On Decidability and Expressiveness of Propositional Interval Neighborhood Logics

Authors:
Davide Bresolin;Valentin Goranko;Angelo Montanari;Guido Sciavicco
Affiliations:
Department of Mathematics and Computer Science, University of Udine, Udine, Italy;School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa;Department of Mathematics and Computer Science, University of Udine, Udine, Italy;Department of Information Engineering and Communications, University of Murcia, Murcia, Spain
Venue:
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Year:
2007

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Abstract

Interval-based temporal logics are an important research area in computer science and artificial intelligence. In this paper we investigate decidability and expressiveness issues for Propositional Neighborhood Logics (PNLs). We begin by comparing the expressiveness of the different PNLs. Then, we focus on the most expressive one, namely, PNL驴+, and we show that it is decidable over various classes of linear orders by reducing its satisfiability problem to that of the two-variable fragment of first-order logic with binary relations over linearly ordered domains, due to Otto. Next, we prove that PNL驴+is expressively complete with respect to such a fragment. We conclude the paper by comparing PNL驴+expressiveness with that of other interval-based temporal logics.