PlanetMath: sole sufficient operator

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sole sufficient operator

(Definition)

A sole sufficient operator or a sole sufficient connective is an operator that is sufficient by itself to define all of the operators in a specified set of operators.

In logical contexts this refers to a logical operator that suffices to define all of the Boolean-valued functions, $f : X \to \mathbb{B}$ , where is an arbitrary set and where $\mathbb{B}$ is a generic 2-element set, typically $\mathbb{B} = \{ 0, 1 \} = \{ \mathrm{false}, \mathrm{true} \}$ , in particular, to define all of the finitary Boolean functions, $f : \mathbb{B}^k \to \mathbb{B}$ .

"sole sufficient operator" is owned by Jon Awbrey.

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See Also: ampheck, logical connective

Other names:

sole sufficient connective

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Cross-references: Boolean functions, generic, Boolean-valued functions, sufficient, operator
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This is version 3 of sole sufficient operator, born on 2008-02-27, modified 2008-04-11.
Object id is 10342, canonical name is SoleSufficientOperator.
Accessed 547 times total.

Classification:

AMS MSC:	03B05 (Mathematical logic and foundations :: General logic :: Classical propositional logic)
	03B22 (Mathematical logic and foundations :: General logic :: Abstract deductive systems)
	03B35 (Mathematical logic and foundations :: General logic :: Mechanization of proofs and logical operations)
	03B70 (Mathematical logic and foundations :: General logic :: Logic in computer science)

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