Merging Logic Programs under Answer Set Semantics

  • James Delgrande
  • Torsten Schaub
  • Hans Tompits
  • Stefan Woltran
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5649)


This paper considers a semantic approach for merging logic programs under answer set semantics. Given logic programs P 1, ..., P n , the goal is to provide characterisations of the merging of these programs. Our formal techniques are based on notions of relative distance between the underlying SE models of the logic programs. Two approaches are examined. The first informally selects those models of the programs that vary the least from the models of the other programs. The second approach informally selects those models of a program P 0 that are closest to the models of programs P 1, ..., P n . P 0 can be thought of as analogous to a set of database integrity constraints. We examine formal properties of these operators and give encodings for computing the mergings of a multiset of logic programs within the same logic programming framework. As a by-product, we provide a complexity analysis revealing that our operators do not increase the complexity of the base formalism.


answer set programming belief merging strong equivalence 


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  1. 1.
    Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)CrossRefzbMATHGoogle Scholar
  2. 2.
    Zhang, Y., Foo, N.: Updating logic programs. In: ECAI 1998, pp. 403–407. IOS Press, Amsterdam (1998)Google Scholar
  3. 3.
    Alferes, J., Leite, J., Pereira, L., Przymusinska, H., Przymusinski, T.: Dynamic updates of non-monotonic knowledge bases. Journal of Logic Programming 45(1–3), 43–70 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Leite, J.: Evolving Knowledge Bases: Specification and Semantics. IOS Press, Amsterdam (2003)zbMATHGoogle Scholar
  5. 5.
    Inoue, K., Sakama, C.: Updating extended logic programs through abduction. In: Gelfond, M., Leone, N., Pfeifer, G. (eds.) LPNMR 1999. LNCS, vol. 1730, pp. 147–161. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Eiter, T., Fink, M., Sabbatini, G., Tompits, H.: On properties of update sequences based on causal rejection. Theory and Practice of Logic Programming 2(6), 711–767 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Delgrande, J., Schaub, T., Tompits, H.: A preference-based framework for updating logic programs. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS, vol. 4483, pp. 71–83. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Delgrande, J., Schaub, T., Tompits, H., Woltran, S.: Belief revision of logic programs under answer set semantics. In: KR 2008, pp. 411–421. AAAI Press, Menlo Park (2008)Google Scholar
  9. 9.
    Turner, H.: Strong equivalence made easy: Nested expressions and weight constraints. Theory and Practice of Logic Programming 3(4-5), 609–622 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Transactions on Computational Logic 2(4), 526–541 (2001)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Gärdenfors, P.: Knowledge in Flux. MIT Press, Cambridge (1988)zbMATHGoogle Scholar
  12. 12.
    Liberatore, P., Schaerf, M.: Arbitration (or how to merge knowledge bases). IEEE Transactions on Knowledge and Data Engineering 10(1), 76–90 (1998)CrossRefGoogle Scholar
  13. 13.
    Konieczny, S., Pino Pérez, R.: Merging information under constraints: A logical framework. Journal of Logic and Computation 12(5), 773–808 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Lifschitz, V., Woo, T.: Answer sets in general nonmonotonic reasoning (preliminary report). In: KR 1992, pp. 603–614. Morgan Kaufmann, San Francisco (1992)Google Scholar
  15. 15.
    Eiter, T., Tompits, H., Woltran, S.: On solution correspondences in answer set programming. In: IJCAI 2005, pp. 97–102. Professional Book Center (2005)Google Scholar
  16. 16.
    Cabalar, P., Ferraris, P.: Propositional theories are strongly equivalent to logic programs. Theory and Practice of Logic Programming 7(6), 745–759 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Baral, C., Kraus, S., Minker, J.: Combining multiple knowledge bases. IEEE Transactions on Knowledge and Data Engineering 3, 208–220 (1991)CrossRefGoogle Scholar
  18. 18.
    Buccafurri, F., Gottlob, G.: Multiagent compromises, joint fixpoints, and stable models. In: Kakas, A.C., Sadri, F. (eds.) Computational Logic: Logic Programming and Beyond. LNCS, vol. 2407, pp. 561–585. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  19. 19.
    Sakama, C., Inoue, K.: Coordination in answer set programming. ACM Transactions on Computational Logic 9, 1–30 (2008)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Baral, C., Kraus, S., Minker, J., Subrahmanian, V.: Combining multiple knowledge bases consisting of first order theories. Computational Intelligence 8(1), 45–71 (1992)CrossRefGoogle Scholar
  21. 21.
    Revesz, P.: On the semantics of theory change: Arbitration between old and new information. In: ACM Principles of Database Systems, pp. 71–82 (1993)Google Scholar
  22. 22.
    Lin, J., Mendelzon, A.: Knowledge base merging by majority. In: Dynamic Worlds: From the Frame Problem to Knowledge Management, pp. 195–218. Kluwer, Dordrecht (1999)CrossRefGoogle Scholar
  23. 23.
    Konieczny, S., Lang, J., Marquis, P.: Distance-based merging: A general framework and some complexity results. In: KR 2002, pp. 97–108 (2002)Google Scholar
  24. 24.
    Meyer, T.: On the semantics of combination operations. Journal of Applied Nonclassical Logics 11(1-2), 59–84 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Spohn, W.: Ordinal conditional functions: A dynamic theory of epistemic states. In: Causation in Decision, Belief Change, and Statistics, pp. 105–134. Kluwer, Dordrecht (1988)CrossRefGoogle Scholar
  26. 26.
    Booth, R.: Social contraction and belief negotiation. In: KR 2002, pp. 375–384 (2002)Google Scholar
  27. 27.
    Benferhat, S., Dubois, D., Kaci, S., Prade, H.: Possibilistic merging and distance-based fusion of propositional information. Annals of Mathematics and AI 34(1-3), 217–252 (2003)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • James Delgrande
    • 1
  • Torsten Schaub
    • 2
  • Hans Tompits
    • 3
  • Stefan Woltran
    • 3
  1. 1.Simon Fraser UniversityBurnabyCanada
  2. 2.Universität PotsdamPotsdamGermany
  3. 3.Technische Universität WienViennaAustria

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