Decidability of the Interval Temporal Logic ABB over the Natural Numbers

Angelo Montanari, Gabriele Puppis, Pietro Sala & Guido Sciavicco
In this paper, we focus our attention on the interval temporal logic of the Allen's relations ``meets'', ``begins'', and ``begun by'' ($\ABB$ for short), interpreted over natural numbers. We first introduce the logic and we show that it is expressive enough to model distinctive interval properties, such as accomplishment conditions, to capture basic modalities of point-based temporal logic, such as the until operator, and to encode relevant metric constraints. Then, we prove that the satisfiability...