Section: New Results

Fundamental results and algorithms: dynamic epistemic logic

Participants : Guillaume Aucher, François Schwarzentruber.

Within the research line related to Dynamic Epistemic Logic (DEL), we have addressed two parallel lines of research, which have resulted in two publications [22] and [21] . The first deals with the computational complexity of the model checking problem and the satisfiability problem of DEL and the second deals with providing formal means to reason about the effects of sequences of events on the beliefs of multiple agents when these events are only partially specified. This second line of research is a continuation of the work started last year and was motivated by concerns and problems stemming from the Univerself project of Eric Fabre about IMS network.

1. Although DEL is an influential logical framework for representing and reasoning about information change, little is known about the computational complexity of its associated decision problems. In fact, we only know that for public announcement logic, a fragment of DEL, the satisfiability problem and the model-checking problem are respectively PSPACE-complete and in P. We contributed to fill this gap by proving that for the DEL language with event models, the model-checking problem is, surprisingly, PSPACE-complete. Also, we proved that the satisfiability problem is NEXPTIME-complete. In doing so, we provided a sound and complete tableau method deciding the satisfiability problem.

2. Let us consider a sequence of formulas providing partial information about an initial situation, about a set of events occurring sequentially in this situation, and about the resulting situation after the occurrence of each event. From this whole sequence, we want to infer more information, either about the initial situation, or about one of the events, or about the resulting situation after one of the events. Within the framework of Dynamic Epistemic Logic, we show that these different kinds of problems are all reducible to the problem of inferring what holds in the final situation after the occurrence of all the events. We then provide a tableau method deciding whether this kind of inference is valid. We implement it in LotrecScheme and show that these inference problems are NEXPTIME-complete. We extend our results to the cases where the accessibility relation is serial and reflexive and illustrate them with the coordinated attack problem.

Parallely to the study of abstract dynamic epistemic logic, we initiate the study of the interaction of argumentation theory and epistemic reasoning [33] .