Decidability of inquisitive modal logic via filtrations

Inquisitive logic is an extension of classical logic which can express questions. To enable this expressiveness, a possible world semantics is used. So, it is natural to combine inquisitive and modal logic, thus obtaining the inquisitive modal logic InqML. This paper contributes to the model theory of InqML.We show that the filtration technique can be adapted to the inquisitive logic semantics. Using filtrations, we prove that InqML has the finite model property, i.e., every satisfiable formula is satisfiable in a finite model. As a consequence, we obtain that InqML is decidable. Finally, we study filtrations over particular model classes and we prove that some extensions of InqML are also decidable.