Difference between revisions of "Sole sufficient operator"

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(copy text from [http://www.opencycle.net/ OpenCycle] of which Jon Awbrey is the sole author)
 
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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>.
 
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>.
  
==References==
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==See also==
  
==See also==
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* [[Ampheck]]
 
* [[Ampheck]]
 
* [[Entitative graph]]
 
* [[Entitative graph]]
 
* [[Existential graph]]
 
* [[Existential graph]]
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* [[Logical graph]]
 
* [[Logical graph]]
 
* [[Logical NAND]]
 
* [[Logical NAND]]
 
* [[Logical NNOR]]
 
* [[Logical NNOR]]
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* [[Minimal negation operator]]
 
* [[Minimal negation operator]]
 
* [[Multigrade operator]]
 
* [[Multigrade operator]]
 
* [[Parametric operator]]
 
* [[Parametric operator]]
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Revision as of 16:16, 27 February 2008

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 functions, \(f : X \to \mathbb{B} \), where \(X\!\) is an arbitrary set and where \(\mathbb{B}\) is a generic 2-element set, typically \(\mathbb{B} = \{ 0, 1 \} = \{ false, true \}\), in particular, to generate all of the finitary boolean functions, \( f : \mathbb{B}^k \to \mathbb{B} \).

See also

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