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Modular Algorithms for Heterogeneous Modal Logics

  • Lutz Schröder
  • Dirk Pattinson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)

Abstract

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.

Keywords

Modal Operator Modal Logic Binary Feature Proof Rule Conditional Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Lutz Schröder
    • 1
  • Dirk Pattinson
    • 2
  1. 1.DFKI-Lab Bremen and Department of Computer Science, Universität Bremen 
  2. 2.Department of Computing, Imperial College London 

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