Deductive closure

Set of logical formulae containing all formulae able to be deduced from itself

In mathematical logic, a set ⁠⁠ of logical formulae is deductively closed if it contains every formula ⁠⁠ that can be logically deduced from ⁠⁠, formally: if ⁠⁠ always implies ⁠⁠. If ⁠⁠ is a set of formulae, the deductive closure of ⁠⁠ is its smallest superset that is deductively closed.

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