Making Use of Advances in Answer-Set Programming for Abstract Argumentation Systems

  • Wolfgang Dvořák
  • Sarah Alice Gaggl
  • Johannes Peter WallnerEmail author
  • Stefan Woltran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7773)


Dung’s famous abstract argumentation frameworks represent the core formalism for many problems and applications in the field of argumentation which significantly evolved within the last decade. Recent work in the field has thus focused on implementations for these frameworks, whereby one of the main approaches is to use Answer-Set Programming (ASP). While some of the argumentation semantics can be nicely expressed within the ASP language, others required rather cumbersome encoding techniques. Recent advances in ASP systems, in particular, the metasp optimization front-end for the ASP-package gringo/claspD provide direct commands to filter answer sets satisfying certain subset-minimality (or -maximality) constraints. This allows for much simpler encodings compared to the ones in standard ASP language. In this paper, we experimentally compare the original encodings (for the argumentation semantics based on preferred, semi-stable, and respectively, stage extensions) with new metasp encodings. Moreover, we provide novel encodings for the recently introduced resolution-based grounded semantics. Our experimental results indicate that the metasp approach works well in those cases where the complexity of the encoded problem is adequately mirrored within the metasp approach.


Abstract argumentation Answer-set programming Meta programming 


  1. 1.
    Baroni, P., Dunne, P.E., Giacomin, M.: On the resolution-based family of abstract argumentation semantics and its grounded instance. Artif. Intell. 175(3–4), 791–813 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Baroni, P., Giacomin, M.: Semantics of abstract argument systems. In: Rahwan, I., Simari, G.R. (eds.) Argumentation in Artificial Intelligence, pp. 25–44. Springer, Berlin (2009)CrossRefGoogle Scholar
  3. 3.
    Bench-Capon, T.J.M., Dunne, P.E.: Argumentation in artificial intelligence. Artif. Intell. 171(10–15), 619–641 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Caminada, M.: Semi-stable semantics. In: Proceedings of COMMA 2006, pp. 121–130 (2006)Google Scholar
  5. 5.
    Dantsin, E., Eiter, T., Gottlob, G., Voronkov, A.: Complexity and expressive power of logic programming. ACM Comput. Surv. 33(3), 374–425 (2001)CrossRefGoogle Scholar
  6. 6.
    Dimopoulos, Y., Torres, A.: Graph theoretical structures in logic programs and default theories. Theor. Comput. Sci. 170(1–2), 209–244 (1996)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77(2), 321–358 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Dunne, P.E., Bench-Capon, T.J.M.: Coherence in finite argument systems. Artif. Intell. 141(1/2), 187–203 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dunne, P.E., Caminada, M.: Computational complexity of semi-stable semantics in abstract argumentation frameworks. In: Hölldobler, S., Lutz, C., Wansing, H. (eds.) JELIA 2008. LNCS (LNAI), vol. 5293, pp. 153–165. Springer, Heidelberg (2008)Google Scholar
  10. 10.
    Dvořák, W., Woltran, S.: Complexity of semi-stable and stage semantics in argumentation frameworks. Inf. Process. Lett. 110(11), 425–430 (2010)CrossRefzbMATHGoogle Scholar
  11. 11.
    Egly, U., Gaggl, S.A., Woltran, S.: Answer-set programming encodings for argumentation frameworks. Argument Comput. 1(2), 147–177 (2010)CrossRefGoogle Scholar
  12. 12.
    Eiter, T., Gottlob, G.: On the computational cost of disjunctive logic programming: propositional case. Ann. Math. Artif. Intell. 15(3–4), 289–323 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Gebser, M., Kaminski, R., Schaub, T.: Complex optimization in answer set programming. Theory Pract. Logic Program. 11(4–5), 821–839 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Gebser, M., Kaufmann, B., Schaub, T.: Solution enumeration for projected boolean search problems. In: van Hoeve, W.J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 71–86. Springer, Heidelberg (2009)Google Scholar
  15. 15.
    Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Gener. Comput. 9(3/4), 365–386 (1991)CrossRefGoogle Scholar
  16. 16.
    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. Log. 7(3), 499–562 (2006)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Toni, F., Sergot, M.: Argumentation and answer set programming. In: Balduccini, M., Son, T.C. (eds.) Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning. LNCS (LNAI), vol. 6565, pp. 164–180. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  18. 18.
    Verheij, B.: Two approaches to dialectical argumentation: admissible sets and argumentation stages. In: Proc. NAIC’96, pp. 357–368 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Wolfgang Dvořák
    • 3
  • Sarah Alice Gaggl
    • 2
  • Johannes Peter Wallner
    • 1
    Email author
  • Stefan Woltran
    • 1
  1. 1.Institute of Information Systems, Database and Artificial Intelligence GroupVienna University of TechnologyWienAustria
  2. 2.Technische Universität DresdenInstitute of Artificial IntelligenceDresdenGermany
  3. 3.Faculty of Computer ScienceUniversity of ViennaWienAustria

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