Boolean function

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

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

There are  2 2 k {\displaystyle 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

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### Focal nodes

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* Inquiry Live
* Logic Live

### Peer nodes

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* Boolean Function @ InterSciWiki
* Boolean Function @ Subject Wikis
* Boolean Function @ Wikiversity
* Boolean Function @ Wikiversity Beta

### Logical operators

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* Exclusive disjunction
* Logical conjunction
* Logical disjunction
* Logical equality

* Logical implication
* Logical NAND
* Logical NNOR
* Negation

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### Related topics

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* Ampheck
* Boolean domain
* Boolean function
* Boolean-valued function
* Differential logic

* Logical graph
* Minimal negation operator
* Multigrade operator
* Parametric operator
* Peirce's law

* Propositional calculus
* Sole sufficient operator
* Truth table
* Universe of discourse
* Zeroth order logic

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### Relational concepts

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* Continuous predicate
* Hypostatic abstraction
* Logic of relatives
* Logical matrix

* Relation
* Relation composition
* Relation construction
* Relation reduction

* Relation theory
* Relative term
* Sign relation
* Triadic relation

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### Information, Inquiry

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* Inquiry
* Dynamics of inquiry

* Semeiotic
* Logic of information

* Descriptive science
* Normative science

* Pragmatic maxim
* Truth theory

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### Related articles

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* Cactus Language
* Futures Of Logical Graphs
* Propositional Equation Reasoning Systems

* Differential Logic : Introduction
* Differential Propositional Calculus
* Differential Logic and Dynamic Systems

* Prospects for Inquiry Driven Systems
* Introduction to Inquiry Driven Systems
* Inquiry Driven Systems : Inquiry Into Inquiry

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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.

* Boolean Function, InterSciWiki
* Boolean Function, PlanetMath
* Boolean Function, Wikinfo
* Boolean Function, Wikiversity
* Boolean Function, Wikiversity Beta
* Boolean Function, Wikipedia