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.