Coalgebraic Hybrid Logic

  • Authors:

  • Rob Myers;Dirk Pattinson;Lutz Schröder

  • Affiliations:

  • Department of Computing, Imperial College London,;Department of Computing, Imperial College London,;DFKI Bremen and Department of Computer Science, Universität Bremen,

  • Venue:
  • FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
  • Year:
  • 2009

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Abstract

We introduce a generic framework for hybrid logics, i.e. modal logics additionally featuring nominals and satisfaction operators , thus providing the necessary facilities for reasoning about individual states in a model. This framework, coalgebraic hybrid logic, works at the same level of generality as coalgebraic modal logic, and in particular subsumes, besides normal hybrid logics such as hybrid K , a wide variety of logics with non-normal modal operators such as probabilistic, graded, or coalitional modalities and non-monotonic conditionals. We prove a generic finite model property and an ensuing weak completeness result, and we give a semantic criterion for decidability in PSPACE. Moreover, we present a fully internalised PSPACE tableau calculus. These generic results are easily instantiated to particular hybrid logics and thus yield a wide range of new results, including e.g. decidability in PSPACE of probabilistic and graded hybrid logics.