PP-2007-30: Bisimulation for Neighbourhood Structuress

PP-2007-30: Hansen, Helle Hvid and Kupke, Clemens and Pacuit, Eric (2007) Bisimulation for Neighbourhood Structuress. [Report]

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Abstract

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 2^2. In our paper, we investigate the coalgebraic equivalence notions of 2^2-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 2^2-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.

Item Type: Report
Report Nr: PP-2007-30
Series Name: Prepublication (PP) Series
Year: 2007
Uncontrolled Keywords: Neighbourhood semantics, non-normal modal logic, bisimulation, behavioural equivalence, invariance.
Subjects: Logic
Depositing User: epaquit1
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/264

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