On the Computational Complexity of Model Checking for Dynamic Epistemic Logic with S5 Models

Dynamic epistemic logic (DEL) is a logical framework for representing and reasoning about knowledge change for multiple agents. An important computational task in this framework is the model checking problem, which has been shown to be PSPACE-hard even for S5 models and two agents---in the presence of other features, such as multi-pointed models. We answer open questions in the literature about the complexity of this problem in more restricted settings. We provide a detailed complexity analysis of the model checking problem for DEL, where we consider various combinations of restrictions, such as the number of agents, whether the models are single-pointed or multi-pointed, and whether postconditions are allowed in the updates. In particular, we show that the problem is already PSPACE-hard in (1) the case of one agent, multi-pointed S5 models, and no postconditions, and (2) the case of two agents, only single-pointed S5 models, and no postconditions. In addition, we study the setting where only semi-private announcements are allowed as updates. We show that for this case the problem is already PSPACE-hard when restricted to two agents and three propositional variables. The results that we obtain in this paper help outline the exact boundaries of the restricted settings for which the model checking problem for DEL is computationally tractable.