Reduction-Based Approaches to Implement Modgil’s Extended Argumentation Frameworks

  • Wolfgang Dvořák
  • Sarah Alice Gaggl
  • Thomas Linsbichler
  • Johannes Peter Wallner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9060)


This paper reconsiders Modgil’s Extended Argumentation Frameworks (EAFs) that extend Dung’s abstract argumentation frameworks by attacks on attacks. This allows to encode preferences directly in the framework and thus also to reason about the preferences themselves. As a first step to reduction-based approaches to implement EAFs, we give an alternative (but equivalent) characterization of acceptance in EAFs. Then we use this characterization to provide EAF encodings for answer set programming and propositional logic. Moreover, we address an open complexity question and the expressiveness of EAFs.


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  1. 1.
    Amgoud, L., Cayrol, C.: A reasoning model based on the production of acceptable arguments. Ann. Math. Artif. Intell. 34(1-3), 197–215 (2002)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Baroni, P., Caminada, M.W.A., Giacomin, M.: An introduction to argumentation semantics. Knowledge Eng. Review 26(4), 365–410 (2011)CrossRefGoogle Scholar
  3. 3.
    Bench-Capon, T.J.M.: Persuasion in practical argument using value-based argumentation frameworks. J. Log. Comput. 13(3), 429–448 (2003)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Besnard, P., Doutre, S.: Checking the acceptability of a set of arguments. In: Proc. NMR, pp. 59–64 (2004)Google Scholar
  5. 5.
    Brewka, G., Woltran, S.: Abstract Dialectical Frameworks. In: Proc. KR 2010, pp. 102–111. AAAI Press (2010)Google Scholar
  6. 6.
    Brewka, G., Eiter, T., Truszczyński, M.: Answer set programming at a glance. Commun. ACM 54(12), 92–103 (2011)CrossRefGoogle Scholar
  7. 7.
    Brewka, G., Ellmauthaler, S., Strass, H., Wallner, J.P., Woltran, S.: Abstract Dialectical Frameworks Revisited. In: Proc. IJCAI, pp. 803–809. AAAI Press / IJCAI (2013)Google Scholar
  8. 8.
    Cerutti, F., Dunne, P.E., Giacomin, M., Vallati, M.: Computing preferred extensions in abstract argumentation: A SAT-based approach. In: Black, E., Modgil, S., Oren, N. (eds.) TAFA 2013. LNCS, vol. 8306, pp. 176–193. Springer, Heidelberg (2014)Google Scholar
  9. 9.
    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)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Dunne, P.E., Bench-Capon, T.J.M.: Coherence in finite argument systems. Artif. Intell. 141(1/2), 187–203 (2002)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Dunne, P.E., Dvořák, W., Linsbichler, T., Woltran, S.: Characteristics of multiple viewpoints in abstract argumentation. In: Proc. KR, pp. 72–81. AAAI Press (2014)Google Scholar
  12. 12.
    Dunne, P.E., Modgil, S., Bench-Capon, T.J.M.: Computation in extended argumentation frameworks. In: Proc. ECAI, pp. 119–124. IOS Press (2010)Google Scholar
  13. 13.
    Dvořák, W., Järvisalo, M., Wallner, J.P., Woltran, S.: Complexity-sensitive decision procedures for abstract argumentation. Artif. Intell. 206, 53–78 (2014)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Dvořák, W., Szeider, S., Woltran, S.: Abstract argumentation via monadic second order logic. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds.) SUM 2012. LNCS, vol. 7520, pp. 85–98. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  15. 15.
    Egly, U., Gaggl, S.A., Woltran, S.: Answer-Set Programming Encodings for Argumentation Frameworks. Argument and Computation 1(2), 147–177 (2010)CrossRefMATHGoogle Scholar
  16. 16.
    Egly, U., Woltran, S.: Reasoning in argumentation frameworks using Quantified Boolean Formulas. In: Proc. COMMA, pp. 133–144. IOS Press (2006)Google Scholar
  17. 17.
    Gebser, M., Kaminski, R., Kaufmann, B., Ostrowski, M., Schaub, T., Schneider, M.: Potassco: The Potsdam Answer Set Solving Collection. AI Communications 24(2), 105–124 (2011)MathSciNetMATHGoogle Scholar
  18. 18.
    Modgil, S.: Reasoning about preferences in argumentation frameworks. Artif. Intell. 173(9-10), 901–934 (2009)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Modgil, S., Prakken, H.: A general account of argumentation with preferences. Artif. Intell. 195, 361–397 (2013)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Niemelä, I.: Logic Programming with Stable Model Semantics as a Constraint Programming Paradigm. Ann. Math. Artif. Intell. 25(3-4), 241–273 (1999)CrossRefMATHGoogle Scholar
  21. 21.
    Nofal, S., Dunne, P.E., Atkinson, K.: Towards experimental algorithms for abstract argumentation. In: Proc. COMMA, pp. 217–228. IOS Press (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Wolfgang Dvořák
    • 1
  • Sarah Alice Gaggl
    • 2
  • Thomas Linsbichler
    • 3
  • Johannes Peter Wallner
    • 3
  1. 1.Faculty of Computer ScienceUniversity of ViennaAustria
  2. 2.Computational Logic GroupTechnische Universität DresdenGermany
  3. 3.Institute of Information SystemsVienna University of TechnologyAustria

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