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Decidability of the Interval Temporal Logic ABB over the Natural Numbers

Authors Angelo Montanari, Gabriele Puppis, Pietro Sala, Guido Sciavicco

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Keywords
  • Interval temporal logics
  • compass structures
  • decidability
  • complexity

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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.

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Angelo Montanari, Gabriele Puppis, Pietro Sala, and Guido Sciavicco. Decidability of the Interval Temporal Logic ABB over the Natural Numbers. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 597-608, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010) https://doi.org/10.4230/LIPIcs.STACS.2010.2488

Author Details

Angelo Montanari
Gabriele Puppis
Pietro Sala
Guido Sciavicco
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