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ISRN Artificial Intelligence
Volume 2012 (2012), Article ID 616087, 19 pages
http://dx.doi.org/10.5402/2012/616087
Review Article

Reasoning with Time Intervals: A Logical and Computational Perspective

Department of Information and Communication Engineering, University of Murcia, 30100 Murcia, Spain

Received 25 June 2012; Accepted 19 July 2012

Academic Editors: K. W. Chau and S. Likothanassis

Copyright © 2012 Guido Sciavicco. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The role of time in artificial intelligence is extremely important. Interval-based temporal reasoning can be seen as a generalization of the classical point-based one, and the first results in this field date back to Hamblin (1972) and Benhtem (1991) from the philosophical point of view, to Allen (1983) from the algebraic and first-order one, and to Halpern and Shoham (1991) from the modal logic one. Without purporting to provide a comprehensive survey of the field, we take the reader to a journey through the main developments in modal and first-order interval temporal reasoning over the past ten years and outline some landmark results on expressiveness and (un)decidability of the satisfiability problem for the family of modal interval logics.