Relation-changing modal operators

Abstract

We study dynamic modal operators that can change the accessibility relation of a model during the evaluation of a formula. In particular, we extend the basic modal language with modalities that are able to delete, add or swap an edge between pairs of elements of the domain. We define a generic framework to characterize this kind of operations. First, we investigate relation-changing modal logics as fragments of classical logics. Then, we use the new framework to get a suitable notion of bisimulation for the logics introduced, and we investigate their expressive power. Finally, we show that the complexity of the model checking problem for the particular operators introduced is PSpace-complete, and we study two subproblems of model checking: formula complexity and program complexity.