Relation reduction - Revision history

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2013-05-19T01:36:18Z

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2013-05-17T02:56:45Z

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Jon Awbrey: Category:Charles Sanders Peirce

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2010-07-21T18:45:00Z

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Jon Awbrey: /* Information, Inquiry */

2010-05-23T11:55:18Z

Information, Inquiry

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 In [[logic]] and [[mathematics]], '''relation reduction''' and '''relational reducibility''' have to do with the extent to which a given [[relation (mathematics)|relation]] is determined by a set of other relations, called the ''relation dataset''.  The relation under examination is called the ''reductandum''.  The relation dataset typically consists of a specified relation over sets of relations, called the ''reducer'', the ''method of reduction'', or the ''relational step'', plus a set of other relations, called the ''reduciens'' or the ''relational base'',  each of which is properly simpler in a specified way than the relation under examination.
-A question of relation reduction or relational reducibility is sometimes posed as a question of '''relation reconstruction''' or '''relational reconstructibility''', since a useful way of stating the question is to ask whether the reductandum can be reconstructed from the reduciens.  See [[Humpty Dumpty]].
+A question of relation reduction or relational reducibility is sometimes posed as a question of '''relation reconstruction''' or '''relational reconstructibility''', since a useful way of stating the question is to ask whether the reductandum can be reconstructed from the reduciens.
 A relation that is not uniquely determined by a particular relation dataset is said to be ''irreducible'' in just that respect.  A relation that is not uniquely determined by any relation dataset in a particular class of relation datasets is said to be ''irreducible'' in respect of that class.

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 * [http://semanticweb.org/wiki/Relation_reduction Relation Reduction], [http://semanticweb.org/ Semantic Web]
-* [http://planetmath.org/encyclopedia/RelationReduction.html Relation Reduction], [http://planetmath.org/ PlanetMath]
+* [http://planetmath.org/RelationReduction Relation Reduction], [http://planetmath.org/ PlanetMath]
 * [http://getwiki.net/-Relational_Reduction Relation Reduction], [http://getwiki.net/ GetWiki]
 * [http://wikinfo.org/index.php/Relation_reduction Relation Reduction], [http://wikinfo.org/ Wikinfo]

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 [[Category:Open Educational Resource]]
 [[Category:Peer Educational Resource]]
 [[Category:Combinatorics]]
 [[Category:Computer Science]]

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 <font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
-In [[logic]] and [[mathematics]], '''relation reduction''' and '''relational reducibility''' have to do with the extent to which a given [[relation (mathematics)|relation]] is determined by a set of other relations, called the ''relation dataset''.  The relation under examination is called the ''reductandum''.  The relation dataset typically consists of a specified relation over sets of relations, called the ''reducer'', the ''method of reduction'', or the ''relational step'', plus a set of other relations, called the ''reduciens'' or the ''relational base'',  each of which is properly simpler in a specified way than relation under examination.
+In [[logic]] and [[mathematics]], '''relation reduction''' and '''relational reducibility''' have to do with the extent to which a given [[relation (mathematics)|relation]] is determined by a set of other relations, called the ''relation dataset''.  The relation under examination is called the ''reductandum''.  The relation dataset typically consists of a specified relation over sets of relations, called the ''reducer'', the ''method of reduction'', or the ''relational step'', plus a set of other relations, called the ''reduciens'' or the ''relational base'',  each of which is properly simpler in a specified way than the relation under examination.
 A question of relation reduction or relational reducibility is sometimes posed as a question of '''relation reconstruction''' or '''relational reconstructibility''', since a useful way of stating the question is to ask whether the reductandum can be reconstructed from the reduciens.  See [[Humpty Dumpty]].

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 * [http://mathweb.org/wiki/Relation_reduction Relation Reduction @ MathWeb Wiki]
 * [http://netknowledge.org/wiki/Relation_reduction Relation Reduction @ NetKnowledge]
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 * [http://p2pfoundation.net/Relation_Reduction Relation Reduction @ P2P Foundation]
 * [http://semanticweb.org/wiki/Relation_reduction Relation Reduction @ SemanticWeb]
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 {{col-break}}
 * [[Pragmatic maxim]]
-* [[Pragmatic theory of truth]]
+* [[Truth theory]]
 {{col-end}}

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 * [[Inquiry]]
 * [[Logic of information]]
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 * [[Pragmatic maxim]]
 * [[Pragmatic theory of truth]]
 {{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;]

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 * Some 3-adic relations are, and other 3-adic relations are not, reducible to, or reconstructible from, their 2-adic projection data.  In short, some 3-adic relations are projectively reducible and some 3-adic relations are projectively irreducible.
-==See also==
+==Syllabus==
 {{col-begin}}
 {{col-break}}
-* [[Binary relation]]
+* [[Exclusive disjunction]]
-* [[Cartesian product]]
+* [[Logical conjunction]]
-* [[Level set|Fiber, level set]]
+* [[Logical disjunction]]
-* [[Function (mathematics)|Function]]
+* [[Logical equality]]
-* [[Image (mathematics)|Functional image]]
+{{col-break}}
-* [[Reconstruction conjecture|Graph reconstruction]]
+* [[Logical implication]]
 {{col-break}}
 * [[Relation (mathematics)|Relation]]
 * [[Relation composition]]
 * [[Relation construction]]
-* [[Tacit extension]]
+* [[Relation reduction]]
 * [[Triadic relation]]
 {{col-end}}
 ==Document history==