Presenting Functors by Operations and Equations

  • Marcello M. Bonsangue
  • Alexander Kurz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3921)


We take the point of view that, if transition systems are coalgebras for a functor T, then an adequate logic for these transition systems should arise from the ‘Stone dual’ L of T. We show that such a functor always gives rise to an ‘abstract’ adequate logic for T-coalgebras and investigate under which circumstances it gives rise to a ‘concrete’ such logic, that is, a logic with an inductively defined syntax and proof system. We obtain a result that allows us to prove adequateness of logics uniformly for a large number of different types of transition systems and give some examples of its usefulness.


Modal Logic Transition System Propositional Logic Free Algebra Modal Algebra 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marcello M. Bonsangue
    • 1
  • Alexander Kurz
    • 2
  1. 1.LIACSLeiden UniversityThe Netherlands
  2. 2.Department of Computer ScienceUniversity of LeicesterUK

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