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The Computer Journal Advance Access published online on February 21, 2009
The Computer Journal, doi:10.1093/comjnl/bxp004
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© The Author 2009. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Modal Logics are Coalgebraic1

Corina Cîrstea1, Alexander Kurz2, Dirk Pattinson3, Lutz Schröder4,* and Yde Venema5

1 School of Electronics and Computer Science, University of Southampton, Highfield, Southampton SO17 1BJ, UK
2 Department of Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, UK
3 Department of Computing, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK
4 DFKI Bremen and Department of Computer Science, Universität Bremen, Cartesium, Enrique-Schmidt-Str. 5, 28359 Bremen, Germany
5 Institute for Logic, Language and Computation, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, he Netherlands

* Corresponding author: lutz.schroeder{at}dfki.de

Received 31 October 2008; Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can, moreover, be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain-specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement and to maintain. This paper substantiates the authors’ firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility.

Key Words: modal logic • coalgebra • knowledge representation • concurrency • compositionality • automata theory

Handling editor: Vladimiro Sassone

1 A preliminary version of this paper was presented at the BCS08 Visions of Computer Science Conference, held on September 22–24, 2008.


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