Which Semantics for Neighbourhood Semantics?
Résumé
In this article we discuss two alternative proposals for neighbourhood semantics (which we call strict and loose neighbourhood semantics, Ny =intarondduNce respectively) that have been previously introduced in the literature. Our main tools are suitable notions of bisimulation. While an elegant notion of bisimulation exists for N, the required bisimulation for N= is rather involved. We propose a simple extension of N= with a universal modality that we call N=(E), which comes together with a natural notion of bisimulation. We also investigate the complexity of the satisfiability problem for N and N=(E).