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The light side of interval temporal logic: the Bernays-Schönfinkel fragment of CDT

The light side of interval temporal logic: the Bernays-Schönfinkel fragment of CDT Decidability and complexity of the satisfiability problem for the logics of time intervals have been extensively studied in the recent years. Even though most interval logics turn out to be undecidable, meaningful exceptions exist, such as the logics of temporal neighborhood and (some of) the logics of the subinterval relation. In this paper, we explore a different path to decidability: instead of restricting the set of modalities or imposing severe semantic restrictions, we take the most expressive interval temporal logic studied so far, namely, Venema’s CDT, and we suitably limit the negation depth of modalities. The decidability of the satisfiability problem for the resulting fragment, called CDTBS, over the class of all linear orders, is proved by embedding it into a well-known decidable quantifier prefix class of first-order logic, namely, Bernays-Schönfinkel class. In addition, we show that CDTBS is in fact NP-complete (Bernays-Schönfinkel class is NEXPTIME-complete), and we prove its expressive completeness with respect to a suitable fragment of Bernays-Schönfinkel class. Finally, we show that any increase in the negation depth of CDTBS modalities immediately yields undecidability. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

The light side of interval temporal logic: the Bernays-Schönfinkel fragment of CDT

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References (36)

Publisher
Springer Journals
Copyright
Copyright © 2013 by Springer Science+Business Media Dordrecht
Subject
Computer Science; Artificial Intelligence (incl. Robotics); Mathematics, general; Computer Science, general; Statistical Physics, Dynamical Systems and Complexity
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/s10472-013-9337-y
Publisher site
See Article on Publisher Site

Abstract

Decidability and complexity of the satisfiability problem for the logics of time intervals have been extensively studied in the recent years. Even though most interval logics turn out to be undecidable, meaningful exceptions exist, such as the logics of temporal neighborhood and (some of) the logics of the subinterval relation. In this paper, we explore a different path to decidability: instead of restricting the set of modalities or imposing severe semantic restrictions, we take the most expressive interval temporal logic studied so far, namely, Venema’s CDT, and we suitably limit the negation depth of modalities. The decidability of the satisfiability problem for the resulting fragment, called CDTBS, over the class of all linear orders, is proved by embedding it into a well-known decidable quantifier prefix class of first-order logic, namely, Bernays-Schönfinkel class. In addition, we show that CDTBS is in fact NP-complete (Bernays-Schönfinkel class is NEXPTIME-complete), and we prove its expressive completeness with respect to a suitable fragment of Bernays-Schönfinkel class. Finally, we show that any increase in the negation depth of CDTBS modalities immediately yields undecidability.

Journal

Annals of Mathematics and Artificial Intelligence – Springer Journals

Published: Mar 9, 2013

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