Decidability of the Interval Temporal Logic ABB over the Natural Numbers

Angelo Montanari (1) , Gabriele Puppis (2) , Pietro Sala (1) , Guido Sciavicco (3)

1 DIMI - Dipartimento di Matematica e Informatica - Universita Udine
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 Department of Information, Engineering and Communications

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 rst 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 satis ability 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.

Domaines: Logique en informatique [cs.LO]

Angelo Montanari, Gabriele Puppis, Pietro Sala, Guido Sciavicco. Decidability of the Interval Temporal Logic ABB over the Natural Numbers. Proceedings of STACS 2010, 2010, Nancy, France. pp.597-608. ⟨hal-00717798⟩