Dynamic Epistemic Logic Games with Epistemic Temporal Goals
This work addresses a theoretical problem in formal methods and game theory for researchers, but it is incremental as it extends existing results to a broader class of winning conditions.
The authors tackled the problem of extending decidability results in Dynamic Epistemic Logic (DEL) games from reachability objectives to more general epistemic temporal goals expressed in LTLK, and they established that the infinite game structures generated by DEL public actions are regular, enabling finite representations for solving these games.
Dynamic Epistemic Logic (DEL) is a logical framework in which one can describe in great detail how actions are perceived by the agents, and how they affect the world. DEL games were recently introduced as a way to define classes of games with imperfect information where the actions available to the players are described very precisely. This framework makes it possible to define easily, for instance, classes of games where players can only use public actions or public announcements. These games have been studied for reachability objectives, where the aim is to reach a situation satisfying some epistemic property expressed in epistemic logic; several (un)decidability results have been established. In this work we show that the decidability results obtained for reachability objectives extend to a much more general class of winning conditions, namely those expressible in the epistemic temporal logic LTLK. To do so we establish that the infinite game structures generated by DEL public actions are regular, and we describe how to obtain finite representations on which we rely to solve them.