Skip to main content
SpringerLink
Log in

Querying Temporal Constraint Networks: A Unifying Approach

  • Published:
Applied Intelligence Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

We develop the scheme of indefinite constraint databases using first-order logic as our representation language. When this scheme is instantiated with temporal constraints, the resulting formalism is more expressive than standard temporal constraint networks. The extra representational power allows us to express temporal knowledge and queries that have been impossible to express before. To make our claim more persuasive, we survey previous works on querying temporal constraint networks and show that they can be viewed as an instance of the scheme of indefinite constraint databases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Allen, “Maintaining knowledge about temporal intervals,” Communications of the ACM, vol. 26, no. 11, pp. 832–843, 1983.

    Google Scholar 

  2. M. Vilain and H. Kautz, “Constraint propagation algorithms for temporal reasoning,” in Proceedings of AAAI-86, 1986, pp. 377–382.

  3. M. Vilain, H. Kautz, and P. van Beek, “Constraint propagation algorithms for temporal reasoning: A revised report,” in Readings in Qualitative Reasoning about Physical Systems, edited by D. Weld and J. de Kleer, Morgan Kaufmann: San Mateo, CA, pp. 373–381, 1989.

    Google Scholar 

  4. P. van Beek and R. Cohen, “Exact and approximate reasoning about temporal relations,” Computational Intelligence, vol. 6, pp. 132–144, 1990.

    Google Scholar 

  5. R. Dechter, I. Meiri, and J. Pearl, “Temporal constraint networks,” Artificial Intelligence, vol. 49, nos. 1-3, pp. 61–95, 1991, Special volume on knowledge representation.

    Google Scholar 

  6. I. Meiri, “Combining qualitative and quantitative constraints in temporal reasoning,” in Proceedings of AAAI-91, 1991, pp. 260–267.

  7. P. van Beek, “Reasoning about qualitative temporal information,” Artificial Intelligence, vol. 58, pp. 297–326, 1992.

    Google Scholar 

  8. P. Ladkin and R. Maddux, “On binary constraint problems,” Journal of the ACM, vol. 41, no. 3, pp. 435–469, 1994.

    Google Scholar 

  9. B. Nebel and H.-J. Bürckert, “Reasoning about temporal relations: A maximal tractable subclass of Allen's interval algebra,” Journal of the ACM, vol. 42, no. 1, pp. 43–66, 1995.

    Google Scholar 

  10. V. Brusoni, L. Console, B. Pernici, and P. Terenziani, “Extending temporal relational databases to deal with imprecise and qualitative temporal information,” in Recent Advances in Temporal Databases (Proceedings of the International Workshop on Temporal Databases, Zürich, Switzerland, September 1995), edited by J. Clifford and A. Tuzhilin. Workshops in Computing. Springer, 1995.

  11. A. Gerevini and L. Schubert, “Efficient algorithms for qualitative reasoning about time,” Artificial Intelligence, vol. 74, pp. 207–248, 1995.

    Google Scholar 

  12. M. Koubarakis, “From local to global consistency in temporal constraint networks,” in Proceedings of the 1st International Conference on Principles and Practice of Constraint Programming (CP'95), Cassis, France, vol. 976 of LNCS, pp. 53–69, 1995.

  13. M. Koubarakis, “From local to global consistency in temporal constraint networks,” Theoretical Computer Science, vol. 173, pp. 89–112, 1997. Invited submission to the special issue dedicated to the 1st International Conference on Principles and Practice of Constraint Programming (CP95), edited by U. Montanari and F. Rossi.

    Google Scholar 

  14. M. Koubarakis, “Tractable disjunctions of linear constraints,” in Proceedings of the 2nd International Conference on Principles and Practice of Constraint Programming (CP'96), Boston, MA, 1996, pp. 297–307.

  15. P. Jonsson and C. Bäckström, “A linear programming approach to temporal reasoning,” in Proceedings of AAAI-96, 1996, AAAI Press/MIT Press, pp. 1235–1240.

  16. P. Jonsson and C. Bäckström, “A unifying approach to temporal constraint reasoning,” Artificial Intelligence, vol. 102, pp. 143–155, 1998.

    Google Scholar 

  17. S. Staab, “On non-binary temporal relations,” in Proceedings of ECAI-98, 1998, pp. 567–571.

  18. A. Gerevini, L. Schubert, and S. Schaeffer, “Temporal reasoning in timegraph I-II,” SIGART Bulletin, vol. 4, no. 3, pp. 21–25, 1993.

    Google Scholar 

  19. E. Yampratoom and J. Allen, “Performance of temporal reasoning systems,” SIGART Bulletin, vol. 4, no. 3, pp. 26–29, 1993.

    Google Scholar 

  20. J. Stillman, R. Arthur, and A. Deitsch, “Tachyon: A constraintbased temporal reasoning model and its implementation,” SIGART Bulletin, vol. 4, no. 3, 1993.

