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Modular algorithms for heterogeneous modal logics via multi-sorted coalgebra

Published online by Cambridge University Press:  25 March 2011

LUTZ SCHRÖDER  and
DIRK PATTINSON
LUTZ SCHRÖDER
Affiliation:
DFKI Bremen and Dept. of Comput. Sci., Univ. Bremen, Cartesium, Enrique-Schmidt-Str. 5, 28359 Bremen, Germany Email: Lutz.Schroeder@dfki.de
DIRK PATTINSON
Affiliation:
Department of Computing, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK Email: dirk@doc.ic.ac.uk
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Abstract

State-based systems and modal logics for reasoning about them often heterogeneously combine a number of features such as non-determinism and probabilities. In this paper, we show that the combination of features can be reflected algorithmically, and we 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 algorithmic description with 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 this is also 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, for example, Segala systems and games with uncertain information.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 21 , Special Issue 2: Coalgebraic Logic , April 2011 , pp. 235 - 266
Copyright
Copyright © Cambridge University Press 2011

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