Selection method for inquisitive modal logic

The selection method is one of the methods to prove that various modal logics have the finite model property. For a given formula that is satisfiable in some model, we select a finite tree-like submodel, while preserving the satisfiability of the observed formula. In this paper, we adapt the selection method for the inquisitive modal logic InqML. We first define a tree-like model in the inquisitive setting and show that each satisfiable formula is satisfiable in a tree-like model. Then, using the notions of n-bisimulation and characteristic formulas, we show that InqML has the finite tree model property, i.e., each satisfiable formula is satisfiable in a finite tree-like model. Furthermore, we show analogous results for the inquisitive neighborhood logic InqNL, and as a consequence we obtain the decidability of InqNL.