Cardinality Constraints in Disjunctive Deductive Databases

  • Dietmar Seipel
  • Ulrich Geske
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2582)

Abstract

We investigate cardinality constraints of the form M ↪θ K, where M is a set and θ is one of the comparison operators “=”, “≤”, or “≥”; such a constraint states that “exactly”, “at most”, or “at least”, respectively, K elements out of the set M have to be chosen.

We show how a set C of constraints can be represented by means of a positive-disjunctive deductive database P C , such that the models of P C correspond to the solutions of C. This allows for embedding cardinality constraints into applications dealing with incomplete knowledge.

We also present a sound calculus represented by a definite logic program P cc , which allows for directly reasoning with sets of exactly-cardinality constraints (i.e., where θ is “=”). Reasoning with P cc is very efficient, and it can be used for performance reasons before P C is evaluated. For obtaining completeness, however, P C is necessary, since we show the theoretical result that a sound and complete calculus for exactly- cardinality constraints does not exist.

Keywords

disjunctive logic programming constraint logic programming cardinality constraints hyperresolution 

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References

  1. 1.
    S. Ceri, G. Gottlob, L. Tanca: Logic Programming and Databases, Springer, 1990.Google Scholar
  2. 2.
    P. Van Hentenryck, Y. Deville: The Cardinality Operator: A new Logical Connective for Constraint Logic Programming, Proc. 8th Intl. Conference on Logic Programming 1991 (ICLP’91), MIT Press, 1991, pages 745–759.Google Scholar
  3. 3.
    R. Kaye: Minesweeper is NP-complete, Mathematical Intelligencer, 22(2), 2000, pages 9–15.MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    J.W. Lloyd: Foundations of Logic Programming, Second Edition, Springer, 1987.Google Scholar
  5. 5.
    J. Lobo, J. Minker, A. Rajasekar: Foundations of Disjunctive Logic Programming, MIT Press, 1992.Google Scholar
  6. 6.
    K. Marriott, P. Stuckey: Programming with Constraints-An Introduction, MIT Press, 1998.Google Scholar
  7. 7.
    J. Minker, A. Rajasekar: A Fixpoint Semantics for Disjunctive Logic Programs. Journal of Logic Programming, 9(1), 1990, pages 45–74.CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    I. Niemelä, P. Simmons: Extending the Smodels System with Cardinality and Weight Constraints, In Jack Minker (ed.): Logic-Based Artificial Intelligence, Kluwer, 2000, pages 491–522.Google Scholar
  9. 9.
    D. Seipel, J. Minker, C. Ruiz: Model Generation and State Generation for Disjunctive Logic Programs, Journal of Logic Programming, 32(1), 1997, pages 48–69.CrossRefMathSciNetGoogle Scholar
  10. 10.
    D. Seipel, H. Thöne: DisLog-A System for Reasoning in Disjunctive Deductive Databases, Proc. Intl. Workshop on the Deductive Approach to Information Systems and Databases 1994 (DAISD’94), pages 325–343.Google Scholar
  11. 11.
    D. Seipel: DisLog-A Disjunctive Deductive Database Prototype, Proc. 12th Workshop on Logic Programming (WLP’97), 1997, pages 136–143. DisLog is available at http://www-info1.informatik.uni-wuerzburg.de/databases/DisLog.
  12. 12.
    D. Seipel, U. Geske: Cardinality Constraints in Disjunctive Deductive Databases, In Workshop on Deductive Databases and Logic Programming (DDLP’2000) at the International Conference on Applications of Prolog (INAP’2000), 2000.Google Scholar
  13. 13.
    A.H. Yahya: Minimal Model Generation for Refined Answering of Generalized Queries in Disjunctive Deductive Databases. Journal of Data and Knowledge Engineering, 34(3), 2000, pages 219–249.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Dietmar Seipel
    • 1
  • Ulrich Geske
    • 2
  1. 1.Department of Computer Science Am HublandUniversity of WürzburgWürzburgGermany
  2. 2.Fraunhofer First BerlinBerlinGermany

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