generate every [[boolean-valued function]], <math>f : X \to \mathbb{B},\!</math> where <math>X\!</math> is an arbitrary set and where <math>\mathbb{B}\!</math> is a generic two-element set, typically <math>\mathbb{B} = \{ 0, 1 \} = \{ \mathrm{false}, \mathrm{true} \},\!</math> in particular, to generate every finitary [[boolean function]], <math>f : \mathbb{B}^k \to \mathbb{B}.\!</math>
  
 
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* [http://beta.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Beta Wikiversity]
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* [http://intersci.ss.uci.edu/wiki/index.php/Sole_sufficient_operator Sole Sufficient Operator @ InterSciWiki]
 
* [http://mywikibiz.com/Sole_sufficient_operator Sole Sufficient Operator @ MyWikiBiz]
 
* [http://mywikibiz.com/Sole_sufficient_operator Sole Sufficient Operator @ MyWikiBiz]
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* [http://www.netknowledge.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ NetKnowledge]
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* [http://ref.subwiki.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Subject Wikis]
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* [http://semanticweb.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ SemanticWeb]
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* [http://en.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Wikiversity Beta]
  
 
===Logical operators===
 
===Logical operators===
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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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* [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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==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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* [http://intersci.ss.uci.edu/wiki/index.php/Sole_sufficient_operator Sole Sufficient Operator], [http://intersci.ss.uci.edu/ InterSciWiki]
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* [http://mywikibiz.com/Sole_sufficient_operator Sole Sufficient Operator], [http://mywikibiz.com/ MyWikiBiz]
 
* [http://mywikibiz.com/Sole_sufficient_operator Sole Sufficient Operator], [http://mywikibiz.com/ MyWikiBiz]
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* [http://mathweb.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://mathweb.org/wiki/ MathWeb Wiki]
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* [http://http://planetmath.org/SoleSufficientOperator Sole Sufficient Operator], [http://planetmath.org/ PlanetMath]
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* [http://netknowledge.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://netknowledge.org/ NetKnowledge]
 
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* [http://p2pfoundation.net/Sole_sufficient_operator Sole Sufficient Operator], [http://p2pfoundation.net/ P2P Foundation]
 
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* [http://http://planetmath.org/encyclopedia/SoleSufficientOperator.html Sole Sufficient Operator], [http://planetmath.org/ PlanetMath]
 
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* [http://planetphysics.org/encyclopedia/SoleSufficientOperator.html Sole Sufficient Operator], [http://planetphysics.org/ PlanetPhysics]
 
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* [http://semanticweb.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://semanticweb.org/ SemanticWeb]
 
* [http://semanticweb.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://semanticweb.org/ SemanticWeb]
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* [http://wikinfo.org/w/index.php/Sole_sufficient_operator Sole Sufficient Operator], [http://wikinfo.org/w/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://en.wikiversity.org/ Wikiversity]
 
* [http://beta.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://beta.wikiversity.org/ Wikiversity Beta]
 
* [http://beta.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [http://getwiki.net/-Sole_Sufficient_Operator Sole Sufficient Operator], [http://getwiki.net/ GetWiki]
 
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* [http://wikinfo.org/index.php/Sole_sufficient_operator Sole Sufficient Operator], [http://wikinfo.org/ Wikinfo]
 
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* [http://textop.org/wiki/index.php?title=Sole_sufficient_operator Sole Sufficient Operator], [http://textop.org/wiki/ Textop Wiki]
 
 
* [http://en.wikipedia.org/w/index.php?title=Sole_sufficient_operator&oldid=156136346 Sole Sufficient Operator], [http://en.wikipedia.org/ Wikipedia]
 
* [http://en.wikipedia.org/w/index.php?title=Sole_sufficient_operator&oldid=156136346 Sole Sufficient Operator], [http://en.wikipedia.org/ Wikipedia]
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Latest revision as of 18:07, 7 November 2015

☞ This page belongs to resource collections on Logic and Inquiry.

A sole sufficient operator is an operator that is sufficient by itself to generate every operator in a specified class of operators.  In the context of logic, it is a logical operator that suffices to generate every boolean-valued function, \(f : X \to \mathbb{B},\!\) where \(X\!\) is an arbitrary set and where \(\mathbb{B}\!\) is a generic two-element set, typically \(\mathbb{B} = \{ 0, 1 \} = \{ \mathrm{false}, \mathrm{true} \},\!\) in particular, to generate every finitary boolean function, \(f : \mathbb{B}^k \to \mathbb{B}.\!\)

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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.

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