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deductive closure
Deductive closure is a property of a set of objects (usually the objects in question are statements). 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.〔Peter D. Klein, ''Closure'', ''The Cambridge Dictionary of Philosophy (second edition)〕 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 (i.e., p q), q is also a member of O.
== Epistemic closure ==
(詳細はepistemology, many philosophers have and continue to debate whether particular subsets of propositions—especially ones ascribing knowledge or justification of a belief to a subject—are closed under deduction.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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