  21. V. Brusoni, L. Console, B. Pernici, and P. Terenziani, “LaTeR: An efficient, general purpose manager of temporal information,” IEEE Expert, vol. 12, no. 4, pp. 56–64, 1997.

    Google Scholar 

  22. V. Brusoni, L. Console, B. Pernici, and P. Terenziani, “LaTeR: A general purpose manager of temporal information,” in Proceedings of the 8th International Symposium on Methodologies for Intelligent Systems, vol. 869 of Lecture Notes in Computer Science, Springer-Verlag: Berlin, 1994.

    Google Scholar 

  23. P. van Beek, “Temporal query processing with indefinite information,” Artificial Intelligence in Medicine, vol. 3, pp. 325–339, 1991.

    Google Scholar 

  24. J. Mylopoulos, A. Borgida, M. Jarke, and M. Koubarakis, “Telos: A language for representing knowledge about information systems,” ACM Transactions on Information Systems, vol. 8, no. 4, pp. 325–362, 1990.

    Google Scholar 

  25. T. Dean and D. McDermott, “Temporal data base management,” Artificial Intelligence, vol. 32, pp. 1–55, 1987.

    Google Scholar 

  26. T. Dean, “Using temporal hierarchies to efficiently maintain large temporal databases,” Journal of ACM, vol. 36, no. 4, pp. 687–718, 1989.

    Google Scholar 

  27. R. Schrag, M. Boddy, and J. Carciofini, “Managing disjunction for practical temporal reasoning,” in Proceedings of KR'92, 1992, pp. 36–46.

  28. M. Boddy, “Temporal reasoning for planning and scheduling,” SIGART Bulletin, vol. 4, no. 3, pp. 17–20, 1993.

    Google Scholar 

  29. M. Koubarakis, “Representation and querying in temporal databases: The power of temporal constraints,” in Proceedings of the 9th International Conference on Data Engineering, 1993, pp. 327–334.

  30. M.Koubarakis, “Database models for infinite and indefinite temporal information,” Information Systems, vol. 19, no. 2, pp. 141–173, 1994.

    Google Scholar 

  31. V. Brusoni, L. Console, and P. Terenziani, “On the computational complexity of querying bounds on differences constraints,” Artificial Intelligence, vol. 74, no. 2, pp. 367–379, 1995.

    Google Scholar 

  32. V. Brusoni, L. Console, P. Terenziani, and B. Pernici, “Qualitative and quantitative temporal constraints and relational databases: Theory, architecture, and applications,” IEEE Transactions on Knowledge and Data Engineering, vol. 1, no. 6, pp. 948–968, 1999.

    Google Scholar 

  33. P. Ladkin, “Satisfying first-order constraints about time intervals,” in Proceedings of AAAI-88, 1988, pp. 512–517.

  34. M. Koubarakis, “Complexity results for first-order theories of temporal constraints,” in Principles of Knowledge Representation and Reasoning: Proceedings of the Fourth International Conference (KR'94), 1994, Morgan Kaufmann: San Francisco, CA, pp. 379–390.

    Google Scholar 

  35. M. Koubarakis, “The complexity of query evaluation in indefinite temporal constraint databases,” Theoretical Computer Science, vol. 171, pp. 25–60, 1997. Special issue on Uncertainty in Databases and Deductive Systems, edited by L.V.S. Lakshmanan.

    Google Scholar 

  36. H. Enderton, A Mathematical Introduction to Logic, Academic Press: New York, 1972.

    Google Scholar 

  37. A. Schrijver (ed.), Theory of Integer and Linear Programming, Wiley: New York, 1986.

    Google Scholar 

  38. M. Koubarakis, “Tractable disjunctions of linear constraints: Basic results and applications to temporal reasoning,” Theoretical Computer Science, vol. 266, pp. 311–339, 2001.

    Google Scholar 

  39. L. Console and P. Terenziani, “Efficient processing of queries and assertions about qualitative and quantitative temporal constraints,” Computational Intelligence, vol. 15, no. 4, pp. 442–465, 1999.

    Google Scholar 

  40. R. Dechter, I. Meiri, and J. Pearl, “Temporal constraint networks,” in Proceedings of 1st International Conference on Principles of Knowledge Representation and Reasoning, Toronto, Ontario, edited by R. Brachman, H. Levesque, and R. Reiter, pp. 83–93, 1989.

  41. A. Gerevini and M. Cristani, “Reasoning with inequations in temporal constraint networks,” Technical report, IRST- Instituto per la Ricerca Scientifica e Tecnologica, Povo TN, Italy, 1995. A shorter version appeared in the Proceedings of the Workshop on Spatial and Temporal Reasoning, IJCAI-95.

  42. H. Kautz and P. Ladkin, “Integrating metric and qualitative temporal reasoning,” in Proceedings of AAAI-91, 1991, pp. 241–246.

  43. A. Gerevini and L. Schubert, “On point-based temporal disjointness,” Artificial Intelligence, vol. 70, pp. 347–361, 1994.

