Towards an Integration of Answer Set and Constraint Solving

  • S. Baselice
  • P. A. Bonatti
  • M. Gelfond
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3668)


Answer set programming (ASP for short) is a declarative problem solving framework that has been recently attracting the attention of researchers for its expressiveness and for its well-engineered and optimized implementations. Still, state-of-the-art answer set solvers have huge memory requirements, because the ground instantiation of the input program must be computed before the actual reasoning starts. This prevents ASP to be effective on several classes of problems. In this paper we integrate answer set generation and constraint solving to reduce the memory requirements for a class of multi-sorted logic programs with cardinality constraints. We prove some theoretical results, introduce a provably sound and complete algorithm, and report experimental results showing that our approach can solve problem instances with significantly larger domains.


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  1. 1.
    Balduccini, M., Gelfond, M., Watson, R., Nogueira, M.: The USA-Advisor: A case study in answer set planning. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 439–442. Springer, Heidelberg (2001)Google Scholar
  2. 2.
    Baselice, S.: Integrazione di tecniche di Answer Set Programming e Constraint Solving. In: Tesi di laurea, Università degli studi di Napoli Federico II, Naples, Italy (October 2004)Google Scholar
  3. 3.
    Cadoli, M., Donini, F.M., Schaerf, M.: Is intractability of nonmonotonic reasoning a real drawback? Artificial Intelligence 88(1-2), 215–251 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Aiello, L.C., Massacci, F.: Verifying security protocols as planning in logic programming. ACM Trans. Comput. Logic 2(4), 542–580 (2001)CrossRefGoogle Scholar
  5. 5.
    Cholewiński, P., Marek, V., Mikitiuk, A., Truszczyński, M.: Experimenting with nonmonotonic reasoning. In: Proceedings of the 12th International Conference on Logic Programming, ICLP 1995, pp. 267–281. MIT Press, Cambridge (1995)Google Scholar
  6. 6.
    Codognet, P., Diaz, D.: Compiling constraints in clp(FD). Journal of Logic Programming 27(3), 185–226 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Eiter, T., Leone, N., Mateis, C., Pfeifer, G., Scarcello, F.: A deductive system for non-monotonic reasoning. In: Fuhrbach, U., Dix, J., Nerode, A. (eds.) LPNMR 1997. LNCS, vol. 1265, pp. 364–375. Springer, Heidelberg (1997)Google Scholar
  8. 8.
    El-Khatib, O., Pontelli, E., Son, T.C.: Asp-prolog: A system for reasoning about answer set programs in prolog. In: Jayaraman, B. (ed.) PADL 2004. LNCS, vol. 3057, pp. 148–162. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proc. of the 5th ICLP, pp. 1070–1080. MIT Press, Cambridge (1988)Google Scholar
  10. 10.
    Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Computing 9(3-4), 365–386 (1991)CrossRefGoogle Scholar
  11. 11.
    Jaffar, J., Maher, M.J.: Constraint logic programming: A survey. Journal of Logic Programming 19/20, 503–582 (May/July 1994)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Lifschitz, V., Turner, H.: Splitting a Logic Program. In: Proceedings of the 12th International Conference on Logic Programming, Kanagawa 1995. MIT Press Series Logic Program, pp. 581–595. MIT Press, Cambridge (1995)Google Scholar
  13. 13.
    Marek, V.W., Remmel, J.B.: On the expressibility of stable logic programming. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 107–120. Springer, Heidelberg (2001)Google Scholar
  14. 14.
    Marek, W., Truszczyński, M.: Stable models and an alternative logic programming paradigm. In: The Logic Programming Paradigm: a 25-Year Perspective, pp. 375–398. Springer, Heidelberg (1999)Google Scholar
  15. 15.
    McCarthy, J.: Circumscription: a form of nonmonotonic reasoning. Artificial Intelligence 13, 27–39 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Moore, R.C.: Semantical considerations on nonmonotonic logics. Artificial Intelligence 25, 75–94 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Niemelä, I., Simons, P.: Smodels — an implementation of the stable model and well-founded semantics for normal lp. In: Fuhrbach, U., Dix, J., Nerode, A. (eds.) LPNMR 1997. LNCS, vol. 1265, pp. 421–430. Springer, Heidelberg (1997)Google Scholar
  18. 18.
    Nogueira, M., Balduccini, M., Gelfond, M., Watson, R., Barry, M.: An A-Prolog decision support system for the Space Shuttle. In: Ramakrishnan, I.V. (ed.) PADL 2001. LNCS, vol. 1990, pp. 169–183. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  19. 19.
    Reiter, R.: A logic for default reasoning. Artificial Intelligence 13, 81–132 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artif. Intell. 138(1-2), 181–234 (2002)zbMATHCrossRefGoogle Scholar
  21. 21.
    Teng, C., Van Hentenryck, P., Deville, Y.: A generic arc-consistency algorithm and its specializations, June 11 (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • S. Baselice
    • 1
  • P. A. Bonatti
    • 1
  • M. Gelfond
    • 2
  1. 1.Università di Napoli Federico II 
  2. 2.Texas Tech University 

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