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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