Multigrade operator - Revision history

Jon Awbrey: /* Document history */

2015-11-07T04:12:40Z

Document history

← Older revision		Revision as of 04:12, 7 November 2015
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	* [http://en.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Wikiversity]		* [http://en.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Wikiversity]
	* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Wikiversity Beta]		* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Wikiversity Beta]
	* [http://en.wikipedia.org/w/~~index.php?title=~~Multigrade_operator~~&oldid=40451309~~ Multigrade Operator], [http://en.wikipedia.org/ Wikipedia]		* [http://web.archive.org/web/20060913000000/http://en.wikipedia.org/wiki/Multigrade_operator Multigrade Operator], [http://en.wikipedia.org/ Wikipedia]

	[[Category:Inquiry]]		[[Category:Inquiry]]

Jon Awbrey: update

2015-11-07T03:32:40Z

update

← Older revision		Revision as of 03:32, 7 November 2015
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	<font size="3">☞</font> This page belongs to resource collections on [[Logic Live\|Logic]] and [[Inquiry Live\|Inquiry]].		<font size="3">☞</font> This page belongs to resource collections on [[Logic Live\|Logic]] and [[Inquiry Live\|Inquiry]].

	~~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.		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.

	The application of a multigrade operator <math>\Omega</math> to a finite sequence of operands ~~(''x''~~<~~sub>1</sub~~>,~~ …~~,~~ ''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>~~,~~ …~~,~~ ''x''<sub>''k''~~</~~sub~~>) may be taken for <math>\~~Omega</math><sub>''k''</sub>~~(~~''x''<sub>1</sub>~~,~~ …~~,~~ ''x''<sub>''k''~~</~~sub~~>).		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>

	==Syllabus==		==Syllabus==
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	===Focal nodes===		===Focal nodes===

	~~{{col-begin}}~~
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	* [[Inquiry Live]]		* [[Inquiry Live]]
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	* [[Logic Live]]		* [[Logic Live]]
	~~{{col-end}}~~

	===Peer nodes===		===Peer nodes===

	~~{{col-begin}}~~		* [http://intersci.ss.uci.edu/wiki/index.php/Multigrade_operator Multigrade Operator @ InterSciWiki]
	~~{{col-break}}~~
	* [http://mywikibiz.com/Multigrade_operator Multigrade Operator @ MyWikiBiz]		* [http://mywikibiz.com/Multigrade_operator Multigrade Operator @ MyWikiBiz]
	* [http://mathweb.org/wiki/Multigrade_operator Multigrade Operator @ MathWeb Wiki]
	* [http://netknowledge.org/wiki/Multigrade_operator Multigrade Operator @ NetKnowledge]
	* [http://wiki.oercommons.org/mediawiki/index.php/Multigrade_operator Multigrade Operator @ OER Commons]
	~~{{col-break}}~~
	* [http://p2pfoundation.net/Multigrade_Operator Multigrade Operator @ P2P Foundation]
	* [http://semanticweb.org/wiki/Multigrade_operator Multigrade Operator @ SemanticWeb]
	* [http://ref.subwiki.org/wiki/Multigrade_operator Multigrade Operator @ Subject Wikis]		* [http://ref.subwiki.org/wiki/Multigrade_operator Multigrade Operator @ Subject Wikis]
			* [http://en.wikiversity.org/wiki/Multigrade_operator Multigrade Operator @ Wikiversity]
	* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator @ Wikiversity Beta]		* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator @ Wikiversity Beta]
	~~{{col-end}}~~

	===Logical operators===		===Logical operators===
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	===Related articles===		===Related articles===

