Dynamic Epistemic Logic Games with Epistemic Temporal Goals

TL;DR

This paper extends decidability results in Dynamic Epistemic Logic games from reachability to more complex epistemic temporal goals by demonstrating the regularity of infinite game structures and providing finite representations for solving them.

Contribution

It introduces a method to handle a broader class of winning conditions in DEL games by proving their associated infinite structures are regular and can be finitely represented.

Findings

Decidability results extend to epistemic temporal logic goals.

Infinite DEL game structures are shown to be regular.

Finite representations enable solving complex game objectives.

Abstract

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.