Difference between revisions of "Sole sufficient operator"

MyWikiBiz, Author Your Legacy — Thursday April 18, 2024
Jump to navigationJump to search
(→‎Peer nodes: fix links)
(update)
 
(8 intermediate revisions by the same user not shown)
Line 1: Line 1:
−
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>.
+
<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
 +
 
 +
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 5: 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===
  
−
* [http://beta.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Beta Wikiversity]
+
* [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]
−
* [http://www.netknowledge.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ NetKnowledge]
+
* [http://ref.subwiki.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Subject Wikis]
−
* [http://semanticweb.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ SemanticWeb]
+
* [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]
  
 
===Logical operators===
 
===Logical operators===
Line 82: Line 81:
 
{{col-break}}
 
{{col-break}}
 
* [[Inquiry]]
 
* [[Inquiry]]
 +
* [[Dynamics of inquiry]]
 +
{{col-break}}
 +
* [[Semeiotic]]
 
* [[Logic of information]]
 
* [[Logic of information]]
 
{{col-break}}
 
{{col-break}}
Line 88: Line 90:
 
{{col-break}}
 
{{col-break}}
 
* [[Pragmatic maxim]]
 
* [[Pragmatic maxim]]
−
* [[Pragmatic theory of truth]]
+
* [[Truth theory]]
−
{{col-break}}
 
−
* [[Semeiotic]]
 
−
* [[Semiotic information]]
 
 
{{col-end}}
 
{{col-end}}
  
 
===Related articles===
 
===Related articles===
  
−
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Introduction To Inquiry Driven Systems&rdquo;]
+
{{col-begin}}
−
 
+
{{col-break}}
−
* [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/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/Papers/Inquiry_Driven_Systems Jon Awbrey, &ldquo;Inquiry Driven Systems : Inquiry Into Inquiry&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/Propositional_Equation_Reasoning_Systems Jon Awbrey, &ldquo;Propositional Equation Reasoning Systems&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/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;]
+
* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
−
 
+
{{col-break}}
−
* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&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://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, &ldquo;Differential Logic and Dynamic Systems&rdquo;]
+
* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
 +
{{col-end}}
  
 
==Document history==
 
==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.
 
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://beta.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://beta.wikiversity.org/ Beta Wikiversity]
+
* [http://http://planetmath.org/SoleSufficientOperator Sole Sufficient Operator], [http://planetmath.org/ PlanetMath]
−
* [http://www.mathweb.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://www.mathweb.org/wiki/ MathWeb Wiki]
 
−
* [http://www.netknowledge.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://www.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]
 
−
{{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://www.getwiki.net/-Sole_Sufficient_Operator Sole Sufficient Operator], [http://www.getwiki.net/ GetWiki]
+
* [http://wikinfo.org/w/index.php/Sole_sufficient_operator Sole Sufficient Operator], [http://wikinfo.org/w/ Wikinfo]
−
* [http://www.wikinfo.org/index.php/Sole_sufficient_operator Sole Sufficient Operator], [http://wikinfo.org/ Wikinfo]
+
* [http://en.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://en.wikiversity.org/ Wikiversity]
−
* [http://www.textop.org/wiki/index.php?title=Sole_sufficient_operator Sole Sufficient Operator], [http://www.textop.org/wiki/ Textop Wiki]
+
* [http://beta.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://beta.wikiversity.org/ Wikiversity Beta]
 
* [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:Open Educational Resource]]
 
[[Category:Peer Educational Resource]]
 
[[Category:Peer Educational Resource]]
 
[[Category:Logic]]
 
[[Category:Logic]]
 
[[Category:Mathematics]]
 
[[Category:Mathematics]]
 
[[Category:Semiotics]]
 
[[Category:Semiotics]]

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"