Interval Temporal Logics over Strongly Discrete Linear Orders: the Complete Picture

Davide Bresolin
(University of Verona, Italy)
Dario Della Monica
(Reykjavik University, Iceland)
Angelo Montanari
(University of Udine, Italy)
Pietro Sala
(University of Verona, Italy)
Guido Sciavicco
(University of Murcia, Spain)

Interval temporal logics provide a general framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as the primitive ontological entities. In this paper, we identify all fragments of Halpern and Shoham's interval temporal logic HS with a decidable satisfiability problem over the class of strongly discrete linear orders. We classify them in terms of both their relative expressive power and their complexity. We show that there are exactly 44 expressively different decidable fragments, whose complexity ranges from NP to EXPSPACE. In addition, we identify some new undecidable fragments (all the remaining HS fragments were already known to be undecidable over strongly discrete linear orders). We conclude the paper by an analysis of the specific case of natural numbers, whose behavior slightly differs from that of the whole class of strongly discrete linear orders. The number of decidable fragments over natural numbers raises up to 47: three undecidable fragments become decidable with a non-primitive recursive complexity.

In Marco Faella and Aniello Murano: Proceedings Third International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2012), Napoli, Italy, September 6-8, 2012, Electronic Proceedings in Theoretical Computer Science 96, pp. 155–168.
Published: 7th October 2012.

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