	* [http://~~mywikibiz~~.~~com~~/~~Directory:Jon_Awbrey~~/~~Papers~~/~~Semiotic_Information Jon Awbrey, “Semiotic Information”~~]		{{col-begin}}
			{{col-break}}
	* [http://~~mywikibiz~~.~~com~~/~~Directory:Jon_Awbrey~~/~~Papers~~/~~Introduction_to_Inquiry_Driven_Systems Jon Awbrey, “Introduction To Inquiry Driven Systems”~~]		* [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language]
			* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
	* [http://~~mywikibiz~~.~~com~~/~~Directory:Jon_Awbrey~~/~~Essays~~/~~Prospects_For_Inquiry_Driven_Systems Jon Awbrey, “Prospects For Inquiry Driven~~ Systems~~”~~]		* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
			{{col-break}}
	* [http://~~mywikibiz~~.~~com~~/~~Directory:Jon_Awbrey~~/~~Papers~~/~~Inquiry_Driven_Systems Jon Awbrey, “Inquiry Driven Systems~~ : ~~Inquiry Into Inquiry”~~]		* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction]
			* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus]
	* [http://~~mywikibiz~~.~~com~~/~~Directory:Jon_Awbrey~~/~~Papers~~/~~Propositional_Equation_Reasoning_Systems Jon Awbrey, “~~Propositional ~~Equation Reasoning Systems”~~]		* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
			{{col-break}}
	* [http://~~mywikibiz~~.~~com~~/~~Directory:Jon_Awbrey~~/~~Papers~~/~~Differential_Logic_:_Introduction Jon Awbrey, “~~Differential Logic ~~: Introduction”~~]		* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]
			* [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
	* [http://~~planetmath~~.~~org~~/~~encyclopedia~~/~~DifferentialPropositionalCalculus~~.~~html Jon Awbrey, “Differential Propositional Calculus”~~]		* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
			{{col-end}}
	* [http://~~mywikibiz~~.~~com~~/~~Directory~~:~~Jon_Awbrey~~/~~Papers~~/~~Differential_Logic_and_Dynamic_Systems_2~~.~~0 Jon Awbrey, “Differential Logic and Dynamic~~ Systems~~”~~]

	==Document history==		==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.		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.

	~~{{col-begin}}~~		* [http://intersci.ss.uci.edu/wiki/index.php/Multigrade_operator Multigrade Operator], [http://intersci.ss.uci.edu/ InterSciWiki]
	~~{{col-break}}~~
	* [http://mywikibiz.com/Multigrade_operator Multigrade Operator], [http://mywikibiz.com/ MyWikiBiz]		* [http://mywikibiz.com/Multigrade_operator Multigrade Operator], [http://mywikibiz.com/ MyWikiBiz]
	* [http://mathweb.org/wiki/Multigrade_operator Multigrade Operator], [http://mathweb.org/wiki/ MathWeb Wiki]		* [http://planetmath.org/MultigradeOperator Multigrade Operator], [http://planetmath.org/ PlanetMath]
	* [http://planetmath.org~~/encyclopedia~~/MultigradeOperator~~.html~~ Multigrade Operator], [http://planetmath.org/ PlanetMath]		* [http://wikinfo.org/w/index.php/Multigrade_operator Multigrade Operator], [http://wikinfo.org/w/ Wikinfo]
	* [http://~~planetphysics~~.org/~~encyclopedia~~/~~MultigradeOperator~~.~~html~~ Multigrade Operator], [http://~~planetphysics~~.org/ ~~PlanetPhysics~~]		* [http://en.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Wikiversity]
	* [http://~~proofwiki~~.org/wiki/~~Definition:Multigrade_Operator~~ Multigrade Operator], [http://~~proofwiki~~.org/ ~~ProofWiki~~]
	~~{{col-break}}~~
	* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Wikiversity Beta]		* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Wikiversity Beta]
	* [http://getwiki.net/-Parametric_Operator&r=multigrade_operator Multigrade Operator], [http://getwiki.net/ GetWiki]
	* [http://wikinfo.org/index.php/Multigrade_operator Multigrade Operator], [http://wikinfo.org/ Wikinfo]
	* [http://textop.org/wiki/index.php?title=Multigrade_operator Multigrade Operator], [http://textop.org/wiki/ Textop Wiki]
	* [http://en.wikipedia.org/w/index.php?title=Multigrade_operator&oldid=40451309 Multigrade Operator], [http://en.wikipedia.org/ Wikipedia]		* [http://en.wikipedia.org/w/index.php?title=Multigrade_operator&oldid=40451309 Multigrade Operator], [http://en.wikipedia.org/ Wikipedia]
	~~{{col-end}}~~

	[[Category:Inquiry]]		[[Category:Inquiry]]

Jon Awbrey: + article

2010-06-20T17:22:18Z

+ article

New page

☞ This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].

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.

The application of a multigrade operator <math>\Omega</math> to a finite sequence of operands (''x''1, …, ''x''''k'') 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''1, …, ''x''''k'') may be taken for <math>\Omega</math>''k''(''x''1, …, ''x''''k'').

