Bisimulation for Neighbourhood Structures

  • Helle Hvid Hansen
  • Clemens Kupke
  • Eric Pacuit
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4624)


Neighbourhood structures are the standard semantic tool used to reason about non-normal modal logics. In coalgebraic terms, a neighbourhood frame is a coalgebra for the contravariant powerset functor composed with itself, denoted by 22. In our paper, we investigate the coalgebraic equivalence notions of 22-bisimulation, behavioural equivalence and neighbourhood bisimulation (a notion based on pushouts), with the aim of finding the logically correct notion of equivalence on neighbourhood structures. Our results include relational characterisations for 22-bisimulation and neighbourhood bisimulation, and an analogue of Van Benthem’s characterisation theorem for all three equivalence notions. We also show that behavioural equivalence gives rise to a Hennessy-Milner theorem, and that this is not the case for the other two equivalence notions.


Neighbourhood semantics non-normal modal logic bisimulation behavioural equivalence invariance 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Helle Hvid Hansen
    • 1
    • 2
  • Clemens Kupke
    • 1
  • Eric Pacuit
    • 3
  1. 1.Centrum voor Wiskunde en Informatica (CWI) 
  2. 2.Vrije Universiteit Amsterdam (VUA) 
  3. 3.Universiteit van Amsterdam (UvA) 

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