Skip to main content
SpringerLink
Log in

Enhancing DLV instantiator by backjumping techniques

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

Disjunctive logic programming (DLP) is a powerful formalism for knowledge representation and reasoning. The high expressiveness of DLP language, together with the recent availability of some efficient DLP system, has favoured the application of DLP in emerging areas like Knowledge Management and Information Integration. These applications have often to deal with huge input data, and have evidenced the need to improve the efficiency of DLP instantiators. Program instantiation is the first phase of a DLP computation; in this phase, variables are replaced by constants to generate a ground program which is then evaluated by propositional algorithms in the second phase of the computation. The instantiation process may be computationally expensive, and in fact its efficiency has been recognized to be a key issue for solving real-world problems by using disjunctive logic programming. Given a program P, a good instantiation for P is a ground program P′ having precisely the same answer sets as P and such that: (1) P′ can be computed efficiently from P, and (2) P′ does not contain “useless” rules, (P′ is as small as possible) and can thus be evaluated efficiently. In this paper, we present a structure-based backjumping algorithm for the instantiation of disjunctive logic programs, that meets the above requirements. In particular, given a rule r to be grounded, our algorithm exploits both the semantical and the structural information about r for computing efficiently the ground instances of r, avoiding the generation of “useless” rules. That is, from each general rule r, we compute only a relevant subset of its ground instances, avoiding the generation of “useless” instances, while fully preserving the semantic of the program. We have implemented this algorithm in DLV—the state-of-the-art implementation of DLP—and we have carried out an experimentation activity on an ample collection of benchmark problems. The experimental results are very positive: the new technique improves sensibly the efficiency of the DLV system on many program classes.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anger, C., Konczak, K., Linke, T.: NoMoRe: A system for non-monotonic reasoning. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR’01), Vienna, Austria. Lecture Notes in Computer Science, vol. 2173, pp. 406–410. Springer Verlag, Vienna, Austria (2001)

    Google Scholar 

  2. Anger, C., Gebser, M., Linke, T., Neumann, A., Schaub, T.: The nomore++ approach to answer set solving. In: Sutcliffe, G., Voronkov, A. (eds.) Proceedings of the 12th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR ’05). Lecture Notes in Computer Science, vol 3835, pp. 95–109. Springer Verlag (2005)

  3. Apt, K.R., Blair, H.A., Walker, A.: Towards a theory of declarative knowledge. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 89–148. Morgan Kaufmann Publishers, Inc., Washington, DC (1988)

    Google Scholar 

  4. Arieli, O., Denecker, M., Van Nuffelen, B., Bruynooghe, M.: Database repair by signed formulae. In: Seipel, D., Turull Torres, J.M. (eds.) Foundations of Information and Knowledge Systems, Third International Symposium (FoIKS 2004). Lecture Notes in Computer Science, vol. 2942, pp. 14–30. Springer (2004)

  5. Babovich, Y.: Cmodels homepage. http://www.cs.utexas.edu/users/tag/cmodels.html (since 2002)

  6. Bruynooghe, M., Pereira, L.: Deduction revision by intelligent backtracking. In: Horwood, E. (ed.) Implementations of Prolog, pp. 194–215 (1984)

  7. Cadoli, M., Eiter, T., Gottlob, G.: Default logic as a query language. IEEE Trans. Knowl. Data Eng. 9(3), 448–463 (1997)

    Article  Google Scholar 

  8. Chandra, A.K., Merlin, P.M.: Optimal implementation of conjunctive queries in relational data bases. In: Conference Record of the Ninth Annual ACM Symposium on Theory of Computing, pp. 77–90 (1977)

  9. Chen, X., van Beek, P.: Conflict-directed backjumping revisited. J. Artif. Intell. Res. 14, 53–81 (2001)

    MATH  MathSciNet  Google Scholar 

  10. Dechter, R.: Enhancement schemes fo constraint processing: backjumping, learning and cutset decomposition. Artif. Intell. 41(3), 273–312 (1990)

    Article  Google Scholar 

  11. Dix, J., Eiter, T., Fink, M., Polleres, A., Zhang, Y.: Monitoring agents using declarative planning. In: Günter, A., Kruse, R., Neumann, B. (eds.) Proceedings of the 26th German Conference on Artificial Intelligence (KI ’03). Lecture Notes in Computer Science, no. 2821, pp. 646–660. Springer (2003)

  12. Downey, R., Fellows, M.: Parameterized Complexity. Springer (1999)

  13. Eiter, T., Leone, N., Mateis, C., Pfeifer, G., Scarcello, F.: A deductive system for nonmonotonic reasoning. In: Dix, J., Furbach, U., Nerode, A. (eds.) Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR’97). Lecture Notes in AI (LNAI), no. 1265, pp. 363–374. Springer, Dagstuhl, Germany (1997)

    Google Scholar 

  14. Faber, W., Leone, N., Mateis, C., Pfeifer, G.: Using database optimization techniques for nonmonotonic reasoning. In: INAP Organizing Committee (ed.) Proceedings of the 7th International Workshop on Deductive Databases and Logic Programming (DDLP’99). Prolog Association of Japan, pp. 135–139 (1999)

  15. Faber, W., Leone, N., Pfeifer, G.: Recursive aggregates in disjunctive logic programs: semantics and complexity. In: Alferes, J.J., Leite, J. (eds.) Proceedings of the 9th European Conference on Artificial Intelligence (JELIA 2004). Lecture Notes in AI (LNAI), no. 3229, pp. 200–212. Springer Verlag (2004)

