Model Checking for Hybrid Logic

Abstract

We consider the model checking problem for Hybrid Logic. Known algorithms so far are global in the sense that they compute, inductively, in every step the set of all worlds of a Kripke structure that satisfy a subformula of the input. Hence, they always exploit the entire structure. Local model checking tries to avoid this by only traversing necessary parts of the input in order to establish or refute the satisfaction relation between a given world and a formula. We present a framework for local model checking of Hybrid Logic based on games. We show that these games are simple reachability games for ordinary Hybrid Logic and weak Büchi games for Hybrid Logic with operators interpreted over the transitive closure of the accessibility relation of the underlying Kripke frame, and show how to solve these games thus solving the local model checking problem. Since the first-order part of Hybrid Logic is inherently hard to localise in model checking, we give examples, in the end, of how global model checkers can be optimised in certain special cases using well-established techniques like fixpoint approximations and divide-and-conquer algorithms.