Difference between revisions of "Boolean-valued function"

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* [[Marvin L. Minsky|Minsky, Marvin L.]], and [[Seymour A. Papert|Papert, Seymour, A.]] (1988), ''[[Perceptrons]], An Introduction to Computational Geometry'', MIT Press, Cambridge, MA, 1969.  Revised, 1972.  Expanded edition, 1988.
 
* [[Marvin L. Minsky|Minsky, Marvin L.]], and [[Seymour A. Papert|Papert, Seymour, A.]] (1988), ''[[Perceptrons]], An Introduction to Computational Geometry'', MIT Press, Cambridge, MA, 1969.  Revised, 1972.  Expanded edition, 1988.
  
==See also==
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==Syllabus==
{|
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===Logical operators===
* [[Boolean algebra]]
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* [[Exclusive disjunction]]
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* [[Logical conjunction]]
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* [[Logical disjunction]]
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* [[Logical equality]]
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* [[Logical implication]]
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* [[Logical NAND]]
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* [[Logical NNOR]]
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* [[Logical negation|Negation]]
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===Related topics===
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* [[Ampheck]]
 
* [[Boolean domain]]
 
* [[Boolean domain]]
* [[Boolean logic]]
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* [[Boolean function]]
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* [[Boolean-valued function]]
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* [[Logical graph]]
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* [[Logical matrix]]
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* [[Minimal negation operator]]
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* [[Peirce's law]]
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* [[Propositional calculus]]
 
* [[Propositional calculus]]
 
* [[Truth table]]
 
* [[Truth table]]
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* [[Universe of discourse]]
 
* [[Zeroth order logic]]
 
* [[Zeroth order logic]]
|}
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{{col-end}}
  
===Equivalent concepts===
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==Document history==
  
* [[Characteristic function]]
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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.
* [[Indicator function]]
 
* [[Predicate]], in some senses.
 
* [[Proposition]], in some senses.
 
  
===Related concepts===
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{{col-break}}
* [[Boolean function]]
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* [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://planetmath.org/encyclopedia/BooleanValuedFunction.html Boolean-Valued Function], [http://planetmath.org/ PlanetMath]
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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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{{aficionados}}<sharethis />
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[[Category:Combinatorics]]
 
[[Category:Combinatorics]]

Revision as of 01:45, 7 April 2010

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 sciencesmathematics, 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

Logical operators

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Related topics

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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.

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<sharethis />