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. 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.