==Syllabus==

===Focal nodes===

{{col-begin}}
{{col-break}}
* [[Inquiry Live]]
{{col-break}}
* [[Logic Live]]
{{col-end}}

===Peer nodes===

{{col-begin}}
{{col-break}}
* [http://mywikibiz.com/Multigrade_operator Multigrade Operator @ MyWikiBiz]
* [http://mathweb.org/wiki/Multigrade_operator Multigrade Operator @ MathWeb Wiki]
* [http://netknowledge.org/wiki/Multigrade_operator Multigrade Operator @ NetKnowledge]
* [http://wiki.oercommons.org/mediawiki/index.php/Multigrade_operator Multigrade Operator @ OER Commons]
{{col-break}}
* [http://p2pfoundation.net/Multigrade_Operator Multigrade Operator @ P2P Foundation]
* [http://semanticweb.org/wiki/Multigrade_operator Multigrade Operator @ SemanticWeb]
* [http://ref.subwiki.org/wiki/Multigrade_operator Multigrade Operator @ Subject Wikis]
* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator @ Wikiversity Beta]
{{col-end}}

===Logical operators===

{{col-begin}}
{{col-break}}
* [[Exclusive disjunction]]
* [[Logical conjunction]]
* [[Logical disjunction]]
* [[Logical equality]]
{{col-break}}
* [[Logical implication]]
* [[Logical NAND]]
* [[Logical NNOR]]
* [[Logical negation|Negation]]
{{col-end}}

===Related topics===

{{col-begin}}
{{col-break}}
* [[Ampheck]]
* [[Boolean domain]]
* [[Boolean function]]
* [[Boolean-valued function]]
* [[Differential logic]]
{{col-break}}
* [[Logical graph]]
* [[Minimal negation operator]]
* [[Multigrade operator]]
* [[Parametric operator]]
* [[Peirce's law]]
{{col-break}}
* [[Propositional calculus]]
* [[Sole sufficient operator]]
* [[Truth table]]
* [[Universe of discourse]]
* [[Zeroth order logic]]
{{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]]
* [[Dynamics of inquiry]]
{{col-break}}
* [[Semeiotic]]
* [[Logic of information]]
{{col-break}}
* [[Descriptive science]]
* [[Normative science]]
{{col-break}}
* [[Pragmatic maxim]]
* [[Truth theory]]
{{col-end}}

===Related articles===

* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Semiotic_Information Jon Awbrey, “Semiotic Information”]

* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, “Introduction To Inquiry Driven Systems”]

* [http://mywikibiz.com/Directory:Jon_Awbrey/Essays/Prospects_For_Inquiry_Driven_Systems Jon Awbrey, “Prospects For Inquiry Driven Systems”]

* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Inquiry_Driven_Systems Jon Awbrey, “Inquiry Driven Systems : Inquiry Into Inquiry”]

* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, “Propositional Equation Reasoning Systems”]

* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, “Differential Logic : Introduction”]

* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, “Differential Propositional Calculus”]

* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, “Differential Logic and Dynamic Systems”]

==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.

{{col-begin}}
{{col-break}}
* [http://mywikibiz.com/Multigrade_operator Multigrade Operator], [http://mywikibiz.com/ MyWikiBiz]
* [http://mathweb.org/wiki/Multigrade_operator Multigrade Operator], [http://mathweb.org/wiki/ MathWeb Wiki]
* [http://planetmath.org/encyclopedia/MultigradeOperator.html Multigrade Operator], [http://planetmath.org/ PlanetMath]
* [http://planetphysics.org/encyclopedia/MultigradeOperator.html Multigrade Operator], [http://planetphysics.org/ PlanetPhysics]
* [http://proofwiki.org/wiki/Definition:Multigrade_Operator Multigrade Operator], [http://proofwiki.org/ ProofWiki]
{{col-break}}
* [http://beta.wikiversity.org/wiki/Multigrade_operator Multigrade Operator], [http://beta.wikiversity.org/ Wikiversity Beta]
* [http://getwiki.net/-Parametric_Operator&r=multigrade_operator Multigrade Operator], [http://getwiki.net/ GetWiki]
* [http://wikinfo.org/index.php/Multigrade_operator Multigrade Operator], [http://wikinfo.org/ Wikinfo]
* [http://textop.org/wiki/index.php?title=Multigrade_operator Multigrade Operator], [http://textop.org/wiki/ Textop Wiki]
* [http://en.wikipedia.org/w/index.php?title=Multigrade_operator&oldid=40451309 Multigrade Operator], [http://en.wikipedia.org/ Wikipedia]
{{col-end}}

[[Category:Inquiry]]
[[Category:Open Educational Resource]]
[[Category:Peer Educational Resource]]
[[Category:Automata Theory]]
[[Category:Combinatorics]]
[[Category:Computer Science]]
[[Category:Differential Logic]]
[[Category:Equational Reasoning]]
[[Category:Formal Languages]]
[[Category:Formal Sciences]]
[[Category:Formal Systems]]
[[Category:Linguistics]]
[[Category:Logic]]
[[Category:Mathematics]]
[[Category:Neural Networks]]
[[Category:Philosophy]]
[[Category:Semiotics]]