Difference between revisions of "Boolean-valued function"

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* [http://mywikibiz.com/Boolean-valued_function Boolean-Valued Function @ MyWikiBiz]
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* [http://mathweb.org/wiki/Boolean-valued_function Boolean-Valued Function @ MathWeb Wiki]
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* [http://netknowledge.org/wiki/Boolean-valued_function Boolean-Valued Function @ NetKnowledge]
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* [http://wiki.oercommons.org/mediawiki/index.php/Boolean-valued_function Boolean-Valued Function @ OER Commons]
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* [http://p2pfoundation.net/Boolean-Valued_Function Boolean-Valued Function @ P2P Foundation]
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* [http://semanticweb.org/wiki/Boolean-valued_function Boolean-Valued Function @ SemanticWeb]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Introduction To Inquiry Driven Systems&rdquo;]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Essays/Prospects_For_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Prospects For Inquiry Driven Systems&rdquo;]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Inquiry_Driven_Systems Jon Awbrey, &ldquo;Inquiry Driven Systems : Inquiry Into Inquiry&rdquo;]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, &ldquo;Propositional Equation Reasoning Systems&rdquo;]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;]
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* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&rdquo;]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, &ldquo;Differential Logic and Dynamic Systems&rdquo;]
  
 
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* [http://mywikibiz.com/Boolean-valued_function Boolean-Valued Function], [http://mywikibiz.com/ MyWikiBiz]
 
* [http://mywikibiz.com/Boolean-valued_function Boolean-Valued Function], [http://mywikibiz.com/ MyWikiBiz]
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* [http://beta.wikiversity.org/wiki/Boolean-valued_function Boolean-Valued Function], [http://beta.wikiversity.org/ Beta Wikiversity]
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* [http://mathweb.org/wiki/Boolean-valued_function Boolean-Valued Function], [http://mathweb.org/ MathWeb Wiki]
 
* [http://planetmath.org/encyclopedia/BooleanValuedFunction.html Boolean-Valued Function], [http://planetmath.org/ PlanetMath]
 
* [http://planetmath.org/encyclopedia/BooleanValuedFunction.html Boolean-Valued Function], [http://planetmath.org/ PlanetMath]
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* [http://planetphysics.org/encyclopedia/BooleanValuedFunction.html Boolean-Valued Function], [http://planetphysics.org/ PlanetPhysics]
 
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* [http://www.wikinfo.org/index.php/Boolean-valued_function Boolean-Valued Function], [http://www.wikinfo.org/ Wikinfo]
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* [http://www.textop.org/wiki/index.php?title=Boolean-valued_function Boolean-Valued Function], [http://www.textop.org/wiki/ Textop Wiki]
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* [http://en.wikipedia.org/w/index.php?title=Boolean-valued_function&oldid=67166584 Boolean-Valued Function], [http://en.wikipedia.org/ Wikipedia]
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* [http://textop.org/wiki/index.php?title=Boolean-valued_function Boolean-Valued Function], [http://textop.org/wiki/ Textop Wiki]
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* [http://en.wikipedia.org/w/index.php?title=Boolean-valued_function&oldid=67166584 Boolean Function], [http://en.wikipedia.org/ Wikipedia]
 
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Revision as of 19:34, 10 May 2010

☞ This page belongs to resource collections on Logic and Inquiry.

A boolean-valued function is a function of the type \(f : X \to \mathbb{B},\) where \(X\!\) is an arbitrary set and where \(\mathbb{B}\) is a boolean domain.

In the formal sciences — 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 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.

Examples

A binary sequence is a boolean-valued function \(f : \mathbb{N}^+ \to \mathbb{B}\), where \(\mathbb{N}^+ = \{ 1, 2, 3, \ldots \},\). In other words, \(f\!\) is an infinite sequence of 0's and 1's.

A binary sequence of length \(k\!\) is a boolean-valued function \(f : [k] \to \mathbb{B}\), where \([k] = \{ 1, 2, \ldots k \}.\)

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.

Syllabus

Focal nodes

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Peer nodes

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Logical operators

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Related topics

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Relational concepts

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Information, Inquiry

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Related articles

Document history

Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.

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