Difference between revisions of "Multigrade 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 '''multigrade operator''' <math>\Omega</math> is a ''[[parametric operator]]'' with ''parameter'' ''k'' in the set '''N''' of non-negative integers.
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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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The application of a multigrade operator <math>\Omega</math> to a finite sequence of operands (''x''<sub>1</sub>,&nbsp;…,&nbsp;''x''<sub>''k''</sub>) is typically denoted with the parameter ''k'' left tacit, as the appropriate application is implicit in the number of operands listed.  Thus <math>\Omega</math>(''x''<sub>1</sub>,&nbsp;…,&nbsp;''x''<sub>''k''</sub>) may be taken for <math>\Omega</math><sub>''k''</sub>(''x''<sub>1</sub>,&nbsp;…,&nbsp;''x''<sub>''k''</sub>).
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A '''multigrade operator''' <math>\Omega\!</math> is a ''[[parametric operator]]'' with ''parameter'' <math>k\!</math> in the set <math>\mathbb{N}\!</math> of non-negative integers.
  
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==See also==
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The application of a multigrade operator <math>\Omega\!</math> to a finite sequence of operands <math>(x_1, \ldots, x_k)\!</math> is typically denoted with the parameter <math>k\!</math> left tacit, as the appropriate application is implicit in the number of operands listed.  Thus <math>\Omega (x_1, \ldots, x_k)\!</math> may be taken for <math>\Omega_k (x_1, \ldots, x_k).\!</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/Multigrade_operator Multigrade Operator @ InterSciWiki]
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* [http://mywikibiz.com/Multigrade_operator Multigrade Operator @ MyWikiBiz]
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* [http://ref.subwiki.org/wiki/Multigrade_operator Multigrade Operator @ Subject Wikis]
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* [http://en.wikiversity.org/wiki/Multigrade_operator Multigrade Operator @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade 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]]
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* [[Multigrade operator]]
 
* [[Parametric operator]]
 
* [[Parametric operator]]
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* [[Peirce's law]]
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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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===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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* [[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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===Related articles===
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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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* [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/Multigrade_operator Multigrade Operator], [http://intersci.ss.uci.edu/ InterSciWiki]
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* [http://mywikibiz.com/Multigrade_operator Multigrade Operator], [http://mywikibiz.com/ MyWikiBiz]
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* [http://planetmath.org/MultigradeOperator Multigrade Operator], [http://planetmath.org/ PlanetMath]
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* [http://wikinfo.org/w/index.php/Multigrade_operator Multigrade Operator], [http://wikinfo.org/w/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [http://web.archive.org/web/20060913000000/http://en.wikipedia.org/wiki/Multigrade_operator Multigrade 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 04:12, 7 November 2015

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

A multigrade operator \(\Omega\!\) is a parametric operator with parameter \(k\!\) in the set \(\mathbb{N}\!\) of non-negative integers.

The application of a multigrade operator \(\Omega\!\) to a finite sequence of operands \((x_1, \ldots, x_k)\!\) is typically denoted with the parameter \(k\!\) left tacit, as the appropriate application is implicit in the number of operands listed. Thus \(\Omega (x_1, \ldots, x_k)\!\) may be taken for \(\Omega_k (x_1, \ldots, x_k).\!\)

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.

Retrieved from "https://mywikibiz.com/index.php?title=Multigrade_operator&oldid=466840"