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| In sum, ''N'' ο ''M'' = 0. This example affords sufficient evidence that relational composition, just like its kindred, matrix multiplication, is a ''[[non-commutative]]'' algebraic operation. | | In sum, ''N'' ο ''M'' = 0. This example affords sufficient evidence that relational composition, just like its kindred, matrix multiplication, is a ''[[non-commutative]]'' algebraic operation. |
− |
| |
− | ==Reduction==
| |
− | : ''Main article : [[Relation reduction]]''
| |
| | | |
| ==References== | | ==References== |
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| * [[Stanislaw Marcin Ulam|Ulam, S.M.]], ''Analogies Between Analogies: The Mathematical Reports of S.M. Ulam and His Los Alamos Collaborators'', A.R. Bednarek and Françoise Ulam (eds.), University of California Press, Berkeley, CA, 1990. | | * [[Stanislaw Marcin Ulam|Ulam, S.M.]], ''Analogies Between Analogies: The Mathematical Reports of S.M. Ulam and His Los Alamos Collaborators'', A.R. Bednarek and Françoise Ulam (eds.), University of California Press, Berkeley, CA, 1990. |
| | | |
− | ==See also== | + | ==Syllabus== |
| + | |
| + | ===Focal nodes=== |
| + | |
| + | {{col-begin}} |
| + | {{col-break}} |
| + | * [[Inquiry Live]] |
| + | {{col-break}} |
| + | * [[Logic Live]] |
| + | {{col-end}} |
| + | |
| + | ===Peer nodes=== |
| + | |
| + | {{col-begin}} |
| + | {{col-break}} |
| + | * [http://mywikibiz.com/Relation_composition Relation Composition @ MyWikiBiz] |
| + | * [http://mathweb.org/wiki/Relation_composition Relation Composition @ MathWeb Wiki] |
| + | * [http://netknowledge.org/wiki/Relation_composition Relation Composition @ NetKnowledge] |
| + | {{col-break}} |
| + | * [http://wiki.oercommons.org/mediawiki/index.php/Relation_composition Relation Composition @ OER Commons] |
| + | * [http://p2pfoundation.net/Relation_Composition Relation Composition @ P2P Foundation] |
| + | * [http://semanticweb.org/wiki/Relation_composition Relation Composition @ SemanticWeb] |
| + | {{col-end}} |
| | | |
− | ===History=== | + | ===Logical operators=== |
| | | |
− | * [[George Boole|Boole, George]] | + | {{col-begin}} |
− | * [[Augustus De Morgan|De Morgan, Augustus]] | + | {{col-break}} |
− | * [[Charles Sanders Peirce|Peirce, Charles Sanders]] | + | * [[Exclusive disjunction]] |
− | * [[Alfred Tarski|Tarski, Alfred]] | + | * [[Logical conjunction]] |
| + | * [[Logical disjunction]] |
| + | * [[Logical equality]] |
| + | {{col-break}} |
| + | * [[Logical implication]] |
| + | * [[Logical NAND]] |
| + | * [[Logical NNOR]] |
| + | * [[Logical negation|Negation]] |
| + | {{col-end}} |
| | | |
| ===Related topics=== | | ===Related topics=== |
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| {{col-begin}} | | {{col-begin}} |
| {{col-break}} | | {{col-break}} |
− | * [[Binary relation]] | + | * [[Ampheck]] |
− | * [[Function composition]] | + | * [[Boolean domain]] |
− | * [[Inverse relation]] | + | * [[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]] | | * [[Logic of relatives]] |
| * [[Logical matrix]] | | * [[Logical matrix]] |
− | * [[Projection (set theory)|Projection]]
| + | {{col-break}} |
| * [[Relation (mathematics)|Relation]] | | * [[Relation (mathematics)|Relation]] |
| + | * [[Relation composition]] |
| * [[Relation construction]] | | * [[Relation construction]] |
| + | * [[Relation reduction]] |
| {{col-break}} | | {{col-break}} |
− | * [[Relation reduction]] | + | * [[Relation theory]] |
− | * [[Relational algebra]] | + | * [[Relative term]] |
− | * [[Relational database]] | + | * [[Sign relation]] |
− | * [[Relational model]]
| |
− | * [[Tacit extension]]
| |
− | * [[Theory of relations]]
| |
| * [[Triadic relation]] | | * [[Triadic relation]] |
− | * [[Types of relations]]
| |
| {{col-end}} | | {{col-end}} |
| + | |
| + | ===Information, Inquiry=== |
| + | |
| + | {{col-begin}} |
| + | {{col-break}} |
| + | * [[Inquiry]] |
| + | * [[Logic of information]] |
| + | {{col-break}} |
| + | * [[Descriptive science]] |
| + | * [[Normative science]] |
| + | {{col-break}} |
| + | * [[Pragmatic maxim]] |
| + | * [[Pragmatic theory of truth]] |
| + | {{col-break}} |
| + | * [[Semeiotic]] |
| + | * [[Semiotic information]] |
| + | {{col-end}} |
| + | |
| + | ===Related articles=== |
| + | |
| + | * [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== | | ==Document history== |
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| [[Category:Open Educational Resource]] | | [[Category:Open Educational Resource]] |
| [[Category:Peer Educational Resource]] | | [[Category:Peer Educational Resource]] |
| + | [[Category:Combinatorics]] |
| + | [[Category:Computer Science]] |
| + | [[Category:Database Theory]] |
| + | [[Category:Discrete Mathematics]] |
| + | [[Category:Formal Sciences]] |
| + | [[Category:Logic]] |
| + | [[Category:Mathematics]] |
| + | [[Category:Relation Theory]] |