A Distributed and Clustering-Based Algorithm for the Enumeration Problem in Abstract Argumentation

  • Sylvie Doutre
  • Mickaël Lafages
  • Marie-Christine Lagasquie-SchiexEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11873)


Computing acceptability semantics of abstract argumentation frameworks is receiving increasing attention. Large-scale instances, with a clustered structure, have shown particularly difficult to compute. This paper presents a distributed algorithm, AFDivider, that enumerates the acceptable sets under several labelling-based semantics. This algorithm starts with cutting the argumentation framework into clusters thanks to a spectral clustering method, before computing simultaneously in each cluster parts of the labellings. This algorithm is proven to be sound and complete for the stable, complete and preferred semantics, and empirical results are presented.


Abstract argumentation Algorithms Clustering Enumeration 


  1. 1.
    Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(1), 47 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Alfano, G., Greco, S., Parisi, F.: Efficient computation of extensions for dynamic abstract argumentation frameworks: an incremental approach. In: IJCAI, pp. 49–55 (2017)Google Scholar
  3. 3.
    Alviano, M.: The pyglaf argumentation reasoner. In: OASIcs-OpenAccess Series in Informatics, vol. 58 (2018)Google Scholar
  4. 4.
    Barabási, A.L., et al.: Network Science. Cambridge University Press, Cambridge (2016)zbMATHGoogle Scholar
  5. 5.
    Baroni, P., Boella, G., Cerutti, F., Giacomin, M., van der Torre, L.W.N., Villata, S.: On input/output argumentation frameworks. In: COMMA, pp. 358–365 (2012)Google Scholar
  6. 6.
    Baroni, P., Caminada, M., Giacomin, M.: An introduction to argumentation semantics. Knowl. Eng. Rev. 26(4), 365–410 (2011)CrossRefGoogle Scholar
  7. 7.
    Baroni, P., Cerutti, F., Giacomin, M., Guida, G.: AFRA: argumentation framework with recursive attacks. Int. J. Approximate Reasoning 52(1), 19–37 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Baroni, P., Giacomin, M., Liao, B.: Locality and modularity in abstract argumentation. In: Handbook of Formal Argumentation, pp. 937–979. College Publication (2018)Google Scholar
  9. 9.
    Baroni, P., Boella, G., Cerutti, F., Giacomin, M., Van Der Torre, L., Villata, S.: On the input/output behavior of argumentation frameworks. Artif. Intell. 217, 144–197 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Baroni, P., Giacomin, M., Liao, B.: On topology-related properties of abstract argumentation semantics. a correction and extension to dynamics of argumentation systems: a division-based method. Artif. Intell. 212, 104–115 (2014)Google Scholar
  11. 11.
    Baumann, R., Brewka, G., Wong, R.: Splitting argumentation frameworks: an empirical evaluation. In: Modgil, S., Oren, N., Toni, F. (eds.) TAFA 2011. LNCS (LNAI), vol. 7132, pp. 17–31. Springer, Heidelberg (2012). Scholar
  12. 12.
    Bistarelli, S., Rossi, F., Santini, F.: Not only size, but also shape counts: abstract argumentation solvers are benchmark-sensitive. J. Log. Comput. 28(1), 85–117 (2018)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Bistarelli, S., Santini, F., Kotthoff, L., Mantadelis, T., Taticchi, C.: Int. Competition on Computational Models of Argumentation (2019).
  14. 14.
    Butterworth, J., Dunne, P.: Spectral techniques in argumentation framework analysis. COMMA 287, 167 (2016)Google Scholar
  15. 15.
    Caminada, M.: On the issue of reinstatement in argumentation. In: JELIA, pp. 111–123 (2006)Google Scholar
  16. 16.
