Generalized DEL-sequents

Guillaume Aucher 1 Bastien Maubert 1 François Schwarzentruber 2
1 S4 - System synthesis and supervision, scenarios
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
2 DISTRIBCOM - Distributed and Iterative Algorithms for the Management of Telecommunications Systems
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : 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 (DEL), 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.
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Guillaume Aucher, Bastien Maubert, François Schwarzentruber. Generalized DEL-sequents. JELIA - Logics in Artificial Intelligence - 2012, Sep 2013, Toulouse, France. ⟨hal-00856472⟩

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