We lay the foundations of a first-order correspondence theory for coalgebraic logics that makes the transition structure explicit in the first-order modelling. In particular, we prove a coalgebraic version of the van Benthem/Rosen theorem stating that both over arbitrary structures and over finite structures, coalgebraic modal logic is precisely the bisimulation invariant fragment of first-order logic.


Modal Logic Propositional Variable Kripke Model Correspondence Theory Modal Formula 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Lutz Schröder
    • 1
  • Dirk Pattinson
    • 2
  1. 1.DFKI Bremen and Department of Computer ScienceUniversität Bremen 
  2. 2.Department of ComputingImperial CollegeLondon

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