Reliable Computing

, Volume 3, Issue 3, pp 209–217 | Cite as

Diagrammatic Representation of Interval Space in Proving Theorems about Interval Relations

  • Zenon Kulpa
Article

Abstract

The paper presents two-dimensional graphical representations for the space of intervals (the IS-diagram) and arrangement interval relations (the W-diagram). The usefulness of the representations is illustrated with the example of proving equivalence of different characterizations of convex interval relations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Allen, J. F.: Maintaining Knowledge about Temporal Relations, Comm. ACM 26 (11) (1983), pp. 832–843.Google Scholar
  2. 2.
    Allwein, G. and Barwise, J. (eds): Logical Reasoning with Diagrams, Oxford Univ. Press, Oxford, 1996.Google Scholar
  3. 3.
    van Beek, P. and Cohen, R.: Exact and Approximate Reasoning about Temporal Relations, Comput. Intell. 6 (1990), pp. 132–144.Google Scholar
  4. 4.
    Freksa, C.: Temporal Reasoning Based on Semi-Intervals, Artificial Intelligence 54 (1–2) (1992), pp. 199–227.Google Scholar
  5. 5.
    Gardeñes, E., Trepat, A., and Janer, J. M.: SIGLA-PL/1: Development and Applications, in: Nickel, K. L. E. (ed.), Interval Mathematics 1980, Academic Press, New York, 1980, pp. 301–315.Google Scholar
  6. 6.
    Hammer, E.: Logic and Visual Information, Cambridge Univ. Press, Cambridge, 1996.Google Scholar
  7. 7.
    Kulpa, Z.: Diagrammatic Representation and Reasoning, Machine GRAPHICS & VISION 3 (1/2) (1994), pp. 77–103. (PostScript file: see http://www.ippt.gov.pl/ ~zkulpa/zkpubl.html#diagrammatic.)Google Scholar
  8. 8.
    Kulpa, Z.: Two-dimensional Representation of Interval Relations: Preliminaries, Internal Report, IFTR, Warsaw, 1995.Google Scholar
  9. 9.
    Kulpa, Z.: Diagrammatic Representation for a Space of Intervals, Machine GRAPHICS & VISION 6 (1) (1997), to appear.Google Scholar
  10. 10.
    Nökel, K.: Temporally Distributed Symptoms in Technical Diagnosis, Lect. Notes in AI 517, Springer-Verlag, Berlin, 1991.Google Scholar
  11. 11.
    Rit, J.-F.: Propagating Temporal Constraints for Scheduling, in: Proc. AAAI-86, Morgan Kaufmann, Los Altos, CA, 1986, pp. 383–388.Google Scholar
  12. 12.
    Simon, H. A.: The Sciences of the Artificial, 2nd ed., MIT Press, Cambridge, MA, 1981.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Zenon Kulpa
    • 1
  1. 1.Institute of Fundamental Technological ResearchPolish Academy of SciencesWarsawPoland

Personalised recommendations