Which Semantics for Neighbourhood Semantics?

Carlos Areces, Diego Figueira

Abstract: In this article we discuss two alternative proposals for neighbourhood semantics (which we call strict and loose neighbourhood semantics, N= and N⊆ 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).