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Specifying over-constrained problems in default logic

  • Abdul Sattar
  • Aditya K. Ghose
  • Randy Goebel
Alternative Paradigms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1106)

Abstract

In the previous studies, it has been shown that the classical constraint satisfaction problem (CSP) is deductive in nature, and can be formulated as a classical theorem proving problem [1, 10]. Constraint satisfaction problems for which an assignment of values to all variables which satisfy all available constraints is not possible are referred to as over-constrained problems. This paper shows how computing partial solutions to over-constrained problems can be viewed as a default reasoning problem. We propose two methods for translating over-constrained problem specifications with finite domains to two different variants of default logic. We argue that default logic provides the appropriate level of abstraction for representing and analyzing over-constrained problem even if other methods are used for actually computing solutions.

Keywords

Constraint Satisfaction Constraint Satisfaction Problem Belief Revision Default Rule Default Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    W. Bibel. Constraint satisfaction from a deductive viewpoint. Artificial Intelligence, 35(3):401–413, July 1988.MathSciNetGoogle Scholar
  2. 2.
    J. P. Delgrande and W. K. Jackson. Default logic revisited. In Proc. of the Second International Conference on the Principles of Knowledge Representation and Reasoning, pages 118–127, 1991.Google Scholar
  3. 3.
    J. P. Delgrande, Torsten Schaub, and W. K. Jackson. An approach to default reasoning based on a first-order conditional logic: Revised report. Artificial Intelligence, 36:63–90, 1988.MathSciNetGoogle Scholar
  4. 4.
    Fox, M.: Constraint Directed Search: A Case Study of Job-Shop Scheduling. Morgan Kaufman, 1987.Google Scholar
  5. 5.
    E. C. Freuder and Richard J. Wallace. Partial constraint satisfaction. Artificial Intelligence, 58:21–70, 1992.MathSciNetGoogle Scholar
  6. 6.
    A.K. Ghose, P. Hadjinian, A. Sattar, J. You, and R. Goebel. Iterated belief change: A preliminary report. In Proceedings of Australian Joint Conference on Artificial Intelligence, pages 39–44, Melbourne, Victoria, November 1993. World Scientific Publishing Co.Google Scholar
  7. 7.
    A.K. Ghose, A. Sattar, and R. Goebel. Default reasoning as partial constraint satisfaction. In Proceedings of Australian Joint Conference on Artificial Intelligence, Armidale, NSW, November 1994. World Scientific Publishing Co.Google Scholar
  8. 8.
    S. Goodwin and A. Sattar. On computing preferred explanation. In Proceedings of Australian Joint Conference on Artificial Intelligence, pages 45–52, Melbourne, Victoria, November 1993. World Scientific Publishing Co.Google Scholar
  9. 9.
    H.A. Kautz and B. Selman. Hard problems for simple default logics. In Proc. of the First International Conference on the Principles of Knowledge Representation and Reasoning, pages 189–197, 1989.Google Scholar
  10. 10.
    A. K. Mackworth. The logic of constraint satisfaction. Artificial Intelligence, 58 (1–3):3–20, December 1992.MathSciNetGoogle Scholar
  11. 11.
    R. Reiter. A logic for default reasoning. Artificial Intelligence, 13(1&2):81–132, 1980.CrossRefGoogle Scholar
  12. 12.
    Satoh K.: Formalizing soft constraints by interpretation ordering. In Proc. of the 9th European Conf. on AI, pages 585–590, 1990.Google Scholar
  13. 13.
    Sattar A. and Goebel R.G.: Constraint Satisfaction as Hypothetical Reasoning. In Proceedings of the Vth International Symposium on Artificial Intelligence Cancun, Mexico, December 1992. AAAI-Press.Google Scholar
  14. 14.
    Molly Wilson and Alan Borning. Hierarchical constraint logic programming. Journal of Logic Programming, 16:277–318, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Abdul Sattar
    • 1
  • Aditya K. Ghose
    • 2
  • Randy Goebel
    • 3
  1. 1.School of Comp. and Info. TechnologyGriffith UniversityBrisbaneAustralia
  2. 2.Knowledge Systems Group, Basser Department of Computer ScienceUniversity of SydneySyndeyAustralia
  3. 3.Department of Computing ScienceUniversity of AlbertaEdmontonCanada

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