Propositional interval neighborhood logics: Expressiveness, decidability, and undecidable extensions

In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics (PNL), we establish their decidability on linearly ordered domains and some important sub-classes, and we prove undecidability of a number of extensions of PNL with additional modalities over interval relations. All together, we show that PNL form a quite expressive and nearly maximal decidable fragment of Halpern-Shoham’s interval logic HS.