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>. | 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>. | ||
| − | == | + | ==See also== |
| − | + | {{col-begin}} | |
| − | { | + | {{col-break}} |
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* [[Ampheck]] | * [[Ampheck]] | ||
* [[Entitative graph]] | * [[Entitative graph]] | ||
* [[Existential graph]] | * [[Existential graph]] | ||
| − | + | {{col-break}} | |
* [[Logical graph]] | * [[Logical graph]] | ||
* [[Logical NAND]] | * [[Logical NAND]] | ||
* [[Logical NNOR]] | * [[Logical NNOR]] | ||
| − | + | {{col-break}} | |
* [[Minimal negation operator]] | * [[Minimal negation operator]] | ||
* [[Multigrade operator]] | * [[Multigrade operator]] | ||
* [[Parametric operator]] | * [[Parametric operator]] | ||
| − | + | {{col-end}} | |
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, \( f : \mathbb{B}^k \to \mathbb{B} \).
