What does deductive closure mean?
Definitions for deductive closure
de·duc·tive clo·sure
This dictionary definitions page includes all the possible meanings, example usage and translations of the word deductive closure.
Wiktionary
deductive closurenoun
The set of all the statements that can be deduced from a given set of statements.
Wikipedia
Deductive closure
In mathematical logic, a set T {\displaystyle {\mathcal {T}}} of logical formulae is deductively closed if it contains every formula φ {\displaystyle \varphi } that can be logically deduced from T {\displaystyle {\mathcal {T}}} , formally: if T ⊢ φ {\displaystyle {\mathcal {T}}\vdash \varphi } always implies φ ∈ T {\displaystyle \varphi \in {\mathcal {T}}} . If T {\displaystyle T} is a set of formulae, the deductive closure of T {\displaystyle T} is its smallest superset that is deductively closed. The deductive closure of a theory T {\displaystyle {\mathcal {T}}} is often denoted Ded ( T ) {\displaystyle \operatorname {Ded} ({\mathcal {T}})} or Th ( T ) {\displaystyle \operatorname {Th} ({\mathcal {T}})} . This is a special case of the more general mathematical concept of closure — in particular, the deductive closure of T {\displaystyle {\mathcal {T}}} is exactly the closure of T {\displaystyle {\mathcal {T}}} with respect to the operation of logical consequence ( ⊢ {\displaystyle \vdash } ).
Wikidata
Deductive closure
Deductive closure is a property of a set of objects. A set of objects, O, is said to exhibit closure or to be closed under a given operation, R, provided that for every object, x, if x is a member of O and x is R-related to any object, y, then y is a member of O. In the context of statements, a deductive closure is the set of all the statements that can be deduced from a given set of statements. In propositional logic, the set of all true propositions exhibits deductive closure: if set O is the set of true propositions, and operation R is logical consequence, then provided that proposition p is a member of O and p is R-related to q, q is also a member of O.
Numerology
Chaldean Numerology
The numerical value of deductive closure in Chaldean Numerology is: 4
Pythagorean Numerology
The numerical value of deductive closure in Pythagorean Numerology is: 6
Translations for deductive closure
From our Multilingual Translation Dictionary
- deduktiver VerschlussGerman
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"deductive closure." Definitions.net. STANDS4 LLC, 2024. Web. 27 Apr. 2024. <https://www.definitions.net/definition/deductive+closure>.
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