Advertisement

Answer Set Programming with Constraints Using Lazy Grounding

  • Alessandro Dal Palù
  • Agostino Dovier
  • Enrico Pontelli
  • Gianfranco Rossi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5649)

Abstract

The paper describes a novel methodology to compute stable models in Answer Set Programming. The proposed approach relies on a bottom-up computation that does not require a preliminary grounding phase. The implementation of the framework can be completely realized within the framework of Constraint Logic Programming over finite domains. The use of a high level language for the implementation and the clean structure of the computation offer an ideal framework for the implementation of extensions of Answer Set Programming. In this work, we demonstrate how non-ground arithmetic constraints can be easily introduced in the computation model. The paper provides preliminary experimental results which confirm the potential for this approach.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Babovich, Y., Maratea, M.: Cmodels-2: SAT-based Answer Sets Solver Enhanced to Non-tight Programs. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS, vol. 2923, pp. 346–350. Springer, Heidelberg (2003)Google Scholar
  2. 2.
    Baral, C.: Knowledge Representation, Reasoning, and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)CrossRefzbMATHGoogle Scholar
  3. 3.
    Bonatti, P., Pontelli, E., Son, T.: Credulous Resolution for ASP. In: AAAI (2008)Google Scholar
  4. 4.
    Brooks, D., Erdem, E., Erdogan, S., Minett, J., Ringe, D.: Inferring Phylogenetic Trees Using Answer Set Programming. JAR 39(4), 471–511 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Codognet, P., Diaz, D.: A Minimal Extension of the WAM for clp(fd). In: ICLP, pp. 774–790. MIT Press, Cambridge (1993)Google Scholar
  6. 6.
    Dovier, A., Formisano, A., Pontelli, E.: A Comparison of CLP(FD) and ASP Solutions to NP-Complete Problems. In: Gabbrielli, M., Gupta, G. (eds.) ICLP 2005. LNCS, vol. 3668, pp. 67–82. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Elkabani, I., Pontelli, E., Son, T.: A System for Computing Answer Sets of Logic Programs with Aggregates. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS, vol. 3662, pp. 427–431. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: Clasp: a Conflict-driven Answer Set Solver. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS, vol. 4483, pp. 260–265. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Gebser, M., Schaub, T., Thiele, S., Usadel, B., Veber, P.: Detecting Inconsistencies in Large Biological Networks with ASP. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 130–144. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Gelfond, M., Lifschitz, V.: The Stable Model Semantics for Logic Programs. In: ICLP, pp. 1070–1080. MIT Press, Cambridge (1988)Google Scholar
  11. 11.
    Lefevre, C., Nicolas, P.: Integrating Grounding in Search Process for Answer Set Computing. In: Work. on Integrating ASP and Other Computing Paradigms (2008)Google Scholar
  12. 12.
    Leone, N., Pfeifer, G., Faber, W., Eiter, T., Perri, G.S., Scarcello, F.: The DLV System for Knowledge Representation and Reasoning. ACM Transactions on Computational Logic 7(3), 499–562 (2006)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Lifschitz, V.: Answer Set Planning. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS, vol. 1705, pp. 373–374. Springer, Heidelberg (1999)Google Scholar
  14. 14.
    Lin, F., Zhao, Y.: ASSAT: Computing answer sets of a logic program by SAT solvers. Artificial Intelligence 157(1-2), 115–137 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Liu, L., Pontelli, E., Tran, S., Truszczynski, M.: Logic Programs with Abstract Constraint Atoms: the Role of Computations. In: Dahl, V., Niemelä, I. (eds.) ICLP 2007. LNCS, vol. 4670, pp. 286–301. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Lloyd, J.W.: Foundations of Logic Programming. Springer, Heidelberg (1987)CrossRefzbMATHGoogle Scholar
  17. 17.
    Marek, V., Remmel, J.: Set Constraints in Logic Programming. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS, vol. 2923, pp. 167–179. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  18. 18.
    Marek, V.W., Truszczyński, M.: Stable Models and an Alternative Logic Programming Paradigm. In: Apt, K.R., Marek, V.W., Truszcziński, M., Warren, D.S. (eds.) The Logic Programming Paradigm. Springer, Heidelberg (1999)Google Scholar
  19. 19.
    Mellarkod, V., Gelfond, M.: Integrating Answer Set Reasoning with Constraint Solving Techniques. In: Garrigue, J., Hermenegildo, M.V. (eds.) FLOPS 2008. LNCS, vol. 4989, pp. 15–31. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  20. 20.
    Niemelä, I.: Logic Programs with Stable Model Semantics as a Constraint Programming Paradigm. Annals of Mathematics and AI 25(3-4), 241–273 (1999)MathSciNetzbMATHGoogle Scholar
  21. 21.
    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)CrossRefGoogle Scholar
  22. 22.
    Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artificial Intelligence 138(1-2), 181–234 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Son, T., Pontelli, E.: Planning for Biochemical Pathways: a Case Study of Answer Set Planning in Large Planning Problem Instances. In: First International Workshop on Software Engineering for Answer Set Programming, pp. 116–130 (2007)Google Scholar
  24. 24.
    Van Gelder, A., Ross, K.A., Schlipf, J.S.: The Well-Founded Semantics for General Logic Programs. Journal of the ACM 38(3), 620–650 (1991)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Zukowski, U., Freitag, B., Brass, S.: Improving the Alternating Fixpoint: The Transformation Approach. In: Fuhrbach, U., Dix, J., Nerode, A. (eds.) LPNMR 1997. LNCS, vol. 1265, pp. 4–59. Springer, Heidelberg (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Alessandro Dal Palù
    • 1
  • Agostino Dovier
    • 2
  • Enrico Pontelli
    • 3
  • Gianfranco Rossi
    • 1
  1. 1.Dip. MatematicaUniv. ParmaItaly
  2. 2.Dip. Matematica e InformaticaUniv. UdineItaly
  3. 3.Dept. Computer ScienceNew Mexico State Univ.USA

Personalised recommendations