 Quantified formulas, like all formulas, are true or false only relative to a world. Thus \(\exists xA\), for example, is true at a world \(w\) if and only if some object in \(\bD_w\) satisfies \(A\). Except in intuitionistic logic, where it has a specialized interpretation, the universal quantifier is interpreted similarly: \(\forall xA\) is true at \(w\) if and only if all objects in \(\bD_w\) satisfy \(A\). Kripke semantics often specify that for each \(w, \bD_w\) is nonempty, so that the resulting free logic is non-inclusive—but we shall not do so.