    Google Scholar 

  44. M. Fischer and M. Rabin, “Super-exponential complexity of presburger arithmetic,” in Proc. of AMS Symposium on Complexity of Real Computational Processes, 1974, vol. III.

  45. J. Ferrante and C. Rackoff, “A decision procedure for the first order theory of real addition with order,” SIAM Journal on Computing, vol. 4, no. 1, pp. 69–76, 1975.

    Google Scholar 

  46. J. Ferrante and J. Geiser, “An efficient decision procedure for the theory of rational order,” Theoretical Computer Science, vol. 4, no. 2, pp. 227–233, 1977.

    Google Scholar 

  47. L. Stockmeyer, “The polynomial-time hierarchy,” Theoretical Computer Science, vol. 3, pp. 1–22, 1977.

    Google Scholar 

  48. C. Reddy and D. Loveland, “Presburger arithmetic with bounded quantifier alternation,” in Proc. of ACM Symposium on the Theory of Computing, 1978, pp. 320–325.

  49. J. Ferrante and C. Rackoff, The Computational Complexity of Logical Theories, Lecture Notes in Mathematics, Springer Verlag: Berlin, 1979.

    Google Scholar 

  50. L. Berman, “The complexity of logical theories,” Theoretical Computer Science, vol. 11, pp. 71–78, 1980.

    Google Scholar 

  51. A. Bruss and A. Meyer, “On time-space classes and their relation to the theory of real addition,” Theoretical Computer Science, vol. 11, pp. 59–69, 1980.

    Google Scholar 

  52. M. Furer, “The complexity of presburger arithmetic with bounded quantifier alternation depth,” Theoretical Computer Science, vol. 18, pp. 105–111, 1982.

    Google Scholar 

  53. E. Sontag, “Real addition and the polynomial time hierarchy,” Information Processing Letters, vol. 20, pp. 115–120, 1985.

    Google Scholar 

  54. P. Kanellakis, G. Kuper, and P. Revesz, “Constraint query languages,” in Proceedings of the 9th ACM SIGACT-SIGMODSIGART Symposium on Principles of Database Systems, 1990, pp. 299–313.

  55. R. Reiter, “Towards a logical reconstruction of relational database theory,” in On Conceptual Modelling: Perspectives from Artificial Intelligence, Databases and Programming Languages, edited by M. Brodie, J. Mylopoulos, and J. Schmidt, Springer Verlag: Berlin, pp. 191–233, 1984.

    Google Scholar 

  56. T. Imielinski and W. Lipski, “Incomplete information in relational databases,” Journal of ACM, vol. 31, no. 4, pp. 761–791, 1984.

    Google Scholar 

  57. G. Grahne, The Problem of Incomplete Information in Relational Databases, vol. 554 of Lecture Notes in Computer Science, Springer Verlag: Berlin, 1991.

    Google Scholar 

  58. H. Levesque, “Foundations of a functional approach to knowledge representation,” Artificial Intelligence, vol. 23, pp. 155–212, 1984.

    Google Scholar 

  59. W.J. Lipski, “On semantic issues connected with incomplete information databases,” ACM Transactions on Database Systems, vol. 4, no. 3, pp. 262–296, 1979.

    Google Scholar 

  60. R. Reiter, “On integrity constraints,” in Proceedings of the 2nd Conference on Theoretical Aspects of Reasoning About Knowledge. Asilomar, CA, 1988, pp. 97–111.

  61. P. Kanellakis, G. Kuper, and P. Revesz, “Constraint query languages,” Journal of Computer and System Sciences, vol. 51, pp. 26–52, 1995.

    Google Scholar 

  62. M. Koubarakis and S. Skiadopoulos, “Querying temporal constraint networks in PTIME,” in Proceedings of AAAI-99, 1999. pp. 745–750.

  63. M. Koubarakis and S. Skiadopoulos, “Tractable query answering in indefinite constraint databases: Basic results and applications to querying spatio-temporal information,” in Spatio-Temporal Database Management (Proceedings of the International Workshop STDBM'99), vol. 1678 of LNCS, Springer: Berlin, pp. 204–223, 1999.

    Google Scholar 

  64. M. Koubarakis and S. Skiadopoulos, “Querying indefinite temporal and spatial information: A new frontier,” in Proceedings of the IJCAI-99 Workshop on Hot Topics in Temporal and Spatial Reasoning, 1999.

  65. M. Koubarakis and S. Skiadopoulos, “Querying temporal and spatial constraint networks in PTIME,” Artificial Intelligence, vol. 123, nos. 1/2, pp. 223–263, 2000.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronic and Computer Engineering, Technical University of Crete, University Campus, Kounoupidiana, 73 100, Chania, Crete, Greece

    Manolis Koubarakis

Authors
  1. Manolis Koubarakis
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koubarakis, M. Querying Temporal Constraint Networks: A Unifying Approach. Applied Intelligence 17, 297–311 (2002). https://doi.org/10.1023/A:1020043517392

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020043517392

Search

Navigation