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

Annals of Pure and Applied Logic 161 (3):289-304 (2010)
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In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics , we establish their decidability on linearly ordered domains and some important subclasses, and we prove the 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
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