Difference between revisions of "Sole sufficient operator"

MyWikiBiz, Author Your Legacy — Monday November 25, 2024
Jump to navigationJump to search
(update)
 
(One intermediate revision by the same user not shown)
Line 1: Line 1:
 
<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]].
  
−
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>.
+
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>
  
 
==Syllabus==
 
==Syllabus==
Line 7: Line 7:
 
===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/Sole_sufficient_operator Sole Sufficient Operator @ InterSciWiki]
−
{{col-break}}
 
 
* [http://mywikibiz.com/Sole_sufficient_operator Sole Sufficient Operator @ MyWikiBiz]
 
* [http://mywikibiz.com/Sole_sufficient_operator Sole Sufficient Operator @ MyWikiBiz]
−
* [http://mathweb.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ MathWeb Wiki]
 
−
* [http://netknowledge.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ NetKnowledge]
 
−
* [http://wiki.oercommons.org/mediawiki/index.php/Sole_sufficient_operator Sole Sufficient Operator @ OER Commons]
 
−
{{col-break}}
 
−
* [http://p2pfoundation.net/Sole_Sufficient_Operator Sole Sufficient Operator @ P2P Foundation]
 
−
* [http://semanticweb.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ SemanticWeb]
 
 
* [http://ref.subwiki.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Subject Wikis]
 
* [http://ref.subwiki.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Subject Wikis]
 +
* [http://en.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Wikiversity]
 
* [http://beta.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Wikiversity Beta]
 
* [http://beta.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Wikiversity Beta]
−
{{col-end}}
 
  
 
===Logical operators===
 
===Logical operators===
Line 106: Line 95:
 
===Related articles===
 
===Related articles===
  
−
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Semiotic_Information Jon Awbrey, &ldquo;Semiotic Information&rdquo;]
+
{{col-begin}}
−
 
+
{{col-break}}
−
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Introduction To Inquiry Driven Systems&rdquo;]
+
* [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, &ldquo;Prospects For Inquiry Driven Systems&rdquo;]
+
* [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, &ldquo;Inquiry Driven Systems : Inquiry Into Inquiry&rdquo;]
+
* [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, &ldquo;Propositional Equation Reasoning Systems&rdquo;]
+
* [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, &ldquo;Differential Logic : Introduction&rdquo;]
+
* [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, &ldquo;Differential Propositional Calculus&rdquo;]
+
* [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, &ldquo;Differential Logic and Dynamic Systems&rdquo;]
 
  
 
==Document history==
 
==Document history==
Line 126: Line 114:
 
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/Sole_sufficient_operator Sole Sufficient Operator], [http://intersci.ss.uci.edu/ InterSciWiki]
−
{{col-break}}
 
 
* [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]
−
* [http://mathweb.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://mathweb.org/wiki/ MathWeb Wiki]
+
* [http://http://planetmath.org/SoleSufficientOperator Sole Sufficient Operator], [http://planetmath.org/ PlanetMath]
−
* [http://netknowledge.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://netknowledge.org/ NetKnowledge]
 
−
* [http://p2pfoundation.net/Sole_sufficient_operator Sole Sufficient Operator], [http://p2pfoundation.net/ P2P Foundation]
 
−
* [http://http://planetmath.org/encyclopedia/SoleSufficientOperator.html Sole Sufficient Operator], [http://planetmath.org/ PlanetMath]
 
−
* [http://planetphysics.org/encyclopedia/SoleSufficientOperator.html Sole Sufficient Operator], [http://planetphysics.org/ PlanetPhysics]
 
−
{{col-break}}
 
 
* [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]
 +
* [http://wikinfo.org/w/index.php/Sole_sufficient_operator Sole Sufficient Operator], [http://wikinfo.org/w/ Wikinfo]
 +
* [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]
−
* [http://getwiki.net/-Sole_Sufficient_Operator Sole Sufficient Operator], [http://getwiki.net/ GetWiki]
 
−
* [http://wikinfo.org/index.php/Sole_sufficient_operator Sole Sufficient Operator], [http://wikinfo.org/ Wikinfo]
 
−
* [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]
−
{{col-end}}
 
−
 
−
<br><sharethis />
 
  
 
[[Category:Inquiry]]
 
[[Category:Inquiry]]

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, \(f : \mathbb{B}^k \to \mathbb{B}.\!\)

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.

Retrieved from "https://mywikibiz.com/index.php?title=Sole_sufficient_operator&oldid=466844"