International Conference on Logic Programming and Nonmonotonic Reasoning

LPNMR 2015: Logic Programming and Nonmonotonic Reasoning pp 467-479

Characterising and Explaining Inconsistency in Logic Programs

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9345)


A logic program under the answer set semantics can be inconsistent because its only answer set is the set of all literals, or because it does not have any answer sets. In both cases, the reason for the inconsistency may be (1) only explicit negation, (2) only negation as failure, or (3) the interplay between these two kinds of negation. Overall, we identify four different inconsistency cases, and show how the respective reason can be further characterised by a set of culprits using semantics which are weaker than the answer set semantics. We also provide a technique for explaining the set of culprits in terms of trees whose nodes are derivations. This can be seen as an important first step towards debugging inconsistent logic programs.


Logic programming Inconsistency Explanation 


  1. 1.
    Brain, M., De Vos, M.: Debugging logic programs under the answer set semantics. In: Vos, M.D., Provetti, A. (eds.) ASP 2005. CEUR Workshop Proceedings, vol. 142, pp. 141–152. (2005)Google Scholar
  2. 2.
    Dung, P.M.: On the relations between stable and well-founded semantics of logic programs. Theoret. Comput. Sci. 105(1), 7–25 (1992)MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Eiter, T., Leone, N., Saccà, D.: On the partial semantics for disjunctive deductive databases. Ann. Math. AI 19(1–2), 59–96 (1997)MATHGoogle Scholar
  4. 4.
    Eshghi, K., Kowalski, R.A.: Abduction compared with negation by failure. In: Levi, G., Martelli, M. (eds.) ICLP 1989, pp. 234–254. MIT Press (1989)Google Scholar
  5. 5.
    Fages, F.: Consistency of clark’s completion and existence of stable models. Methods Logic CS 1(1), 51–60 (1994)Google Scholar
  6. 6.
    Gebser, M., Kaufmann, B., Kaminski, R., Ostrowski, M., Schaub, T., Schneider, M.T.: Potassco: the Potsdam answer set solving collection. AI Commun. 24(2), 107–124 (2011)MATHMathSciNetGoogle Scholar
  7. 7.
    Gebser, M., Pührer, J., Schaub, T., Tompits, H.: A meta-programming technique for debugging answer-set programs. In: Fox, D., Gomes, C.P. (eds.) AAAI 2008, pp. 448–453. AAAI Press (2008)Google Scholar
  8. 8.
    Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Gener. Comput. 9(3–4), 365–385 (1991)CrossRefGoogle Scholar
  9. 9.
    Inoue, K.: Studies on Abductive and Nonmonotonic Reasoning. Ph.D. thesis, Kyoto University (1993)Google Scholar
  10. 10.
    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. Logic 7(3), 499–562 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Niemelä, I., Simons, P., Syrjänen, T.: Smodels: A system for answer set programming. In: Baral, C., Truszczynski, M. (eds.) NMR 2000, vol. cs.AI/0003033. CoRR (2000)Google Scholar
  12. 12.
    Oetsch, J., Pührer, J., Tompits, H.: Catching the ouroboros: on debugging non-ground answer-set programs. TPLP 10(4–6), 513–529 (2010)MATHGoogle Scholar
  13. 13.
    Oetsch, J., Pührer, J., Tompits, H.: Stepping through an answer-set program. In: Delgrande, J.P., Faber, W. (eds.) LPNMR 2011. LNCS, vol. 6645, pp. 134–147. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  14. 14.
    Pontelli, E., Son, T.C., Elkhatib, O.: Justifications for logic programs under answer set semantics. TPLP 9(1), 1–56 (2009)MATHMathSciNetGoogle Scholar
  15. 15.
    Przymusinski, T.C.: Stable semantics for disjunctive programs. New Gener. Comput. 9(3–4), 401–424 (1991)CrossRefGoogle Scholar
  16. 16.
    Schulz, C., Toni, F.: Justifying answer sets using argumentation. TPLP FirstView, 1–52 (2015)Google Scholar
  17. 17.
    Syrjänen, T.: Debugging inconsistent answer set programs. In: Dix, J., Hunter, A. (eds.) NMR 2006. Technical report Series, vol. IfI-06-04, pp. 77–83. Clausthal University of Technology, Institute of Informatics (2006)Google Scholar
  18. 18.
    Van Gelder, A.: The alternating fixpoint of logic programs with negation. J. Comput. Syst. Sci. 47(1), 185–221 (1993)MATHCrossRefGoogle Scholar
  19. 19.
    Van Gelder, A., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. J. ACM 38(3), 619–649 (1991)CrossRefGoogle Scholar
  20. 20.
    You, J.H., Yuan, L.Y.: A three-valued semantics for deductive databases and logic programs. J. Comput. Syst. Sci. 49(2), 334–361 (1994)MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of ComputingImperial College LondonLondonUK
  2. 2.National Institute of InformaticsTokyoJapan

Personalised recommendations