Convex Relations Between Time Intervals

  • Klaus Nökel
Conference paper
Part of the Informatik-Fachberichte book series (INFORMATIK, volume 208)


We describe a fragment of Allen’s full algebra of time interval relations (the algebra of convex relations) that is useful for describing the dynamic behavior of technical systems. After an intuitive description of the fragment we give two formal definitions and prove that they are equivalent. This provides the basis for the major result of the paper: in a time net in which all interval relations are convex the test for the global consistency of the edge labelling can be carried out in polynomial time (in the general case it is NP-complete). This result makes convex interval relations an attractive candidate whereever qualitative reasoning about technical systems requires testing for global instead of local consistency.


Technical System Relation Algebra Left Endpoint Local Consistency Global Consistency 
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  1. [Allen83]
    J.F. Allen: Maintaining Knowledge about Temporal Intervals, CACM 26(11), Nov.83Google Scholar
  2. [Allen/Hayes85]
    J.F. Allen, P.F. Hayes: A Common Sense Theory of Time, Proc.9th IJCAI, 1985Google Scholar
  3. [deKleer/Brown84]
    J. deKleer, J.S. Brown: A Qualitative Physics Based on Confluences, in: D.G. Bobrow (ed.): Qualitative Reasoning about Physical Systems, Amsterdam 1984Google Scholar
  4. [Forbus84]
    K.D.Forbes: Qualitative Process Theory, in:D.G.Bobrow (ed.): Qualitative Reasoning about Physical Systems, Amsterdam 1984Google Scholar
  5. [Vilain/Kautz86]
    M. Vilain, H. Kautz: Constraint Propagation Algorithms for Temporal Reasoning, Proc. AAAI-86.Google Scholar
  6. [Voß87]
    H. Voß: Representing and Analyzing Causal, Temporal, and Hierarchical Relations of Devices, Universität Kaiserslautern, SEKI-Report SR-87-17.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Klaus Nökel
    • 1
  1. 1.FB InformatikUniversität KaiserslauternKaiserslauternGermany

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