Towards Automated Integration of Guess and Check Programs in Answer Set Programming

  • Thomas Eiter
  • Axel Polleres
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2923)

Abstract

Many NP-complete problems can be encoded in the answer set semantics of logic programs in a very concise way, where the encoding reflects the typical “guess and check” nature of NP problems: The property is encoded in a way such that polynomial size certificates for it correspond to stable models of a program. However, the problem-solving capacity of full disjunctive logic programs (DLPs) is beyond NP at the second level of the polynomial hierarchy. While problems there also have a “guess and check” structure, an encoding in a DLP is often non-obvious, in particular if the “check” itself is coNP-complete; usually, such problems are solved by interleaving separate “guess” and “check” programs, where the check is expressed by inconsistency of the check program. We present general transformations of head-cycle free (extended) logic programs into stratified disjunctive logic programs which enable one to integrate such “guess” and “check” programs automatically into a single disjunctive logic program. Our results complement recent results on meta-interpretation in ASP, and extend methods and techniques for a declarative “guess and check” problem solving paradigm through ASP.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ben-Eliyahu, R., Dechter, R.: Propositional semantics for disjunctive logic programs. Annals of Mathematics and Artificial Intelligence 12, 53–87 (1994)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Delgrande, J., Schaub, T., Tompits, H.: plp: A generic compiler for ordered logic programs. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 411–415. Springer, Heidelberg (2001)Google Scholar
  3. 3.
    Eiter, T., Faber, W., Leone, N., Pfeifer, G.: Computing preferred answer sets by meta-interpretation in answer set programming. Theory & Practice of Logic Progr. 3(4-5), 463–498 Google Scholar
  4. 4.
    Eiter, T., Faber, W., Leone, N., Pfeifer, G., Polleres, A.: A logic programming approach to knowledge-state planning, II: The DLVK system. Artif. Intell. 144(1-2), 157–211 (2003)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Eiter, T., Fink, M., Sabbatini, G., Tompits, H.: On properties of update sequences based on causal rejection. Theory & Practice of Logic Prog. 2(6), 721–777 (2002)Google Scholar
  6. 6.
    Eiter, T., Gottlob, G., Mannila, H.: Disjunctive datalog. ACM TODS 22(3), 364–418 (1997)CrossRefGoogle Scholar
  7. 7.
    Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385 (1991)CrossRefGoogle Scholar
  8. 8.
    Goldman, R., Boddy, M.: Expressive planning and explicit knowledge. In: Proc. 3rd Int’l Conf. on AI Planning and Scheduling (AIPS 1996), pp. 110–117 (1996)Google Scholar
  9. 9.
    Janhunen, T.: On the effect of default negation on the expressiveness of disjunctive rules. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 93–106. Springer, Heidelberg (2001)Google Scholar
  10. 10.
    Lee, J., Lifschitz, V.: Loop formulas for disjunctive logic programs. In: Palamidessi, C. (ed.) ICLP 2003. LNCS, vol. 2916, pp. 451–465. Springer, Heidelberg (2003) (to appear)CrossRefGoogle Scholar
  11. 11.
    Leone, N., Pfeifer, G., Faber, W., et al.: The DLV system for knowledge representation and reasoning. Tech. Rep. INFSYS RR-1843-02-14, Information Sys. Institute, TU Wien (2002)Google Scholar
  12. 12.
    Leone, N., Rosati, R., Scarcello, F.: Enhancing answer set planning. In: Proc. IJCAI 2001 Workshop on Planning under Uncertainty & Incomplete Information, pp. 33–42 (2001)Google Scholar
  13. 13.
    Lifschitz, V., Turner, H.: Splitting a logic program. In: Proc. ICLP 1994, pp. 23–37 (1994)Google Scholar
  14. 14.
    Lifschitz, V.: Answer set programming and plan generation. Artif. Intell. 138, 39–54 (2002)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Lin, F., Zhao, Y.: ASSAT: Computing answer sets of a logic program by SAT solvers. In: Proc. 18th National Conf. on Artificial Intelligence, AAAI 2002 (2002)Google Scholar
  16. 16.
    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
  17. 17.
    McDermott, D.: A critique of pure reason. Computational Intelligence 3, 151–237 (1987)CrossRefGoogle Scholar
  18. 18.
    Papadimitriou, C.H.: A note on the expressive power of Prolog. Bulletin of the EATCS 26, 21–23 (1985)MathSciNetGoogle Scholar
  19. 19.
    In: Provetti, A., Son, T.C. (eds.) Proc. AAAI 2001 Spring Symposium on Answer Set Programming, Stanford, CA, March 2001, Workshop Technical Report SS-01-01, AAAI Press, Menlo Park (2001)Google Scholar
  20. 20.
    Przymusinski, T.: On the declarative and procedural semantics of logic programs. Journal of Automated Reasoning 5(2), 167–205 (1989)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Przymusinski, T.: Stable semantics for disjunctive programs. New Gen. Comp. 9 (1991)Google Scholar
  22. 22.
    Turner, H.: Polynomial-length planning spans the Polynomial Hierarchy. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 111–124. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Thomas Eiter
    • 1
  • Axel Polleres
    • 2
  1. 1.Institut für InformationssystemeTU WienWienAustria
  2. 2.Institut für InformatikUniversität InnsbruckInnsbruckAustria

Personalised recommendations