  16. Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: Conflict-driven answer set solving. In: Veloso, M.M. (ed.) Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI ’07), pp. 386–392. Morgan Kaufmann Publishers (2007)

  17. Gebser, M., Schaub, T., Thiele, S.: Gringo : a new grounder for answer set programming. In: Baral, C., Brewka, G., Schlipf, J.S. (eds.) Proceedings of the 9th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR ’07), vol. 4483, pp. 266–271. Tempe, AZ, USA (2007)

  18. Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Gener. Comput. 9(3/4), 365–385 (1991)

    Article  Google Scholar 

  19. Janhunen, T., Niemelä, I., Seipel, D., Simons, P., You, J.H.: Unfolding partiality and disjunctions in stable model semantics. ACM Trans. Comput. Log. 7(1), 1–37 (2006)

    Article  MathSciNet  Google Scholar 

  20. Knuth, D.E.: The Stanford GraphBase : A Platform for Combinatorial Computing. ACM Press, New York (1994)

    MATH  Google Scholar 

  21. Leone, N., Perri, S., Scarcello, F.: Improving ASP instantiators by join-ordering methods. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR ’01). Lecture Notes in AI (LNAI), no. 2173, pp. 280–294. Springer Verlag, Vienna, Austria (2001)

    Google Scholar 

  22. Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV system for knowledge representation and reasoning. ACM Trans. Comput. Log. 7(3), 499–562 (2006)

    Article  MathSciNet  Google Scholar 

  23. Lierler, Y.: Cmodels—SAT-based disjunctive answer set solver. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) Proceedings of 8th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR ’05). Lecture Notes in Computer Science, vol. 3662, pp. 447–451. Springer, Diamante, Italy (2005)

    Chapter  Google Scholar 

  24. Lierler, Y., Maratea, M.: Cmodels-2: SAT-based Answer Set Solver Enhanced to Non-tight Programs. In: Lifschitz, V., Niemelä, I. (eds.) Proceedings of the 7th International Conference on Logic Programming and Non-Monotonic Reasoning (LPNMR ’07). Lecture Notes in Computer Science, pp. 346–350. Springer (2004)

  25. Lin, F., Zhao, Y.: ASSAT: Computing answer sets of a logic program by SAT solvers. In: Proceedings of the 18th National Conference on Artificial Intelligence (AAAI-2002), AAAI Press, Edmonton, Alberta, Canada (2002)

    Google Scholar 

  26. Lin, F., Zhao, Y.: ASSAT: computing answer sets of a logic program by SAT solvers. Artif. Intell. 157(1-2), 115–137 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  27. Minker, J.: On indefinite data bases and the closed world assumption. In: Loveland, D. (ed.) Proceedings of the 6th Conference on Automated Deduction (CADE ’82). Lecture Notes in Computer Science, vol. 138, pp. 292–308. Springer, New York, USA (1982)

    Chapter  Google Scholar 

  28. Minker, J.: Overview of disjunctive logic programming. Ann. Math. Artif. Intell. 12(1–2), 1–24 (1994)

    Article  MathSciNet  Google Scholar 

  29. Niemelä, I., Simons, P.: Smodels—an implementation of the stable model and well-founded semantics for normal logic programs. In: Dix, J., Furbach, U., Nerode, A. (eds.) Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR’97). Lecture Notes in AI (LNAI), vol. 1265, pp. 420–429. Springer Verlag, Dagstuhl, Germany (1997)

    Google Scholar 

  30. Prosser, P.: Hybrid algorithms for the constraint satisfaction problem. Comput. Intell. 9(3), 268–299 (1993)

    Article  Google Scholar 

  31. Przymusinski, T.C.: Stable semantics for disjunctive programs. New Gener. Comput. 9, 401–424 (1991)

    Article  Google Scholar 

  32. Radziszowski, S.P.: Small Ramsey numbers. Electron. J. Comb. 1, revision 11: August 1, 2006 (1994)

  33. Shen, K.: Overview of DASWAM: exploitation of dependent and-parallelism. J. Log. Program. 29(1–3), 245–293 (1996)

    Article  MATH  Google Scholar 

  34. Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artif. Intell. 138(1–2), 181–234 (2002)

    Article  MATH  Google Scholar 

  35. Syrjänen, T.: Lparse 1.0 User’s Manual. http://www.tcs.hut.fi/Software/smodels/lparse.ps.gz (2002)

  36. Tsang, E.: Foundations of Constraint Satisfaction. Academic Press (1993)

  37. Ullman, J.D.: Principles of Database and Knowledge Base Systems. Computer Science Press (1989)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Calabria, 87036, Rende (CS), Italy

    Simona Perri, Gelsomina Catalano & Nicola Leone

  2. DEIS, University of Calabria, 87036, Rende (CS), Italy

    Francesco Scarcello

Authors
  1. Simona Perri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesco Scarcello
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gelsomina Catalano
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nicola Leone
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nicola Leone.

Additional information

A preliminary version of part of this work has been presented at the 10th International Workshop on Non-Monotonic Reasoning (NMR 2004).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Perri, S., Scarcello, F., Catalano, G. et al. Enhancing DLV instantiator by backjumping techniques. Ann Math Artif Intell 51, 195–228 (2007). https://doi.org/10.1007/s10472-008-9090-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-008-9090-9

Keywords

Mathematics Subject Classifications (2000)

Search

Navigation