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Boolean-valued function (view source)

Revision as of 16:14, 6 September 2007

203 bytes removed , 16:14, 6 September 2007

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A '''boolean-valued function''', in some usages a '''predicate''' or a '''proposition''', is a [[function (mathematics)|function]] of the type ''f'' : ''X'' → '''B''', where ''X'' is an arbitrary [[set]] and where '''B''' is a [[boolean domain]].

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A '''boolean domain''' '''B''' is a generic 2-element set, say, '''B''' = {0, 1}, whose elements are interpreted as [[logical value]]s, for example, 0 = false and 1 = true.

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In the [[formal science]]s — [[mathematics]], [[mathematical logic]], [[statistics]] — and their applied disciplines, a boolean-valued function may also be referred to as a [[characteristic function]], [[indicator function]], [[predicate]], or [[proposition]]. In all of these uses it is understood that the various terms refer to a mathematical object and not the corresponding [[semiotic]] sign or syntactic expression.

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In the [[formal science]]s, [[mathematics]], [[mathematical logic]], [[statistics]], and their applied disciplines, a boolean-valued function may also be referred to as a [[characteristic function]], [[indicator function]], [[predicate]], or [[proposition]]. In all of these uses it is understood that the various terms refer to a mathematical object and not the corresponding [[semiotic]] sign or syntactic expression.

In [[semantics|formal semantic]] theories of [[truth]], a '''truth predicate''' is a predicate on the [[sentence]]s of a [[formal language]], interpreted for logic, that formalizes the intuitive concept that is normally expressed by saying that a sentence is true. A truth predicate may have additional domains beyond the formal language domain, if that is what is required to determine a final truth value.

Jon Awbrey

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