Modular Algorithms for Heterogeneous Modal Logics

Lutz Schröder, Dirk Pattinson

In: Lars Arge , Andrzej Tarlecki , Christian Cachin (Hrsg.). Automata, Languages and Programming. International Colloquium on Automata, Languages and Programming (ICALP-07) colocated with the 22nd Annual IEEE Symposium on Logic In Computer Science (LICS 2007), Logic Colloquium 2007 (LC07), and the 9th International Symposium on Principles and Practice of Declarative Programming (PPDP 2007) July 9-13 Wroclaw/Breslau Poland Seiten 459-471 Lecture Notes in Computer Science (LNCS) 4596 Springer 2007.


State-based systems and modal logics for reasoning about them often heterogeneously combine a number of features such as non-determinism and probabilities. Here, we show that the combination of features can be reflected algorithmically and develop modular decision procedures for heterogeneous modal logics. The modularity is achieved by formalising the underlying state-based systems as multi-sorted coalgebras and associating both a logical and an algorithmic description to a number of basic building blocks. Our main result is that logics arising as combinations of these building blocks can be decided in polynomial space provided that this is the case for the components. By instantiating the general framework to concrete cases, we obtain PSPACE decision procedures for a wide variety of structurally different logics, describing e.g. Segala systems and games with uncertain information.

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Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence