Advertisement

Applied Intelligence

, Volume 6, Issue 1, pp 29–38 | Cite as

Lattice structure of temporal interval relations

  • Frank D. Anger
  • Rita V. Rodríguez
Article

Abstract

Due to increasing interest in representation of temporal knowledge, automation of temporal reasoning, and analysis of distributed systems, literally dozens of temporal models have been proposed and explored during the last decade. Interval-based temporal models are especially appealing when reasoning about events with temporal extent but pose special problems when deducing possible relationships among events. The paper delves deeply into the structure of the set of atomic relations in a class of temporal interval models assumed to satisfy density and homogeneity properties. An order structure is imposed on the atomic relations of a given model allowing the characterization of the compositions of atomic relations (or even lattice intervals) as lattice intervals. By allowing the utilization of lattice intervals rather than individual relations, this apparently abstract result explicitly leads to a concrete approach which speeds up constraint propagation algorithms.

Keywords

branching time constraint propagation lattices relativistic time temporal intervals temporal reasoning time 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Allen, “Maintaining knowledge about temporal intervals,” Comm. of ACM, vol. 26, no. 11, pp. 832–843, 1983.Google Scholar
  2. 2.
    J. Allen, “Towards a general theory of action and time,” Artificial Intelligence, vol. 23, pp. 123–154, 1984.Google Scholar
  3. 3.
    F. Anger, P. Ladkin, and R. Rodriguez, “Atomic temporal interval relations in branching time: Calculation and application,” Applications of Artificial Intelligence IX, SPIE, Orlando, April 1991, pp. 122–136.Google Scholar
  4. 4.
    F. Anger and R. Rodriguez, “F-complexes: A set theoretic approach to temporal modeling,” IEA/AIE-91: Proceedings of the Fourth International Conference on Industrial and Engineering Applications of Artificial Intelligence and Expert Systems, Hawaii, June 1991, pp. 609–617.Google Scholar
  5. 5.
    F. Anger and R. Rodriguez, “Time, tense, and relativity revisited,” in Lecture Notes in Computer Science, edited by B. Bouchon-Meunier, R. Yager, and L. Zadeh, Springer-Verlag: NY, pp. 286–295, 1991.Google Scholar
  6. 6.
    F. Anger, “On lamport's interprocessor communication model,” ACM Trans. on Prog. Lang. and Systems, vol. 11, no. 3, pp. 404–417, July 1989.Google Scholar
  7. 7.
    F. Anger and E. Clarke, “New and used temporal models: An issue of time,” Applied Intelligence Journal, vol. 3, no. 1, pp. 5–15, March 1993.Google Scholar
  8. 8.
    F. Anger, J. Allen, and R. Rodriguez, “Determining the greatest lower bound of schedules for tasks constrained by temporal interval relations,” Computer Science Department, University of West Florida, Pensacola FL, Technical Report CS-TR-93–001, January 1993.Google Scholar
  9. 9.
    P. van Beek, “Exact and approximate reasoning about qualitative temporal relations,” Ph.D. Thesis, University of Alberta, 1990.Google Scholar
  10. 10.
    J.van Benthem, “Time, logic and computation,” in Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, edited by J.de Bakker, W.-P.de Roever, and G. Rozenberg, Springer-Verlag: NY, pp. 1–49, 1989.Google Scholar
  11. 11.
    J.van Benthem, “Modal logic as a theory of information,” in Logic and Reality: Essays in Pure and Applied Logic, In Memory of Arthur Prior, edited by J. Copeland, Oxford University Press: Oxford, 1995.Google Scholar
  12. 12.
    C. Freksa, “Temporal reasoning based on semi-intervals,” Artificial Intelligence, vol. 54, pp. 199–227, 1992.Google Scholar
  13. 13.
    H. Guesgen, “Spatial reasoning based on Allen's temporal logic,” International Computer Science Institute, Berkeley, CA, Technical Report ICSI TR-89–049, 1989.Google Scholar
  14. 14.
    R. Hartley, “A uniform representation for time and space and their mutual constraints,” Computers Math. Applic., vol. 23, no. 6–9, pp. 441–457, 1992.Google Scholar
  15. 15.
    S. Keretho and R. Loganantharaj, “Reasoning about networks of temporal relations and its application to problem solving,” Applied Intelligence Journal, vol. 3, no. 1, pp. 45–57, 1993.Google Scholar
  16. 16.
    P. Ladkin and A. Reinefeld, “Effective solution of qualitative interval constraint problems,” Artificial Intelligence, vol. 57, pp. 105–124, 1992.Google Scholar
  17. 17.
    P. Ladkin and R. Maddux, “Representation and reasoning with convex time intervals,” Kestrel Institute, Palo Alto CA, Technical Report KES.U.88.2, 1988.Google Scholar
  18. 18.
    L. Lamport, “The mutual exclusion problem: Part I-a theory of interprocess communication”; “Part II—Statement and solutions,” Journal ACM, vol. 33, no. 2, pp. 313–348, April 1986.Google Scholar
  19. 19.
    G. Ligozat, “On generalized interval calculi,” Proceedings of the Ninth National Conference on Artificial Intelligence, Anaheim, CA, July 1991, pp. 234–240.Google Scholar
  20. 20.
    Z. Manna and A. Pnueli, “The anchored version of the temporal framework,” in Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, edited by J.de Bakker, W.-P.de Roever, and G. Rozenberg, Springer-Verlag: NY, pp. 201–284, 1989.Google Scholar
  21. 21.
    A. Mukerjee and G. Joe, “A qualitative model for space,” Proceedings AAAI-90, Boston MA, 1990, pp. 721–727.Google Scholar
  22. 22.
    D. Randell and A. Cohn, “Modeling topological and metrical properties of physical processes,” Proceedings of KR'89, Principles of Knowledge Representation and Reasoning, San Mateo CA, 1989, pp. 357–368.Google Scholar
  23. 23.
    D. Randell and A. Cohn, “Exploiting lattices in a theory of space and time,” Computers Math. Applic., vol. 23, no. 6–9, pp. 459–476, 1992.Google Scholar
  24. 24.
    R. Rodriguez, F. Anger, and K. Ford, “Temporal reasoning: A relativistic model,” International Journal of Intelligent Systems, vol. 6, pp. 237–254, June 1991.Google Scholar
  25. 25.
    R. Rodriguez, “A relativistic temporal algebra for Efficient Design of Distributed Systems,” Applied Intelligence Journal, vol. 3, no. 1, pp. 31–45, 1993.Google Scholar
  26. 26.
    R. Rodriguez and F. Anger, “Prior's temporal legacy in computer science,” in Logic and Reality: Essays in Pure and Applied Logic, In Memory of Arthur Prior, edited by J. Copeland, Oxford University Press: Oxford, 1993.Google Scholar
  27. 27.
    R. Rodriguez and F. Anger, “An analysis of the temporal relations of intervals in relativistic space-time,” in Lecture Notes in Computer Science: Advanced Methods in Artificial Intelligence, edited by B. Bouchon-Meunier, L. Valverde, and R. Yager, Springer-Verlag: Berlin, pp. 139–148, 1993.Google Scholar
  28. 28.
    M. Vilain and H. Kautz, “Constraint propagation algorithms for temporal reasoning,” Proceedings of the Fifth National Conference of AAAI, Pittsburgh, PA, August 1986, pp. 377–382.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Frank D. Anger
    • 1
  • Rita V. Rodríguez
    • 1
  1. 1.Computer Science DepartmentThe University of West FloridaPensacola(USA)

Personalised recommendations