Hennessy-Milner Logic with Greatest Fixed Points as a Complete Behavioural Specification Theory

  • Nikola Beneš
  • Benoît Delahaye
  • Uli Fahrenberg
  • Jan Křetínský
  • Axel Legay
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8052)


There are two fundamentally different approaches to specifying and verifying properties of systems. The logical approach makes use of specifications given as formulae of temporal or modal logics and relies on efficient model checking algorithms; the behavioural approach exploits various equivalence or refinement checking methods, provided the specifications are given in the same formalism as implementations.

In this paper we provide translations between the logical formalism of Hennessy-Milner logic with greatest fixed points and the behavioural formalism of disjunctive modal transition systems. We also introduce a new operation of quotient for the above equivalent formalisms, which is adjoint to structural composition and allows synthesis of missing specifications from partial implementations. This is a substantial generalisation of the quotient for deterministic modal transition systems defined in earlier papers.


Model Check Modal Logic Residuated Lattice Linear Logic Structural Composition 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Nikola Beneš
    • 1
  • Benoît Delahaye
    • 2
  • Uli Fahrenberg
    • 2
  • Jan Křetínský
    • 1
    • 3
  • Axel Legay
    • 2
  1. 1.Masaryk UniversityBrnoCzech Republic
  2. 2.Irisa / INRIARennesFrance
  3. 3.Technische Universität MünchenGermany

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