Bisimulation Quotient in Inquisitive Modal Logic

Inquisitive modal logic InqML⊞ is a natural generalization of basic modal logic, with ⊞ as a primitive modal operator. In this paper, we study the bisimulation quotients in the logic InqML⊞. For a given inquisitive modal model M=(W,Σ,V), we first show that the bisimilarity relation is an equivalence relation on W and that there is the largest bisimulation on M. We then define the bisimulation quotient and prove that a model is connected to its bisimulation quotient by a surjective bounded morphism. Finally, we prove that two models are globally bisimilar if and only if their bisimulation quotients are isomorphic.