Comparing Alternative Solutions for Unfounded Set Propagation in ASP

  • Mario Alviano
  • Carmine Dodaro
  • Francesco Ricca
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8249)


Answer Set Programming (ASP) is a logic programming language for nonmonotonic reasoning. Propositional ASP programs are usually evaluated by DPLL algorithms combining unit propagation with operators that are specific of ASP. Among them, unfounded set propagation is used for handling recursive programs by many ASP solvers. This paper reports a comparison of two available solutions for unfounded set propagation, the one adopted in DLV and that based on source pointers. The paper also discusses the impact of splitting the input program in components according to head-to-body dependencies. Both solutions and variants have been implemented in the same solver, namely WASP. An advantage in properly splitting the program in components is highlighted by an experiment on a selection of problems taken from the 3rd ASP Competition. In this experiment the algorithm based on source pointers performs better.


Source Pointer Inference Rule Dependency Graph Input Program Nonmonotonic Reasoning 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gelfond, M., Lifschitz, V.: Classical Negation in Logic Programs and Disjunctive Databases. New Generation Computing 9, 365–385 (1991)CrossRefGoogle Scholar
  2. 2.
    Lifschitz, V.: Answer Set Planning. In: Proceedings of the 16th International Conference on Logic Programming (ICLP 1999), Las Cruces, New Mexico, USA, pp. 23–37. The MIT Press (1999)Google Scholar
  3. 3.
    Eiter, T., Gottlob, G., Mannila, H.: Disjunctive Datalog. ACM Transactions on Database Systems 22, 364–418 (1997)CrossRefGoogle Scholar
  4. 4.
    Calimeri, F., Ianni, G., Ricca, F., Alviano, M., Bria, A., Catalano, G., Cozza, S., Faber, W., Febbraro, O., Leone, N., Manna, M., Martello, A., Panetta, C., Perri, S., Reale, K., Santoro, M.C., Sirianni, M., Terracina, G., Veltri, P.: The Third Answer Set Programming Competition: Preliminary Report of the System Competition Track. In: Delgrande, J.P., Faber, W. (eds.) LPNMR 2011. LNCS, vol. 6645, pp. 388–403. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Davis, M., Logemann, G., Loveland, D.: A Machine Program for Theorem Proving. Communications of the ACM 5, 394–397 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Faber, W., Leone, N., Pfeifer, G.: Pushing Goal Derivation in DLP Computations. In: Gelfond, M., Leone, N., Pfeifer, G. (eds.) LPNMR 1999. LNCS (LNAI), vol. 1730, pp. 177–191. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  7. 7.
    Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV System for Knowledge Representation and Reasoning. ACM Transactions on Computational Logic 7, 499–562 (2006)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Simons, P., Niemelä, I., Soininen, T.: Extending and Implementing the Stable Model Semantics. Artificial Intelligence 138, 181–234 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Zhang, L., Madigan, C.F., Moskewicz, M.W., Malik, S.: Efficient Conflict Driven Learning in Boolean Satisfiability Solver. In: Proceedings of the International Conference on Computer-Aided Design (ICCAD 2001), pp. 279–285 (2001)Google Scholar
  10. 10.
    Gaschnig, J.: Performance measurement and analysis of certain search algorithms. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, USA, Technical Report CMU-CS-79-124 (1979)Google Scholar
  11. 11.
    Gomes, C.P., Selman, B., Kautz, H.A.: Boosting Combinatorial Search Through Randomization. In: Proceedings of AAAI/IAAI 1998, pp. 431–437. AAAI Press (1998)Google Scholar
  12. 12.
    Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: Proceedings of the 38th Design Automation Conference, DAC 2001, Las Vegas, NV, USA, pp. 530–535. ACM (2001)Google Scholar
  13. 13.
    Alviano, M., Dodaro, C., Faber, W., Leone, N., Ricca, F.: WASP: A native ASP solver based on constraint learning. In: Cabalar, P., Son, T.C. (eds.) LPNMR 2013. LNCS, vol. 8148, pp. 54–66. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  14. 14.
    Koch, C., Leone, N., Pfeifer, G.: Enhancing Disjunctive Logic Programming Systems by SAT Checkers. Artificial Intelligence 15, 177–212 (2003)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Calimeri, F., Faber, W., Leone, N., Pfeifer, G.: Pruning Operators for Disjunctive Logic Programming Systems. Fundamenta Informaticae 71, 183–214 (2006)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Janhunen, T., Niemelä, I.: GNT — A solver for disjunctive logic programs. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 331–335. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  17. 17.
    Lierler, Y.: cmodels – SAT-Based Disjunctive Answer Set Solver. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 447–451. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Lin, F., Zhao, Y.: ASSAT: computing answer sets of a logic program by SAT solvers. Artificial Intelligence 157, 115–137 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Anger, C., Gebser, M., Schaub, T.: Approaching the core of unfounded sets. In: Proceedings of the International Workshop on Nonmonotonic Reasoning, pp. 58–66 (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Mario Alviano
    • 1
  • Carmine Dodaro
    • 1
  • Francesco Ricca
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of CalabriaRendeItaly

Personalised recommendations