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>. | ||
| − | == | + | ==Syllabus== |
| + | |||
| + | ===Focal nodes=== | ||
{{col-begin}} | {{col-begin}} | ||
{{col-break}} | {{col-break}} | ||
| − | * [[ | + | * [[Inquiry Live]] |
| − | * [[ | + | {{col-break}} |
| − | * [[ | + | * [[Logic Live]] |
| + | {{col-end}} | ||
| + | |||
| + | ===Peer nodes=== | ||
| + | |||
| + | * [http://beta.wikiversity.org/wiki/Differential_logic Differential Logic @ Beta Wikiversity] | ||
| + | * [http://mywikibiz.com/Differential_logic Differential Logic @ MyWikiBiz] | ||
| + | * [http://www.netknowledge.org/wiki/Differential_logic Differential Logic @ NetKnowledge] | ||
| + | * [http://semanticweb.org/wiki/Differential_logic Differential Logic @ SemanticWeb] | ||
| + | |||
| + | ===Logical operators=== | ||
| + | |||
| + | {{col-begin}} | ||
| + | {{col-break}} | ||
| + | * [[Exclusive disjunction]] | ||
| + | * [[Logical conjunction]] | ||
| + | * [[Logical disjunction]] | ||
| + | * [[Logical equality]] | ||
{{col-break}} | {{col-break}} | ||
| − | * [[Logical | + | * [[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}} | {{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]] | ||
| + | * [[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== | ||
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
Template:Col-breakTemplate:Col-breakTemplate:Col-endPeer nodes
- Differential Logic @ Beta Wikiversity
- Differential Logic @ MyWikiBiz
- Differential Logic @ NetKnowledge
- Differential Logic @ SemanticWeb
Logical operators
Related topics
- Propositional calculus
- Sole sufficient operator
- Truth table
- Universe of discourse
- Zeroth order logic
