Modular construction of complete coalgebraic logics

  • Authors:
  • Corina Crstea;Dirk Pattinson

  • Affiliations:
  • School of Electronics and Computer Science, University of Southampton, UK;Department of Computing, Imperial College London, UK

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2007

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Abstract

We present a modular approach to defining logics for a wide variety of state-based systems. The systems are modelled as coalgebras, and we use modal logics to specify their observable properties. We show that the syntax, semantics and proof systems associated with such logics can all be derived in a modular fashion. Moreover, we show that the logics thus obtained inherit soundness, completeness and expressiveness properties from their building blocks. We apply these techniques to derive sound, complete and expressive logics for a wide variety of probabilistic systems, for which no complete axiomatisation has been obtained so far.