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Multigrade operator (view source)

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<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
 
<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
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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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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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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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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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==Related topic==
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==Syllabus==
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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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* [[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]]
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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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==Document history==
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===Relational concepts===
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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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===Information, Inquiry===
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* [[Inquiry]]
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* [[Dynamics of inquiry]]
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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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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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===Related articles===
    
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* [http://mywikibiz.com/Multigrade_operator Multigrade Operator], [http://mywikibiz.com/ MyWikiBiz]
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* [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language]
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* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Beta Wikiversity]
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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://planetmath.org/encyclopedia/MultigradeOperator.html Multigrade Operator], [http://planetmath.org/ PlanetMath]
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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://www.proofwiki.org/wiki/Definition:Multigrade_Operator Multigrade Operator], [http://www.proofwiki.org/ ProofWiki]
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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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* [http://www.getwiki.net/-Parametric_Operator&r=multigrade_operator Multigrade Operator], [http://www.getwiki.net/ GetWiki]
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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://www.wikinfo.org/index.php/Multigrade_operator Multigrade Operator], [http://www.wikinfo.org/ Wikinfo]
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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://www.textop.org/wiki/index.php?title=Multigrade_operator Multigrade Operator], [http://www.textop.org/wiki/ Textop Wiki]
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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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* [http://en.wikipedia.org/w/index.php?title=Multigrade_operator&oldid=40451309 Multigrade Operator], [http://en.wikipedia.org/ Wikipedia]
   
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<br><sharethis />
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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]
    
[[Category:Inquiry]]
 
[[Category:Inquiry]]
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[[Category:Open Educational Resource]]
 
[[Category:Peer Educational Resource]]
 
[[Category:Peer Educational Resource]]
 
[[Category:Automata Theory]]
 
[[Category:Automata Theory]]
Jon Awbrey
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