Reachability Games in Dynamic Epistemic Logic
Bastien Maubert, Sophie Pinchinat, François Schwarzentruber · 2019
We define reachability games based on Dynamic Epistemic Logic (DEL), where the players? actions are finely described as DEL action models. We first consider the setting where a controller with perfect information interacts with an environment and aims at reaching some desired state of knowledge regarding the observers of the system. We study the problem of existence of a strategy for the controller, which generalises the classic epistemic planning problem, and we solve it for several types of actions such as public announcements and public actions. We then consider a yet richer setting where observers themselves are players, whose strategies must be based on their observations. We establish several decidability and undecidability results for the problem of existence of a distributed strategy, depending on the type of actions the players can use, and relate them to results from the literature on multiplayer games with imperfect information.