 where \(\Def \subseteq \mathbf{W}^{\prime }\subseteq \wp (\mathbf{W})\). The sets \(\Def\) and \(\mathbf{W}^{\prime }\) contain all the members in the family \(\langle P^{\mathcal{A}}\rangle _{P\in \Atom}\) and are closed under several  operations.[22]  It can be proved that the set of worlds where a modal formula \(\varphi\) is true in a modal structure \(\mathcal{A}\) is the same set its translation defines in the general structure \(\mathcal{AG}\) built on \(\mathcal{A}\).