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 problem for $\ABB$ over natural numbers is decidable by providing a small model theorem based on an original contraction method. Finally, we prove the EXPSPACE-completeness of the problem.
Decidability of the Interval Temporal Logic ABB over the Natural Numbers
SALA, Pietro
2010-01-01
Abstract
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 problem for $\ABB$ over natural numbers is decidable by providing a small model theorem based on an original contraction method. Finally, we prove the EXPSPACE-completeness of the problem.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.