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First-Order Encodings for Modular Nonmonotonic Datalog Programs

  • Minh Dao-Tran
  • Thomas Eiter
  • Michael Fink
  • Thomas Krennwallner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6702)

Abstract

Recently Modular Nonmonotonic Logic Programs (MLP) have been introduced which incorporate a call-by-value mechanism and allow for unrestricted calls between modules, including mutual and self recursion, as an approach to provide module constructs akin to those in conventional programming in Nonmonotonic Logic Programming under Answer Set Semantics. This paper considers MLPs in a Datalog setting and provides characterizations of their answers sets in terms of classical (Herbrand) models of a first-order formula, extending a line of research for ordinary logic programs. To this end, we lift the well-known loop formulas method to MLPs, and we also consider the recent ordered completion approach that avoids explicit construction of loop formulas using auxiliary predicates. Independent of computational perspectives, the novel characterizations widen our understanding of MLPs and they may prove useful for semantic investigations.

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References

  1. 1.
    Apt, K., Blair, H., Walker, A.: Towards a Theory of Declarative Knowledge. In: Foundations of Deductive Databases and Logic Programming, pp. 89–148. Morgan Kaufmann, San Francisco (1988)CrossRefGoogle Scholar
  2. 2.
    Arni, F., et al.: The deductive database system LDL++. Theor. Pract. Log. Prog. 3(1), 61–94 (2003)CrossRefzbMATHGoogle Scholar
  3. 3.
    Asuncion, V., Lin, F., Zhang, Y., Zhou, Y.: Ordered completion for first-order logic programs on finite structures. In: AAAI 2010, pp. 249–254. AAAI Press, Menlo Park (2010)Google Scholar
  4. 4.
    Chen, X., Ji, J., Lin, F.: Computing loops with at most one external support rule for disjunctive logic programs. In: Hill, P.M., Warren, D.S. (eds.) ICLP 2009. LNCS, vol. 5649, pp. 130–144. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Clark, K.L.: Negation as failure. In: Logic and Data Bases, pp. 293–322 (1978)Google Scholar
  6. 6.
    Dao-Tran, M., Eiter, T., Fink, M., Krennwallner, T.: Modular Nonmonotonic Logic Programming Revisited. In: Hill, P.M., Warren, D.S. (eds.) ICLP 2009. LNCS, vol. 5649, pp. 145–159. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Eiter, T., Gottlob, G., Mannila, H.: Disjunctive Datalog. ACM T. Database Syst. 22(3), 364–417 (1997)CrossRefGoogle Scholar
  8. 8.
    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
  9. 9.
    Eiter, T., Leone, N., Saccà, D.: On the Partial Semantics for Disjunctive Deductive Databases. Ann. Math. Artif. Intell. 19(1/2), 59–96 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Faber, W.: Unfounded sets for disjunctive logic programs with arbitrary aggregates. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 40–52. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Faber, W., Leone, N., Pfeifer, G.: Semantics and complexity of recursive aggregates in answer set programming. Artif. Intell. 175(1), 278–298 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Ferraris, P., Lee, J., Lifschitz, V.: A generalization of the Lin-Zhao theorem. Ann. Math. Artif. Intell. 47(1-2), 79–101 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Gaifman, H., Shapiro, E.: Fully abstract compositional semantics for logic programs. In: POPL 1989, pp. 134–142. ACM, New York (1989)Google Scholar
  14. 14.
    Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generat. Comput. 9(3-4), 365–385 (1991)CrossRefzbMATHGoogle Scholar
  15. 15.
    Janhunen, T., Oikarinen, E., Tompits, H., Woltran, S.: Modularity Aspects of Disjunctive Stable Models. J. Artif. Intell. Res. 35, 813–857 (2009)MathSciNetzbMATHGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    Lee, J., Meng, Y.: On reductive semantics of aggregates in answer set programming. In: Erdem, E., Lin, F., Schaub, T. (eds.) LPNMR 2009. LNCS, vol. 5753, pp. 182–195. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  18. 18.
    Lifschitz, V., Turner, H.: Splitting a Logic Program. In: ICLP 1994, pp. 23–38. MIT-Press, Cambridge (1994)Google Scholar
  19. 19.
    Lin, F., Zhao, Y.: ASSAT: computing answer sets of a logic program by SAT solvers. Artif. Intell. 157(1-2), 115–137 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Ross, K.: Modular Stratification and Magic Sets for Datalog Programs with Negation. J. ACM 41(6), 1216–1267 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Truszczyński, M.: Reducts of propositional theories, satisfiability relations, and generalizations of semantics of logic programs. Artif. Intell. 174(16-17), 1285–1306 (2010)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

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

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