Computing Preferred Extensions in Abstract Argumentation: A SAT-Based Approach

  • Federico Cerutti
  • Paul E. Dunne
  • Massimiliano Giacomin
  • Mauro Vallati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8306)


This paper presents a novel SAT-based approach for the computation of extensions in abstract argumentation, with focus on preferred semantics, and an empirical evaluation of its performances. The approach is based on the idea of reducing the problem of computing complete extensions to a SAT problem and then using a depth-first search method to derive preferred extensions. The proposed approach has been tested using two distinct SAT solvers and compared with three state-of-the-art systems for preferred extension computation. It turns out that the proposed approach delivers significantly better performances in the large majority of the considered cases.


Constraint Satisfaction Problem Conjunctive Normal Form Abstract Argumentation Argumentation Framework Complete Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Amgoud, L., Devred, C.: Argumentation frameworks as constraint satisfaction problems. Annals of Mathematics and Artificial Intelligence, 1–18 (2013)Google Scholar
  2. 2.
    Ansótegui, C., Bonet, M.L., Levy, J.: SAT-based MaxSAT. Artificial Intelligence 196, 77–105 (2013)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: Proceedings of IJCAI 2009, pp. 399–404 (2009)Google Scholar
  4. 4.
    Audemard, G., Simon, L.: Glucose 2.1 (2012),
  5. 5.
    Baroni, P., Caminada, M., Giacomin, M.: An introduction to argumentation semantics. Knowledge Engineering Review 26(4), 365–410 (2011)CrossRefGoogle Scholar
  6. 6.
    Baroni, P., Giacomin, M.: Semantics of abstract argumentation systems. In: Argumentation in Artificial Intelligence, pp. 25–44. Springer (2009)Google Scholar
  7. 7.
    Baroni, P., Giacomin, M., Guida, G.: SCC-recursiveness: a general schema for argumentation semantics. Artificial Intelligence 168(1-2), 165–210 (2005)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Baroni, P., Cerutti, F., Dunne, P.E., Giacomin, M.: Automata for infinite argumentation structures. Artificial Intelligence 203, 104–150 (2013)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Besnard, P., Doutre, S.: Checking the acceptability of a set of arguments. In: Proceedings of NMR 2004, pp. 59–64 (2004)Google Scholar
  10. 10.
    Biere, A.: P{re,ic}oSAT@sc 2009. In: SAT Competition (2009)Google Scholar
  11. 11.
    Bistarelli, S., Santini, F.: Modeling and solving AFs with a constraint-based tool: Conarg. In: Modgil, S., Oren, N., Toni, F. (eds.) TAFA 2011. LNCS (LNAI), vol. 7132, pp. 99–116. Springer, Heidelberg (2012)Google Scholar
  12. 12.
    Caminada, M.: On the issue of reinstatement in argumentation. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds.) JELIA 2006. LNCS (LNAI), vol. 4160, pp. 111–123. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Caminada, M.: Semi-stable semantics. In: Proceedings of COMMA 2006, pp. 121–130 (2006)Google Scholar
  14. 14.
    Caminada, M., Gabbay, D.M.: A logical account of formal argumentation. Studia Logica (Special Issue: New Ideas in Argumentation Theory) 93(2-3), 109–145 (2009)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Cerutti, F., Dunne, P.E., Giacomin, M., Vallati, M.: Computing Preferred Extensions in Abstract Argumentation: a SAT-based Approach. Tech. rep. (2013),
  16. 16.
    Dimopoulos, Y., Nebel, B., Toni, F.: Preferred arguments are harder to compute than stable extensions. In: Proceedings of IJCAI 1999, pp. 36–43 (1999)Google Scholar
  17. 17.
    Dimopoulos, Y., Torres, A.: Graph theoretical structures in logic programs and default theories. Journal Theoretical Computer Science 170, 209–244 (1996)MATHMathSciNetGoogle Scholar
  18. 18.
    Doutre, S., Mengin, J.: Preferred extensions of argumentation frameworks: Query answering and computation. In: Goré, R., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 272–288. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  19. 19.
    Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming, and n-person games. Artificial Intelligence 77(2), 321–357 (1995)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Dung, P., Mancarella, P., Toni, F.: A dialectic procedure for sceptical, assumption-based argumentation. In: Proceedings of COMMA 2006, pp. 145–156 (2006)Google Scholar
  21. 21.
    Dunne, P.E., Wooldridge, M.: Complexity of abstract argumentation. In: Argumentation in Artificial Intelligence, pp. 85–104. Springer (2009)Google Scholar
  22. 22.
    Dvǒrák, W., Gaggl, S.A., Wallner, J., Woltran, S.: Making use of advances in answer-set programming for abstract argumentation systems. In: Proceedings of INAP 2011 (2011)Google Scholar
  23. 23.
    Dvǒrák, W., Järvisalo, M., Wallner, J.P., Woltran, S.: Complexity-sensitive decision procedures for abstract argumentation. In: Proceedings of KR 2012. AAAI Press (2012)Google Scholar
  24. 24.
    Egly, U., Gaggl, S.A., Woltran, S.: Aspartix: Implementing argumentation frameworks using answer-set programming. In: de la Garcia Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 734–738. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  25. 25.
    Jiménez, S., de la Rosa, T., Fernández, S., Fernández, F., Borrajo, D.: A review of machine learning for automated planning. Knowledge Engineering Review 27(4), 433–467 (2012)CrossRefGoogle Scholar
  26. 26.
    Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV system for knowledge representation and reasoning. ACM Transactions on Computational Logic 7(3), 499–562 (2006)Google Scholar
  27. 27.
    Modgil, S., Caminada, M.: Proof theories and algorithms for abstract argumentation frameworks. In: Argumentation in Artificial Intelligence, pp. 105–129. Springer (2009)Google Scholar
  28. 28.
    Nofal, S., Dunne, P.E., Atkinson, K.: On preferred extension enumeration in abstract argumentation. In: Proceedings of COMMA 2012, pp. 205–216 (2012)Google Scholar
  29. 29.
    South, M., Vreeswijk, G., Fox, J.: Dungine: A Java Dung reasoner. In: Proceedings of COMMA 2008, pp. 360–368 (2008)Google Scholar
  30. 30.
    Wallner, J.P., Weissenbacher, G., Woltran, S.: Advanced SAT techniques for abstract argumentation. In: Leite, J., Son, T.C., Torroni, P., van der Torre, L., Woltran, S. (eds.) CLIMA XIV 2013. LNCS (LNAI), vol. 8143, pp. 138–154. Springer, Heidelberg (2013)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Federico Cerutti
    • 1
  • Paul E. Dunne
    • 2
  • Massimiliano Giacomin
    • 3
  • Mauro Vallati
    • 4
  1. 1.School of Natural and Computing Science, King’s CollegeUniversity of AberdeenAberdeenUnited Kingdom
  2. 2.Department of Computer Science, Ashton BuildingUniversity of LiverpoolLiverpoolUnited Kingdom
  3. 3.Department of Information EngineeringUniversity of BresciaBresciaItaly
  4. 4.School of Computing and EngineeringUniversity of HuddersfieldHuddersfieldUnited Kingdom

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