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://intersci.ss.uci.edu/wiki/index.php/Boolean_function Boolean Function @ InterSciWiki]
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* [http://mywikibiz.com/Boolean_function Boolean Function @ MyWikiBiz]
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* [http://ref.subwiki.org/wiki/Boolean_function Boolean Function @ Subject Wikis]
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* [http://en.wikiversity.org/wiki/Boolean_function Boolean Function @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Boolean_function Boolean Function @ Wikiversity Beta]
  
 
===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]]
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==Document history==
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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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* [[Inquiry]]
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* [[Dynamics of inquiry]]
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* [[Semeiotic]]
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* [[Logic of information]]
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* [[Descriptive science]]
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* [[Normative science]]
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* [[Pragmatic maxim]]
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* [[Truth theory]]
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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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===Related articles===
  
 
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* [http://mywikibiz.com/Boolean_function Boolean Function], [http://mywikibiz.com/ MyWikiBiz]
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* [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language]
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* [http://beta.wikiversity.org/wiki/Boolean_function Boolean Function], [http://beta.wikiversity.org/ Beta Wikiversity]
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* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
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* [http://planetmath.org/encyclopedia/BooleanFunction.html Boolean Function], [http://planetmath.org/ PlanetMath]
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* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
 
{{col-break}}
 
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* [http://www.wikinfo.org/index.php/Boolean_function Boolean Function], [http://www.wikinfo.org/ Wikinfo]
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* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]
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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://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
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* [http://en.wikipedia.org/w/index.php?title=Boolean_function&oldid=60886833 Boolean Function], [http://en.wikipedia.org/ Wikipedia]
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* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
 
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<br><sharethis />
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==Document history==
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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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* [http://intersci.ss.uci.edu/wiki/index.php/Boolean_function Boolean Function], [http://intersci.ss.uci.edu/ InterSciWiki]
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* [http://mywikibiz.com/Boolean_function Boolean Function], [http://mywikibiz.com/ MyWikiBiz]
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* [http://planetmath.org/BooleanValuedFunction Boolean Function], [http://planetmath.org/ PlanetMath]
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* [http://wikinfo.org/w/index.php/Boolean_function Boolean Function], [http://wikinfo.org/w/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Boolean_function Boolean Function], [http://en.wikiversity.org/ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Boolean_function Boolean Function], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [http://en.wikipedia.org/w/index.php?title=Boolean_function&oldid=60886833 Boolean Function], [http://en.wikipedia.org/ Wikipedia]
  
 
[[Category:Inquiry]]
 
[[Category:Inquiry]]
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[[Category:Open Educational Resource]]
 
[[Category:Peer Educational Resource]]
 
[[Category:Peer Educational Resource]]
 
[[Category:Combinatorics]]
 
[[Category:Combinatorics]]

Latest revision as of 20:24, 5 November 2015

☞ 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

Peer nodes

Logical operators

Template:Col-breakTemplate:Col-breakTemplate:Col-end

Related topics

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Relational concepts

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Information, Inquiry

Template:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-breakTemplate:Col-end

Related articles

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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.

Retrieved from "https://mywikibiz.com/index.php?title=Boolean_function&oldid=466830"