Simulations and Bisimulations for Coalgebraic Modal Logics

  • Daniel Gorín
  • Lutz Schröder
Conference paper

DOI: 10.1007/978-3-642-40206-7_19

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8089)
Cite this paper as:
Gorín D., Schröder L. (2013) Simulations and Bisimulations for Coalgebraic Modal Logics. In: Heckel R., Milius S. (eds) Algebra and Coalgebra in Computer Science. CALCO 2013. Lecture Notes in Computer Science, vol 8089. Springer, Berlin, Heidelberg

Abstract

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.

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Copyright information

© 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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