The complexity of certain modal formulas on binary ramified subset trees

In the present note we determine the complexity of the satisfiability problem of a certain modal logic of subset spaces which was proposed in [6]. The corresponding semantics is defined w.r.t. binary ramified subset trees consisting of a set X and a distinguished set O of subsets of X such that the relation of reverse set inclusion makes O a binary ramified tree. It turns out that the satisfiability problem of the logic is complete in NP.