Relevance-Driven Evaluation of Modular Nonmonotonic Logic Programs

  • Minh Dao-Tran
  • Thomas Eiter
  • Michael Fink
  • Thomas Krennwallner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5753)

Abstract

Modular nonmonotonic logic programs (MLPs) under the answer-set semantics have been recently introduced as an ASP formalism in which modules can receive context-dependent input from other modules, while allowing (mutually) recursive module calls. This can be used for more succinct and natural problem representation at the price of an exponential increase of evaluation time. In this paper, we aim at an efficient top-down evaluation of MLPs, considering only calls to relevant module instances. To this end, we generalize the well-known Splitting Theorem to the MLP setting and present notions of call stratification, for which we determine sufficient conditions. Call-stratified MLPs allow to split module instantiations into two parts, one for computing input of module calls, and one for evaluating the calls themselves with subsequent computations. Based on these results, we develop a top-down evaluation procedure that expands only relevant module instantiations. Finally, we discuss syntactic conditions for its exploitation.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Eiter, T., Gottlob, G., Veith, H.: Modular Logic Programming and Generalized Quantifiers. In: Fuhrbach, U., Dix, J., Nerode, A. (eds.) LPNMR 1997. LNCS, vol. 1265, pp. 290–309. Springer, Heidelberg (1997)Google Scholar
  2. 2.
    Lifschitz, V., Turner, H.: Splitting a logic program. In: ICLP 1994, pp. 23–37. MIT Press, Cambridge (1994)Google Scholar
  3. 3.
    Janhunen, T., Oikarinen, E., Tompits, H., Woltran, S.: Modularity Aspects of Disjunctive Stable Models. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 175–187. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Oikarinen, E., Janhunen, T.: Achieving compositionality of the stable model semantics for Smodels programs. Theory Pract. Log. Program. 8(5-6), 717–761 (2008)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Baral, C., Dzifcak, J., Takahashi, H.: Macros, Macro calls and Use of Ensembles in Modular Answer Set Programming. In: Etalle, S., Truszczyński, M. (eds.) ICLP 2006. LNCS, vol. 4079, pp. 376–390. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Calimeri, F., Ianni, G.: Template programs for Disjunctive Logic Programming: An operational semantics. AI Commun. 19(3), 193–206 (2006)MathSciNetMATHGoogle Scholar
  7. 7.
    Bugliesi, M., Lamma, E., Mello, P.: Modularity in Logic Programming. J. Log. Program. 19/20, 443–502 (1994)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Brogi, A., Mancarella, P., Pedreschi, D., Turini, F.: Modular logic programming. ACM Trans. Program. Lang. Syst. 16(4), 1361–1398 (1994)CrossRefGoogle Scholar
  9. 9.
    Dao-Tran, M., Eiter, T., Fink, M., Krennwallner, T.: Modular Nonmonotonic Logic Programming Revisited. In: ICLP 2009, pp. 145–159. Springer, Heidelberg (2009)Google Scholar
  10. 10.
    Faber, W., Leone, N., Pfeifer, G.: Recursive Aggregates in Disjunctive Logic Programs: Semantics and Complexity. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 200–212. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Eiter, T., Ianni, G., Schindlauer, R., Tompits, H.: Effective integration of declarative rules with external evaluations for semantic web reasoning. In: Sure, Y., Domingue, J. (eds.) ESWC 2006. LNCS, vol. 4011, pp. 273–287. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Gelfond, M., Lifschitz, V.: Classical negation in logic programs and deductive databases. New Gener. Comput. 9, 365–385 (1991)CrossRefMATHGoogle Scholar
  13. 13.
    Ferraris, P., Lee, J., Lifschitz, V., Palla, R.: Symmetric Splitting in the General Theory of Stable Models. In: IJCAI 2009, pp. 797–803. AAAI Press, Menlo Park (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Minh Dao-Tran
    • 1
  • Thomas Eiter
    • 1
  • Michael Fink
    • 1
  • Thomas Krennwallner
    • 1
  1. 1.Institut für InformationssystemeTechnische Universität WienViennaAustria

Personalised recommendations