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

Annals of Pure and Applied Logic 161 (3):289-304 (2010)
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Abstract

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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Valentin Goranko
Stockholm University

Citations of this work

A separation theorem for discrete-time interval temporal logic.Dimitar P. Guelev & Ben Moszkowski - 2022 - Journal of Applied Non-Classical Logics 32 (1):28-54.
Advances in Modal Logic 8.Lev Dmitrievich Beklemishev, Valentin Goranko & Valentin Shehtman (eds.) - 2010 - London, England: College Publications.
Simulation of Two Dimensions in Unimodal Logics.Ilya Shapirovsky - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 371-391.

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References found in this work

Events, instants and temporal reference.Hans Kamp - 1979 - In Rainer Bäuerle, Urs Egli & Arnim von Stechow (eds.), Semantics from different points of view. New York: Springer Verlag. pp. 376--418.
On languages with two variables.Michael Mortimer - 1975 - Mathematical Logic Quarterly 21 (1):135-140.
Expressiveness and completeness of an interval tense logic.Yde Venema - 1990 - Notre Dame Journal of Formal Logic 31 (4):529-547.

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