The translation of a modal formula φ is true at a world of this general structure if and only if φ belongs to that world

Given a Kripke structure \[\mathcal{A}=\langle \mathbf{W},\mathbf{R},\langle P^{\mathcal{A}}\rangle _{P\in \Atom}\rangle\] we say that \(\mathcal{AG}\) is a general structure built on \(\mathcal{A}\) if and only if \[\mathcal{AG}=\langle \mathbf{W},\mathbf{W}^{\prime },\mathbf{R},\epsilon _{1}^{\mathcal{A}},\langle P^{\mathcal{A}}\rangle _{P\in \Atom}\rangle\] where \(\Def \subseteq \mathbf{W}^{\prime }\subseteq \wp (\mathbf{W})\). [22] It can be proved that the set of worlds where a moda