Neighborhood Contingency Logic: A New Perspective

In this paper, we propose a new neighborhood semantics for contingency logic, by introducing a simple property in standard neighborhood models. This simplifies the neighborhood semantics given in Fan and van Ditmarsch [4], but does not change the set of valid formulas. Under this perspective, among various notions of bisimulation and respective Hennessy-Milner Theorems, we show that c-bisimulation is equivalent to nbh-∆-bisimulation in the literature, which guides us to understand the essence of the latter notion. This perspective also provides various frame definability and axiomatization results.