http://debianws.lexgopc.com/wiki143/index.php?action=history&feed=atom&title=Boolean-valued_functionBoolean-valued function - Revision history2026-05-01T15:40:45ZRevision history for this page on the wikiMediaWiki 1.43.1http://debianws.lexgopc.com/wiki143/index.php?title=Boolean-valued_function&diff=1928893&oldid=previmported>Tc14Hd: Updated short description2025-01-27T20:56:30Z<p>Updated short description</p>
<p><b>New page</b></p><div>{{Short description|Function that outputs either true or false}}<br />
{{Cleanup rewrite|date=March 2011}}<br />
{{Functions}}<br />
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A '''Boolean-valued function''' (sometimes called a [[Predicate (logic)|predicate]] or a [[proposition]]) is a [[function (mathematics)|function]] of the type f : X → '''B''', where X is an arbitrary [[Set (mathematics)|set]] and where '''B''' is a [[Boolean domain]], i.e. a generic two-element set, (for example '''B''' = {0, 1}), whose elements are interpreted as [[logical value]]s, for example, 0 = [[false (logic)|false]] and 1 = [[truth value|true]], i.e., a single [[bit]] of [[information]].<br />
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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.<br />
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In [[semantics|formal semantic]] theories of [[truth]], a '''truth predicate''' is a predicate on the [[Sentence (mathematical logic)|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]].<br />
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==See also==<br />
{{colbegin|colwidth=18em}}<br />
* [[Bit]]<br />
* [[Boolean data type]]<br />
* [[Boolean algebra (logic)]]<br />
* [[Boolean domain]]<br />
* [[Boolean logic]]<br />
* [[Propositional calculus]]<br />
* [[Truth table]]<br />
* [[Logic minimization]]<br />
* [[Indicator function]]<br />
* [[Predicate (logic)|Predicate]]<br />
* [[Proposition]]<br />
* [[Boolean function]]<br />
{{colend}}<br />
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==References==<br />
* [[Frank Markham Brown|Brown, Frank Markham]] (2003), ''[https://books.google.com/books?id=QPzCAgAAQBAJ Boolean Reasoning: The Logic of Boolean Equations]'', 1st edition, Kluwer Academic Publishers, Norwell, MA. 2nd edition, Dover Publications, Mineola, NY, 2003.<br />
* [[Zvi Kohavi|Kohavi, Zvi]] (1978), ''[https://books.google.com/books?id=jZIxam8Rb9AC Switching and Finite Automata Theory]'', 1st edition, McGraw–Hill, 1970. 2nd edition, McGraw–Hill, 1978. 3rd edition, McGraw–Hill, 2010.<br />
* [[Robert R. Korfhage|Korfhage, Robert R.]] (1974), ''Discrete Computational Structures'', Academic Press, New York, NY.<br />
* [[Mathematical Society of Japan]], ''Encyclopedic Dictionary of Mathematics'', 2nd edition, 2 vols., Kiyosi Itô (ed.), MIT Press, Cambridge, MA, 1993. Cited as EDM.<br />
* [[Marvin L. Minsky|Minsky, Marvin L.]], and [[Seymour A. Papert|Papert, Seymour, A.]] (1988), ''[[Perceptrons]], An Introduction to Computational Geometry'', MIT Press, Cambridge, MA, 1969. Revised, 1972. Expanded edition, 1988.<br />
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[[Category:Boolean algebra]]</div>imported>Tc14Hd