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Decidable and undecidable fragments of Halpern and Shoham’s interval temporal logic: towards a complete classification (2008)
| Venue: | In Proc. of the 15th Int. Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR), volume 5330 of LNCS |
| Citations: | 17 - 15 self |
BibTeX
@INPROCEEDINGS{Bresolin08decidableand,
author = {Davide Bresolin and Dario Della Monica and Valentin Goranko and Angelo Montanari and Guido Sciavicco},
title = {Decidable and undecidable fragments of Halpern and Shoham’s interval temporal logic: towards a complete classification},
booktitle = {In Proc. of the 15th Int. Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR), volume 5330 of LNCS},
year = {2008},
pages = {590--604},
publisher = {Springer}
}
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Abstract
Abstract. Interval temporal logics are based on temporal structures where time intervals, rather than time instants, are the primitive onto-logical entities. They employ modal operators corresponding to various relations between intervals, known as Allen’s relations. Technically, va-lidity in interval temporal logics translates to dyadic second-order logic, thus explaining their complex computational behavior. The full modal logic of Allen’s relations, called HS, has been proved to be undecidable by Halpern and Shoham under very weak assumptions on the class of interval structures, and this result was discouraging attempts for prac-tical applications and further research in the field. A renewed interest has been recently stimulated by the discovery of interesting decidable fragments of HS. This paper contributes to the characterization of the boundary between decidability and undecidability of HS fragments. It summarizes known positive and negative results, it describes the main techniques applied so far in both directions, and it establishes a number of new undecidability results for relatively small fragments of HS. 1
Keyphrases
interval temporal logic undecidable fragment complete classification allen relation interval structure interval temporal logic translates time interval new undecidability result time instant small fragment various relation complex computational behavior modal operator full modal logic negative result second-order logic h fragment temporal structure decidable fragment prac-tical application primitive onto-logical entity main technique weak assumption
