Difference between revisions of "Parametric operator"

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(copy text from [http://www.opencycle.net/ OpenCycle] of which Jon Awbrey is the sole author)
 
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In [[logic]] and [[mathematics]], a '''parametric operator''' <math>\Omega\!</math> with '''parameter''' <math>\alpha\!</math> in the '''parametric set''' <math>\Alpha\!</math> is a [[family (mathematics)|indexed family]] of operators <math>(\Omega_{\alpha})_{\Alpha} = \{\Omega_{\alpha} : \alpha \in \Alpha\}</math> with index <math>\alpha\!</math> in the index set <math>\Alpha\!</math>.
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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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==See also==
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A '''parametric operator''' <math>\Omega\!</math> with '''parameter''' <math>\alpha\!</math> in the '''parameter set''' <math>\Alpha\!</math> is an indexed family of operators <math>(\Omega_\alpha)_\Alpha = \{ \Omega_\alpha : \alpha \in \Alpha \}\!</math> with index <math>\alpha\!</math> in the index set <math>\Alpha.\!</math>
  
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* [[Operation (mathematics)|Operation]]
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==Syllabus==
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* [[Operator]]
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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/Parametric_operator Parametric Operator @ InterSciWiki]
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* [http://mywikibiz.com/Parametric_operator Parametric Operator @ MyWikiBiz]
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* [http://ref.subwiki.org/wiki/Parametric_operator Parametric Operator @ Subject Wikis]
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* [http://en.wikiversity.org/wiki/Parametric_operator Parametric Operator @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Parametric_operator Parametric Operator @ Wikiversity Beta]
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===Logical operators===
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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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{{col-break}}
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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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{{col-end}}
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===Related topics===
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* [[Ampheck]]
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* [[Boolean domain]]
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* [[Boolean function]]
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* [[Boolean-valued function]]
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* [[Differential logic]]
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* [[Logical graph]]
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* [[Minimal negation operator]]
 
* [[Multigrade operator]]
 
* [[Multigrade operator]]
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* [[Parametric operator]]
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* [[Peirce's law]]
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{{col-break}}
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* [[Propositional calculus]]
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* [[Sole sufficient operator]]
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* [[Truth table]]
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* [[Universe of discourse]]
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* [[Zeroth order logic]]
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{{col-end}}
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===Relational concepts===
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{{col-break}}
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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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{{col-break}}
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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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{{col-end}}
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===Information, Inquiry===
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{{col-break}}
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* [[Inquiry]]
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* [[Dynamics of inquiry]]
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{{col-break}}
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* [[Semeiotic]]
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* [[Logic of information]]
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{{col-break}}
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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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{{col-end}}
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===Related articles===
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{{col-begin}}
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{{col-break}}
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* [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language]
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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://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
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{{col-break}}
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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]
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{{col-break}}
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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://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
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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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{{col-end}}
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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/Parametric_operator Parametric Operator], [http://intersci.ss.uci.edu/ InterSciWiki]
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* [http://mywikibiz.com/Parametric_operator Parametric Operator], [http://mywikibiz.com/ MyWikiBiz]
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* [http://planetmath.org/ParametricOperator Parametric Operator], [http://planetmath.org/ PlanetMath]
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* [http://wikinfo.org/w/index.php/Parametric_operator Parametric Operator], [http://wikinfo.org/w/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Parametric_operator Parametric Operator], [http://en.wikiversity.org/ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Parametric_operator Parametric Operator], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [http://en.wikipedia.org/w/index.php?title=Parametric_operator&oldid=40451935 Parametric Operator], [http://en.wikipedia.org/ Wikipedia]
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[[Category:Inquiry]]
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[[Category:Open Educational Resource]]
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[[Category:Peer Educational Resource]]
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[[Category:Automata Theory]]
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[[Category:Combinatorics]]
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[[Category:Computer Science]]
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[[Category:Differential Logic]]
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[[Category:Equational Reasoning]]
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[[Category:Formal Languages]]
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[[Category:Formal Sciences]]
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[[Category:Formal Systems]]
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[[Category:Linguistics]]
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[[Category:Logic]]
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[[Category:Mathematics]]
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[[Category:Neural Networks]]
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[[Category:Philosophy]]
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[[Category:Semiotics]]

Latest revision as of 04:16, 7 November 2015

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

A parametric operator \(\Omega\!\) with parameter \(\alpha\!\) in the parameter set \(\Alpha\!\) is an indexed family of operators \((\Omega_\alpha)_\Alpha = \{ \Omega_\alpha : \alpha \in \Alpha \}\!\) with index \(\alpha\!\) in the index set \(\Alpha.\!\)

Syllabus

Focal nodes

Peer nodes

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

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

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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