TY - BOOK
T1 - Bisimulation for neighbourhood structures
AU - Hansen, H.H.
AU - Kupke, C.A.
AU - Pacuit, E.
PY - 2007
Y1 - 2007
N2 - 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.
AB - 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.
M3 - Report
T3 - Prepublication Series
BT - Bisimulation for neighbourhood structures
PB - Institute for Logic, Language and Computation (ILLC), University of Amsterdam
CY - Amsterdam
ER -