Difference between revisions of "Sole sufficient operator"

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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>.
 
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>.
  
==See also==
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==Syllabus==
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===Focal nodes===
  
 
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* [[Ampheck]]
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* [[Inquiry Live]]
* [[Entitative graph]]
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* [[Existential graph]]
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* [[Logic Live]]
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===Peer nodes===
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* [http://beta.wikiversity.org/wiki/Differential_logic Differential Logic @ Beta Wikiversity]
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* [http://mywikibiz.com/Differential_logic Differential Logic @ MyWikiBiz]
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* [http://www.netknowledge.org/wiki/Differential_logic Differential Logic @ NetKnowledge]
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* [http://semanticweb.org/wiki/Differential_logic Differential Logic @ SemanticWeb]
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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 graph]]
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* [[Logical implication]]
 
* [[Logical NAND]]
 
* [[Logical NAND]]
 
* [[Logical NNOR]]
 
* [[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]]
 
* [[Minimal negation operator]]
 
* [[Minimal negation operator]]
 
* [[Multigrade operator]]
 
* [[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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===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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* [[Logic of information]]
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* [[Descriptive science]]
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* [[Normative science]]
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* [[Pragmatic maxim]]
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* [[Pragmatic theory of truth]]
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* [[Semeiotic]]
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* [[Semiotic information]]
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===Related articles===
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* [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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* [http://mywikibiz.com/Directory:Jon_Awbrey/Essays/Prospects_For_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Prospects For Inquiry Driven Systems&rdquo;]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Inquiry_Driven_Systems Jon Awbrey, &ldquo;Inquiry Driven Systems : Inquiry Into Inquiry&rdquo;]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, &ldquo;Propositional Equation Reasoning Systems&rdquo;]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;]
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* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&rdquo;]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, &ldquo;Differential Logic and Dynamic Systems&rdquo;]
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==Document history==

Revision as of 00:43, 2 May 2010

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 functions, \(f : X \to \mathbb{B} \), where \(X\!\) is an arbitrary set and where \(\mathbb{B}\) is a generic 2-element set, typically \(\mathbb{B} = \{ 0, 1 \} = \{ false, true \}\), in particular, to generate all of the finitary boolean functions, \( f : \mathbb{B}^k \to \mathbb{B} \).

Syllabus

Focal nodes

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Peer nodes

Logical operators

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Related topics

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Relational concepts

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Information, Inquiry

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Related articles

Document history