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Rank-1 Modal Logics Are Coalgebraic

  • Lutz Schröder
  • Dirk Pattinson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)

Abstract

Coalgebras provide a unifying semantic framework for a wide variety of modal logics. It has previously been shown that the class of coalgebras for an endofunctor can always be axiomatised in rank 1. Here we establish the converse, i.e. every rank 1 modal logic has a sound and strongly complete coalgebraic semantics. As a consequence, recent results on coalgebraic modal logic, in particular generic decision procedures and upper complexity bounds, become applicable to arbitrary rank 1 modal logics, without regard to their semantic status; we thus obtain purely syntactic versions of these results. As an extended example, we apply our framework to recently defined deontic logics.

Keywords

Modal Logic Natural Transformation Canonical Model Propositional Variable Deontic 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 Berlin Heidelberg 2007

Authors and Affiliations

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

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