Boolean function

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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.

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Logical operators

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


 * Logical implication
 * Logical NAND
 * Logical NNOR
 * Negation

Related topics

 * 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

Relational concepts

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


 * Relation
 * Relation composition
 * Relation construction
 * Relation reduction


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

Information, Inquiry

 * Inquiry
 * Dynamics of inquiry


 * Semeiotic
 * Logic of information


 * Descriptive science
 * Normative science


 * Pragmatic maxim
 * Truth theory

Related articles

 * Jon Awbrey, &ldquo;Semiotic Information&rdquo;


 * Jon Awbrey, &ldquo;Introduction To Inquiry Driven Systems&rdquo;


 * Jon Awbrey, &ldquo;Prospects For Inquiry Driven Systems&rdquo;


 * Jon Awbrey, &ldquo;Inquiry Driven Systems : Inquiry Into Inquiry&rdquo;


 * Jon Awbrey, &ldquo;Propositional Equation Reasoning Systems&rdquo;


 * Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;


 * Jon Awbrey, &ldquo;Differential Propositional Calculus&rdquo;


 * Jon Awbrey, &ldquo;Differential Logic and Dynamic Systems&rdquo;

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.


 * Boolean Function, MyWikiBiz
 * Boolean Function, MathWeb Wiki
 * Boolean Function, PlanetMath
 * Boolean Function, PlanetPhysics


 * Boolean Function, Wikiversity Beta
 * Boolean Function, Wikinfo
 * Boolean Function, Textop Wiki
 * Boolean Function, Wikipedia