Skip to main content

Answer Set Programming with Constraints Using Lazy Grounding

  • Conference paper
Logic Programming (ICLP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5649))

Included in the following conference series:

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.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. Baral, C.: Knowledge Representation, Reasoning, and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  3. Bonatti, P., Pontelli, E., Son, T.: Credulous Resolution for ASP. In: AAAI (2008)

    Google Scholar 

  4. Brooks, D., Erdem, E., Erdogan, S., Minett, J., Ringe, D.: Inferring Phylogenetic Trees Using Answer Set Programming. JAR 39(4), 471–511 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  10. Gelfond, M., Lifschitz, V.: The Stable Model Semantics for Logic Programs. In: ICLP, pp. 1070–1080. MIT Press, Cambridge (1988)

    Google Scholar 

  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. 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)

    Article  MathSciNet  Google Scholar 

  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. Lin, F., Zhao, Y.: ASSAT: Computing answer sets of a logic program by SAT solvers. Artificial Intelligence 157(1-2), 115–137 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  16. Lloyd, J.W.: Foundations of Logic Programming. Springer, Heidelberg (1987)

    Book  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  22. Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artificial Intelligence 138(1-2), 181–234 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    MathSciNet  MATH  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dal Palù, A., Dovier, A., Pontelli, E., Rossi, G. (2009). Answer Set Programming with Constraints Using Lazy Grounding. In: Hill, P.M., Warren, D.S. (eds) Logic Programming. ICLP 2009. Lecture Notes in Computer Science, vol 5649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02846-5_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02846-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02845-8

  • Online ISBN: 978-3-642-02846-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics