Deductive closure is a property of a set of objects (usually the objects in question are statements). A set of objects, <var>O</var>, is said to exhibit closure or to be closed under a given operation, <var>R</var>, provided that for every object, <var>x</var>, if <var>x</var> is a member of <var>O</var> and <var>x</var> is <var>R</var>-related to any object, <var>y</var>, then <var>y</var> is a member of <var>O</var>. 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.