    Carrera, Á., Iglesias, C.A.: A systematic review of argumentation techniques for multi-agent systems research. Artif. Intell. Rev. 44(4), 509–535 (2015)CrossRefGoogle Scholar
  17. 17.
    Cayrol, C., Lagasquie-Schiex, M.C.: On the acceptability of arguments in bipolar argumentation frameworks. In: Godo, L. (ed.) ECSQARU, pp. 378–389 (2005)Google Scholar
  18. 18.
    Cerutti, F., Giacomin, M., Vallati, M., Zanella, M.: An SCC recursive meta-algorithm for computing preferred labellings in abstract argumentation. In: KR (2014)Google Scholar
  19. 19.
    Cerutti, F., Tachmazidis, I., Vallati, M., Batsakis, S., Giacomin, M., Antoniou, G.: Exploiting parallelism for hard problems in abstract argumentation. In: AAAI, pp. 1475–1481 (2015)Google Scholar
  20. 20.
    Cerutti, F., Vallati, M., Giacomin, M., Zanetti, T.: ArgSemSAT-2017 (2017)Google Scholar
  21. 21.
    Charwat, G., Dvořák, W., Gaggl, S.A., Wallner, J.P., Woltran, S.: Methods for solving reasoning problems in abstract argumentation-a survey. Artif. Intell. 220, 28–63 (2015)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Corea, C., Thimm, M.: Using matrix exponentials for abstract argumentation. In: SAFA Workshop, pp. 10–21 (2016)Google Scholar
  23. 23.
    Dung, P.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and \(n\)-person games. Artif. Intell. 77, 321–357 (1995)Google Scholar
  24. 24.
    Dvořák, W., Pichler, R., Woltran, S.: Towards fixed-parameter tractable algorithms for abstract argumentation. Artif. Intell. 186, 1–37 (2012)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Kröll, M., Pichler, R., Woltran, S.: On the complexity of enumerating the extensions of abstract argumentation frameworks. In: IJCAI, pp. 1145–1152 (2017)Google Scholar
  26. 26.
    Lagniez, J.M., Lonca, E., Mailly, J.G.: CoQuiAAS v3.0. ICCMA 2019 Solver Description (2019)Google Scholar
  27. 27.
    Liao, B.: Toward incremental computation of argumentation semantics: a decomposition-based approach. Ann. Math. Artif. Intell. 67(3–4), 319–358 (2013)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Liao, B., Huang, H.: Partial semantics of argumentation: basic properties and empirical. J. Logic Comput. 23(3), 541–562 (2013)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Liao, B., Jin, L., Koons, R.C.: Dynamics of argumentation systems: a division-based method. Artif. Intell. 175(11), 1790–1814 (2011)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Lloyd, S.: Least squares quantization in PCM. IEEE Trans. Inf. Theory 28(2), 129–137 (1982)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Malliaros, F.D., Vazirgiannis, M.: Clustering and community detection in directed networks: a survey. Phys. Rep. 533(4), 95–142 (2013)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Niskanen, A., Järvisal, M.: \(\mu \)-toksia. Participating in ICCMA 2019 (2019)Google Scholar
  33. 33.
    Robert, M.K.: Elementary linear algebra. University of Queenland (2013)Google Scholar
  34. 34.
    Rodrigues, O., Black, E., Luck, M., Murphy, J.: On structural properties of argumentation frameworks: lessons from ICCMA. In: SAFA Workshop, pp. 22–35 (2018) Google Scholar
  35. 35.
    Schaeffer, S.E.: Graph clustering. Comput. Sci. Rev. 1(1), 27–64 (2007)CrossRefGoogle Scholar
  36. 36.
    Von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Xu, Y., Cayrol, C.: Initial sets in abstract argumentation frameworks. J. Appl. Non-Classical Logics 28(2–3), 260–279 (2018)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sylvie Doutre
    • 1
  • Mickaël Lafages
    • 1
  • Marie-Christine Lagasquie-Schiex
    • 1
    Email author
  1. 1.IRIT, UT1-UT3ToulouseFrance

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