Difference between revisions of "Sole sufficient operator"

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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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<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
  
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==References==
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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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==See also==
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==Syllabus==
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{|
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===Focal nodes===
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* [[Inquiry Live]]
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* [[Logic Live]]
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===Peer nodes===
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* [http://intersci.ss.uci.edu/wiki/index.php/Sole_sufficient_operator Sole Sufficient Operator @ InterSciWiki]
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* [http://mywikibiz.com/Sole_sufficient_operator Sole Sufficient Operator @ MyWikiBiz]
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* [http://ref.subwiki.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Subject Wikis]
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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]
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===Logical operators===
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{{col-break}}
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* [[Exclusive disjunction]]
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* [[Logical conjunction]]
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* [[Logical disjunction]]
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* [[Logical equality]]
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{{col-break}}
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* [[Logical implication]]
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* [[Logical NAND]]
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* [[Logical NNOR]]
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* [[Logical negation|Negation]]
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{{col-end}}
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===Related topics===
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{{col-begin}}
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{{col-break}}
 
* [[Ampheck]]
 
* [[Ampheck]]
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* [[Entitative graph]]
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* [[Boolean domain]]
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* [[Existential graph]]
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* [[Boolean function]]
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* [[Boolean-valued function]]
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* [[Differential logic]]
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{{col-break}}
 
* [[Logical graph]]
 
* [[Logical graph]]
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* [[Logical NAND]]
 
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* [[Logical NNOR]]
 
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| valign=top |
 
 
* [[Minimal negation operator]]
 
* [[Minimal negation operator]]
 
* [[Multigrade operator]]
 
* [[Multigrade operator]]
 
* [[Parametric operator]]
 
* [[Parametric operator]]
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|}
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* [[Peirce's law]]
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{{col-break}}
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* [[Propositional calculus]]
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* [[Sole sufficient operator]]
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* [[Truth table]]
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* [[Universe of discourse]]
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* [[Zeroth order logic]]
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{{col-end}}
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===Relational concepts===
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{{col-begin}}
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{{col-break}}
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* [[Continuous predicate]]
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* [[Hypostatic abstraction]]
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* [[Logic of relatives]]
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* [[Logical matrix]]
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{{col-break}}
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* [[Relation (mathematics)|Relation]]
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* [[Relation composition]]
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* [[Relation construction]]
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* [[Relation reduction]]
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{{col-break}}
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* [[Relation theory]]
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* [[Relative term]]
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* [[Sign relation]]
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* [[Triadic relation]]
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{{col-end}}
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===Information, Inquiry===
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{{col-begin}}
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{{col-break}}
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* [[Inquiry]]
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* [[Dynamics of inquiry]]
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{{col-break}}
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* [[Semeiotic]]
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* [[Logic of information]]
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{{col-break}}
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* [[Descriptive science]]
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* [[Normative science]]
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{{col-break}}
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* [[Pragmatic maxim]]
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* [[Truth theory]]
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{{col-end}}
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===Related articles===
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{{col-begin}}
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{{col-break}}
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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://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://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://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://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://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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==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.
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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]
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* [http://http://planetmath.org/SoleSufficientOperator Sole Sufficient Operator], [http://planetmath.org/ PlanetMath]
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* [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]
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* [http://beta.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [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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[[Category:Inquiry]]
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[[Category:Open Educational Resource]]
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[[Category:Peer Educational Resource]]
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[[Category:Logic]]
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[[Category:Mathematics]]
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[[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.

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