 as translations of modal axioms of system K are theorems of the MSL logic, while translations of \(T\) and 4 are theorems of \(\Delta _{S4}\). To prove the reverse deductive correspondence between MSL and PML the canonical  model[25]  \(\mathcal{B}_{K}\) (or \(\mathcal{B}_{S4}\)) could be used to build the general structure \(\mathcal{B}_{K}\mathfrak{G}\) (or \(\mathcal{B}_{S4}\mathfrak{G}\)). The final step is reached by using the general structure built onto the canonical model. It is easy to prove that the translation of a modal formula \(\varphi\) is true at a world of this structure if and only if formula \(\varphi\) belongs to this world.