Discrete-time temporal reasoning with horn DLRs

  • Authors:

  • Peter Jonsson;Tomas Lööw

  • Affiliations:

  • Department of Computer and Information Science, Linköping University;Department of Computer and Information Science, Linköping University

  • Venue:
  • IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
  • Year:
  • 2011

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Abstract

Temporal reasoning problems arise in many areas of AI, including planning, natural language understanding, and reasoning about physical systems. The computational complexity of continuous-time temporal constraint reasoning is fairly well understood. There are, however, many different cases where discrete time must be considered; various scheduling problems and reasoning about sampled physical systems are two examples. Here, the complexity of temporal reasoning is not as well-studied nor as well-understood. In order to get a better understanding, we consider the powerful Horn DLR formalism adapted for discrete time and study its computational complexity. We show that the full formalism is NP-hard and identify several maximal tractable subclasses. We also 'lift' the maximality results to obtain hardness results for other families of constraints. Finally, we discuss how the results and techniques presented in this paper can be used for studying even more expressive classes of temporal constraints.