Simulations and Bisimulations for Coalgebraic Modal Logics

  • Daniel Gorín
  • Lutz Schröder
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8089)


Simulations serve as a proof tool to compare the behaviour of reactive systems. We define a notion of Λ-simulation for coalgebraic modal logics, parametric in the choice of a set Λ of monotone predicate liftings for a functor T. That is, we obtain a generic notion of simulation that can be flexibly instantiated to a large variety of systems and logics, in particular in settings that semantically go beyond the classical relational setup, such as probabilistic, game-based, or neighbourhood-based systems. We show that this notion is adequate in several ways: i) Λ-simulations preserve truth of positive formulas, ii) for Λ a separating set of monotone predicate liftings, the associated notion of Λ-bisimulation corresponds to T-behavioural equivalence (moreover, this correspondence extends to the respective finite-lookahead counterparts), and iii) Λ-bisimulations remain sound when taken up to difunctional closure. In essence, we arrive at a modular notion of equivalence that, when used with a separating set of monotone predicate liftings, coincides with T-behavioural equivalence regardless of whether T preserves weak pullbacks. That is, for finitary set-based coalgebras, Λ-bisimulation works under strictly more general assumptions than T-bisimulation in the sense of Aczel and Mendler.


Modal Logic Kripke Frame Positive Formula Coalgebra Structure Monotone Boolean Function 
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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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Daniel Gorín
    • 1
  • Lutz Schröder
    • 1
  1. 1.Department of Computer ScienceUniversität Erlangen-NürnbergGermany

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