Difference between revisions of "Boolean-valued function"

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

Revision as of 16:16, 6 September 2007

A boolean-valued function is a function of the type f : X → B, where X is an arbitrary set and where B is a boolean domain.

In the formal sciencesmathematics, 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 formal semantic theories of truth, a truth predicate is a predicate on the sentences 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.

References

  • Brown, Frank Markham (2003), Boolean Reasoning: The Logic of Boolean Equations, 1st edition, Kluwer Academic Publishers, Norwell, MA. 2nd edition, Dover Publications, Mineola, NY, 2003.
  • Kohavi, Zvi (1978), Switching and Finite Automata Theory, 1st edition, McGraw–Hill, 1970. 2nd edition, McGraw–Hill, 1978.
  • Mathematical Society of Japan, Encyclopedic Dictionary of Mathematics, 2nd edition, 2 vols., Kiyosi Itô (ed.), MIT Press, Cambridge, MA, 1993. Cited as EDM.

See also

Equivalent concepts

Related concepts

Aficionados



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