Deductive closure

In mathematical logic, a set ⁠

⁠ is a set of formulae, the deductive closure of ⁠

⁠ is its smallest superset that is deductively closed.

The deductive closure of a theory ⁠

[citation needed] Some authors do not define a theory as deductively closed (thus, a theory is defined as any set of sentences), but such theories can always be 'extended' to a deductively closed set.

A theory may be referred to as a deductively closed theory to emphasize it is defined as a deductively closed set.

⁠ with respect to the operation of logical consequence (⁠

In 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.

This mathematical logic-related article is a stub.