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− | A '''sole sufficient operator''' or a '''sole sufficient connective''' is an operator that is sufficient by itself to generate all of the operators in a specified class of operators. In [[logic]], it is a logical operator that suffices to generate all of the [[boolean-valued function]]s, <math>f : X \to \mathbb{B} </math>, where <math>X\!</math> is an arbitrary set and where <math>\mathbb{B}</math> is a generic 2-element set, typically <math>\mathbb{B} = \{ 0, 1 \} = \{ false, true \}</math>, in particular, to generate all of the [[finitary boolean function]]s, <math> f : \mathbb{B}^k \to \mathbb{B} </math>.
| + | <font size="3">☞</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. |
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− | ==See also== | + | A '''sole sufficient operator''' is an operator that is sufficient by itself to generate every operator in a specified class of operators. In the context of [[logic]], it is a logical operator that suffices to generate every [[boolean-valued function]], <math>f : X \to \mathbb{B},\!</math> where <math>X\!</math> is an arbitrary set and where <math>\mathbb{B}\!</math> is a generic two-element set, typically <math>\mathbb{B} = \{ 0, 1 \} = \{ \mathrm{false}, \mathrm{true} \},\!</math> in particular, to generate every finitary [[boolean function]], <math>f : \mathbb{B}^k \to \mathbb{B}.\!</math> |
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| + | ==Syllabus== |
| + | |
| + | ===Focal nodes=== |
| + | |
| + | * [[Inquiry Live]] |
| + | * [[Logic Live]] |
| + | |
| + | ===Peer nodes=== |
| + | |
| + | * [http://intersci.ss.uci.edu/wiki/index.php/Sole_sufficient_operator Sole Sufficient Operator @ InterSciWiki] |
| + | * [http://mywikibiz.com/Sole_sufficient_operator Sole Sufficient Operator @ MyWikiBiz] |
| + | * [http://ref.subwiki.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Subject Wikis] |
| + | * [http://en.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Wikiversity] |
| + | * [http://beta.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator @ Wikiversity Beta] |
| + | |
| + | ===Logical operators=== |
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| {{col-begin}} | | {{col-begin}} |
| {{col-break}} | | {{col-break}} |
− | * [[Ampheck]] | + | * [[Exclusive disjunction]] |
− | * [[Entitative graph]] | + | * [[Logical conjunction]] |
− | * [[Existential graph]] | + | * [[Logical disjunction]] |
| + | * [[Logical equality]] |
| {{col-break}} | | {{col-break}} |
− | * [[Logical graph]] | + | * [[Logical implication]] |
| * [[Logical NAND]] | | * [[Logical NAND]] |
| * [[Logical NNOR]] | | * [[Logical NNOR]] |
| + | * [[Logical negation|Negation]] |
| + | {{col-end}} |
| + | |
| + | ===Related topics=== |
| + | |
| + | {{col-begin}} |
| {{col-break}} | | {{col-break}} |
| + | * [[Ampheck]] |
| + | * [[Boolean domain]] |
| + | * [[Boolean function]] |
| + | * [[Boolean-valued function]] |
| + | * [[Differential logic]] |
| + | {{col-break}} |
| + | * [[Logical graph]] |
| * [[Minimal negation operator]] | | * [[Minimal negation operator]] |
| * [[Multigrade operator]] | | * [[Multigrade operator]] |
| * [[Parametric 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}} | | {{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=== |
| + | |
| + | {{col-begin}} |
| + | {{col-break}} |
| + | * [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://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems] |
| + | {{col-break}} |
| + | * [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://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems] |
| + | {{col-break}} |
| + | * [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://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry] |
| + | {{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. |
| + | |
| + | * [http://intersci.ss.uci.edu/wiki/index.php/Sole_sufficient_operator Sole Sufficient Operator], [http://intersci.ss.uci.edu/ InterSciWiki] |
| + | * [http://mywikibiz.com/Sole_sufficient_operator Sole Sufficient Operator], [http://mywikibiz.com/ MyWikiBiz] |
| + | * [http://http://planetmath.org/SoleSufficientOperator Sole Sufficient Operator], [http://planetmath.org/ PlanetMath] |
| + | * [http://semanticweb.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://semanticweb.org/ SemanticWeb] |
| + | * [http://wikinfo.org/w/index.php/Sole_sufficient_operator Sole Sufficient Operator], [http://wikinfo.org/w/ Wikinfo] |
| + | * [http://en.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://en.wikiversity.org/ Wikiversity] |
| + | * [http://beta.wikiversity.org/wiki/Sole_sufficient_operator Sole Sufficient Operator], [http://beta.wikiversity.org/ Wikiversity Beta] |
| + | * [http://en.wikipedia.org/w/index.php?title=Sole_sufficient_operator&oldid=156136346 Sole Sufficient Operator], [http://en.wikipedia.org/ Wikipedia] |
| + | |
| + | [[Category:Inquiry]] |
| + | [[Category:Open Educational Resource]] |
| + | [[Category:Peer Educational Resource]] |
| + | [[Category:Logic]] |
| + | [[Category:Mathematics]] |
| + | [[Category:Semiotics]] |