Bisimulation for Neighbourhood Structures
- Cite this paper as:
- Hansen H.H., Kupke C., Pacuit E. (2007) Bisimulation for Neighbourhood Structures. In: Mossakowski T., Montanari U., Haveraaen M. (eds) Algebra and Coalgebra in Computer Science. CALCO 2007. Lecture Notes in Computer Science, vol 4624. Springer, Berlin, Heidelberg
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.
KeywordsNeighbourhood semantics non-normal modal logic bisimulation behavioural equivalence invariance
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