Difference between revisions of "Boolean-valued function"

MyWikiBiz, Author Your Legacy — Monday November 04, 2024
Jump to navigationJump to search
(<font size="3">☞</font> This page belongs to resource collections on Logic and Inquiry.)
(update)
Line 26: Line 26:
  
 
==Syllabus==
 
==Syllabus==
 +
 +
===Focal nodes===
 +
 +
{{col-begin}}
 +
{{col-break}}
 +
* [[Inquiry Live]]
 +
{{col-break}}
 +
* [[Logic Live]]
 +
{{col-end}}
 +
 +
===Peer nodes===
 +
 +
{{col-begin}}
 +
{{col-break}}
 +
* [http://mywikibiz.com/Boolean-valued_function Boolean-Valued Function @ MyWikiBiz]
 +
* [http://mathweb.org/wiki/Boolean-valued_function Boolean-Valued Function @ MathWeb Wiki]
 +
* [http://netknowledge.org/wiki/Boolean-valued_function Boolean-Valued Function @ NetKnowledge]
 +
{{col-break}}
 +
* [http://wiki.oercommons.org/mediawiki/index.php/Boolean-valued_function Boolean-Valued Function @ OER Commons]
 +
* [http://p2pfoundation.net/Boolean-Valued_Function Boolean-Valued Function @ P2P Foundation]
 +
* [http://semanticweb.org/wiki/Boolean-valued_function Boolean-Valued Function @ SemanticWeb]
 +
{{col-end}}
  
 
===Logical operators===
 
===Logical operators===
Line 50: Line 72:
 
* [[Boolean function]]
 
* [[Boolean function]]
 
* [[Boolean-valued function]]
 
* [[Boolean-valued function]]
 +
* [[Differential logic]]
 
{{col-break}}
 
{{col-break}}
 
* [[Logical graph]]
 
* [[Logical graph]]
−
* [[Logical matrix]]
 
 
* [[Minimal negation operator]]
 
* [[Minimal negation operator]]
 +
* [[Multigrade operator]]
 +
* [[Parametric operator]]
 
* [[Peirce's law]]
 
* [[Peirce's law]]
 
{{col-break}}
 
{{col-break}}
 
* [[Propositional calculus]]
 
* [[Propositional calculus]]
 +
* [[Sole sufficient operator]]
 
* [[Truth table]]
 
* [[Truth table]]
 
* [[Universe of discourse]]
 
* [[Universe of discourse]]
 
* [[Zeroth order logic]]
 
* [[Zeroth order logic]]
 
{{col-end}}
 
{{col-end}}
 +
 +
===Relational concepts===
 +
 +
{{col-begin}}
 +
{{col-break}}
 +
* [[Continuous predicate]]
 +
* [[Hypostatic abstraction]]
 +
* [[Logic of relatives]]
 +
* [[Logical matrix]]
 +
{{col-break}}
 +
* [[Relation (mathematics)|Relation]]
 +
* [[Relation composition]]
 +
* [[Relation construction]]
 +
* [[Relation reduction]]
 +
{{col-break}}
 +
* [[Relation theory]]
 +
* [[Relative term]]
 +
* [[Sign relation]]
 +
* [[Triadic relation]]
 +
{{col-end}}
 +
 +
===Information, Inquiry===
 +
 +
{{col-begin}}
 +
{{col-break}}
 +
* [[Inquiry]]
 +
* [[Logic of information]]
 +
{{col-break}}
 +
* [[Descriptive science]]
 +
* [[Normative science]]
 +
{{col-break}}
 +
* [[Pragmatic maxim]]
 +
* [[Pragmatic theory of truth]]
 +
{{col-break}}
 +
* [[Semeiotic]]
 +
* [[Semiotic information]]
 +
{{col-end}}
 +
 +
===Related articles===
 +
 +
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Introduction To Inquiry Driven Systems&rdquo;]
 +
 +
* [http://mywikibiz.com/Directory:Jon_Awbrey/Essays/Prospects_For_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Prospects For Inquiry Driven Systems&rdquo;]
 +
 +
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Inquiry_Driven_Systems Jon Awbrey, &ldquo;Inquiry Driven Systems : Inquiry Into Inquiry&rdquo;]
 +
 +
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, &ldquo;Propositional Equation Reasoning Systems&rdquo;]
 +
 +
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;]
 +
 +
* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&rdquo;]
 +
 +
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, &ldquo;Differential Logic and Dynamic Systems&rdquo;]
  
 
==Document history==
 
==Document history==
Line 69: Line 147:
 
{{col-break}}
 
{{col-break}}
 
* [http://mywikibiz.com/Boolean-valued_function Boolean-Valued Function], [http://mywikibiz.com/ MyWikiBiz]
 
* [http://mywikibiz.com/Boolean-valued_function Boolean-Valued Function], [http://mywikibiz.com/ MyWikiBiz]
−
* [http://beta.wikiversity.org/wiki/Boolean-valued_function Boolean-Valued Function], [http://beta.wikiversity.org/ Beta Wikiversity]
+
* [http://mathweb.org/wiki/Boolean-valued_function Boolean-Valued Function], [http://mathweb.org/ MathWeb Wiki]
 
* [http://planetmath.org/encyclopedia/BooleanValuedFunction.html Boolean-Valued Function], [http://planetmath.org/ PlanetMath]
 
* [http://planetmath.org/encyclopedia/BooleanValuedFunction.html Boolean-Valued Function], [http://planetmath.org/ PlanetMath]
 +
* [http://planetphysics.org/encyclopedia/BooleanValuedFunction.html Boolean-Valued Function], [http://planetphysics.org/ PlanetPhysics]
 
{{col-break}}
 
{{col-break}}
−
* [http://www.wikinfo.org/index.php/Boolean-valued_function Boolean-Valued Function], [http://www.wikinfo.org/ Wikinfo]
+
* [http://beta.wikiversity.org/wiki/Boolean-valued_function Boolean-Valued Function], [http://beta.wikiversity.org/ Wikiversity Beta]
−
* [http://www.textop.org/wiki/index.php?title=Boolean-valued_function Boolean-Valued Function], [http://www.textop.org/wiki/ Textop Wiki]
+
* [http://wikinfo.org/index.php/Boolean-valued_function Boolean-Valued Function], [http://wikinfo.org/ Wikinfo]
−
* [http://en.wikipedia.org/w/index.php?title=Boolean-valued_function&oldid=67166584 Boolean-Valued Function], [http://en.wikipedia.org/ Wikipedia]
+
* [http://textop.org/wiki/index.php?title=Boolean-valued_function Boolean-Valued Function], [http://textop.org/wiki/ Textop Wiki]
 +
* [http://en.wikipedia.org/w/index.php?title=Boolean-valued_function&oldid=67166584 Boolean Function], [http://en.wikipedia.org/ Wikipedia]
 
{{col-end}}
 
{{col-end}}
  
Line 80: Line 160:
  
 
[[Category:Inquiry]]
 
[[Category:Inquiry]]
 +
[[Category:Open Educational Resource]]
 
[[Category:Peer Educational Resource]]
 
[[Category:Peer Educational Resource]]
 
[[Category:Combinatorics]]
 
[[Category:Combinatorics]]

Revision as of 19:34, 10 May 2010

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

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 sciences — mathematics, 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

Focal nodes

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

Peer nodes

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

Logical operators

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

Related topics

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

Relational concepts

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

Information, Inquiry

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

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.

Template:Col-breakTemplate:Col-breakTemplate:Col-end
<sharethis />
Retrieved from "https://mywikibiz.com/index.php?title=Boolean-valued_function&oldid=117384"