Difference between revisions of "Boolean function"

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<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
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A '''finitary boolean function''' is a [[function (mathematics)|function]] of the form <math>f : \mathbb{B}^k \to \mathbb{B},</math> where <math>\mathbb{B} = \{ 0, 1 \}</math> is a [[boolean domain]] and where <math>k\!</math> is a nonnegative integer.  In the case where <math>k = 0,\!</math> the function is simply a constant element of <math>\mathbb{B}.</math>
 
A '''finitary boolean function''' is a [[function (mathematics)|function]] of the form <math>f : \mathbb{B}^k \to \mathbb{B},</math> where <math>\mathbb{B} = \{ 0, 1 \}</math> is a [[boolean domain]] and where <math>k\!</math> is a nonnegative integer.  In the case where <math>k = 0,\!</math> the function is simply a constant element of <math>\mathbb{B}.</math>
  
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==Syllabus==
 
==Syllabus==
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===Focal nodes===
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* [[Inquiry Live]]
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* [[Logic Live]]
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===Peer nodes===
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* [http://mywikibiz.com/Boolean_function Boolean Function @ MyWikiBiz]
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* [http://mathweb.org/wiki/Boolean_function Boolean Function @ MathWeb Wiki]
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* [http://netknowledge.org/wiki/Boolean_function Boolean Function @ NetKnowledge]
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* [http://wiki.oercommons.org/mediawiki/index.php/Boolean_function Boolean Function @ OER Commons]
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* [http://p2pfoundation.net/Boolean_Function Boolean Function @ P2P Foundation]
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* [http://semanticweb.org/wiki/Boolean_function Boolean Function @ SemanticWeb]
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===Logical operators===
 
===Logical operators===
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* [[Boolean function]]
 
* [[Boolean function]]
 
* [[Boolean-valued function]]
 
* [[Boolean-valued function]]
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* [[Differential logic]]
 
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* [[Logical graph]]
 
* [[Logical graph]]
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* [[Logical matrix]]
 
 
* [[Minimal negation operator]]
 
* [[Minimal negation operator]]
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* [[Multigrade operator]]
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* [[Parametric operator]]
 
* [[Peirce's law]]
 
* [[Peirce's law]]
 
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* [[Propositional calculus]]
 
* [[Propositional calculus]]
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* [[Sole sufficient operator]]
 
* [[Truth table]]
 
* [[Truth table]]
 
* [[Universe of discourse]]
 
* [[Universe of discourse]]
 
* [[Zeroth order logic]]
 
* [[Zeroth order logic]]
 
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===Relational concepts===
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* [[Continuous predicate]]
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* [[Hypostatic abstraction]]
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* [[Logic of relatives]]
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* [[Logical matrix]]
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* [[Relation (mathematics)|Relation]]
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* [[Relation composition]]
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* [[Relation construction]]
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* [[Relation reduction]]
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* [[Relation theory]]
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* [[Relative term]]
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* [[Sign relation]]
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* [[Triadic relation]]
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===Information, Inquiry===
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* [[Logic of information]]
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* [[Pragmatic maxim]]
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* [[Pragmatic theory of truth]]
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* [[Semeiotic]]
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* [[Semiotic information]]
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===Related articles===
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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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==Document history==
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* [http://mywikibiz.com/Boolean_function Boolean Function], [http://mywikibiz.com/ MyWikiBiz]
 
* [http://mywikibiz.com/Boolean_function Boolean Function], [http://mywikibiz.com/ MyWikiBiz]
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* [http://beta.wikiversity.org/wiki/Boolean_function Boolean Function], [http://beta.wikiversity.org/ Beta Wikiversity]
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* [http://mathweb.org/wiki/Boolean_function Boolean Function], [http://mathweb.org/ MathWeb Wiki]
 
* [http://planetmath.org/encyclopedia/BooleanFunction.html Boolean Function], [http://planetmath.org/ PlanetMath]
 
* [http://planetmath.org/encyclopedia/BooleanFunction.html Boolean Function], [http://planetmath.org/ PlanetMath]
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* [http://planetphysics.org/encyclopedia/BooleanFunction.html Boolean Function], [http://planetphysics.org/ PlanetPhysics]
 
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* [http://www.wikinfo.org/index.php/Boolean_function Boolean Function], [http://www.wikinfo.org/ Wikinfo]
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* [http://beta.wikiversity.org/wiki/Boolean_function Boolean Function], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [http://www.textop.org/wiki/index.php?title=Boolean_function Boolean Function], [http://www.textop.org/wiki/ Textop Wiki]
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* [http://wikinfo.org/index.php/Boolean_function Boolean Function], [http://wikinfo.org/ Wikinfo]
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* [http://textop.org/wiki/index.php?title=Boolean_function Boolean Function], [http://textop.org/wiki/ Textop Wiki]
 
* [http://en.wikipedia.org/w/index.php?title=Boolean_function&oldid=60886833 Boolean Function], [http://en.wikipedia.org/ Wikipedia]
 
* [http://en.wikipedia.org/w/index.php?title=Boolean_function&oldid=60886833 Boolean Function], [http://en.wikipedia.org/ Wikipedia]
 
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[[Category:Combinatorics]]
 
[[Category:Combinatorics]]

Revision as of 18:22, 10 May 2010

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

A finitary boolean function is a function of the form \(f : \mathbb{B}^k \to \mathbb{B},\) where \(\mathbb{B} = \{ 0, 1 \}\) is a boolean domain and where \(k\!\) is a nonnegative integer. In the case where \(k = 0,\!\) the function is simply a constant element of \(\mathbb{B}.\)

There are \(2^{2^k}\) such functions. These play a basic role in questions of complexity theory as well as the design of circuits and chips for digital computers.

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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