International Workshop on Theorie and Applications of Formal Argumentation

Theory and Applications of Formal Argumentation pp 40-58 | Cite as

Abstract Solvers for Dung’s Argumentation Frameworks

  • Remi Brochenin
  • Thomas Linsbichler
  • Marco Maratea
  • Johannes Peter Wallner
  • Stefan Woltran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9524)


Abstract solvers are a quite recent method to uniformly describe algorithms in a rigorous formal way and have proven successful in declarative paradigms such as Propositional Satisfiability and Answer Set Programming. In this paper, we apply this machinery for the first time to a dedicated AI formalism, namely Dung’s abstract argumentation frameworks. We provide descriptions of several advanced algorithms for the preferred semantics in terms of abstract solvers and, moreover, show how slight adaptions thereof directly lead to new algorithms.


  1. 1.
    Baroni, P., Caminada, M.W.A., Giacomin, M.: An introduction to argumentation semantics. Knowl. Eng. Rev. 26(4), 365–410 (2011)CrossRefGoogle Scholar
  2. 2.
    Bench-Capon, T.J.M., Dunne, P.E.: Argumentation in artificial intelligence. Artif. Intell. 171(10–15), 619–641 (2007)MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Besnard, P., Doutre, S.: Checking the acceptability of a set of arguments. In: Delgrande, J.P., Schaub, T. (eds.) Proceedings of the 10th International Workshop on Non-Monotonic Reasoning, NMR 2004, pp. 59–64 (2004)Google Scholar
  4. 4.
    Brochenin, R., Lierler, Y., Maratea, M.: Abstract disjunctive answer set solvers. In: Schaub, T., Friedrich, G., O’Sullivan, B. (eds.) Proceedings of the 21st European Conference on Artificial Intelligence, ECAI 2014. FAIA, vol. 263, pp. 165–170. IOS Press (2014)Google Scholar
  5. 5.
    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
  6. 6.
    Cerutti, F., Giacomin, M., Vallati, M.: ArgSemSAT: Solving argumentation problems using SAT. In: Parsons, S., Oren, N., Reed, C., Cerutti, F. (eds.) Proceedings of the 5th International Conference on Computational Models of Argument, COMMA 2014. FAIA, vol. 266, pp. 455–456. IOS Press (2014)Google Scholar
  7. 7.
    Cerutti, F., Oren, N., Strass, H., Thimm, M., Vallati, M.: A benchmark framework for a computational argumentation competition. In: Parsons, S., Oren, N., Reed, C., Cerutti, F. (eds.) Proceedings of the 5th International Conference on Computational Models of Argument, COMMA 2014. FAIA, vol. 266, pp. 459–460. IOS Press (2014)Google Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    Davis, M., Logemann, G., Loveland, D.: A machine program for theorem proving. Commun. ACM 5(7), 394–397 (1962)MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Dimopoulos, Y., Torres, A.: Graph theoretical structures in logic programs and default theories. Theoret. Comput. Sci. 170(1–2), 209–244 (1996)MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Doutre, S., Mengin, J.: Preferred extensions of argumentation frameworks: query answering and computation. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 272–288. Springer, Heidelberg (2001) CrossRefGoogle Scholar
  12. 12.
    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)MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Dunne, P.E., Bench-Capon, T.J.M.: Coherence in finite argument systems. Artif. Intell. 141(1/2), 187–203 (2002)MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Dvořák, W., Järvisalo, M., Wallner, J.P., Woltran, S.: Complexity-sensitive decision procedures for abstract argumentation. Artif. Intell. 206, 53–78 (2014)CrossRefGoogle Scholar
  15. 15.
    Dvořák, W., Woltran, S.: Complexity of semi-stable and stage semantics in argumentation frameworks. Inf. Process. Lett. 110(11), 425–430 (2010)MATHCrossRefGoogle Scholar
  16. 16.
    Lierler, Y.: Abstract answer set solvers with backjumping and learning. Theory Pract. Log. Program. 11(2–3), 135–169 (2011)MATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Lierler, Y.: Relating constraint answer set programming languages and algorithms. Artif. Intell. 207, 1–22 (2014)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Modgil, S., Caminada, M.W.A.: Proof theories and algorithms for abstract argumentation frameworks. In: Rahwan, I., Simari, G.R. (eds.) Argumentation in Artificial Intelligence, pp. 105–129. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: From an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). J. ACM 53(6), 937–977 (2006)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Nofal, S., Atkinson, K., Dunne, P.E.: Algorithms for decision problems in argument systems under preferred semantics. Artif. Intell. 207, 23–51 (2014)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Rahwan, I., Simari, G.R. (eds.): Argumentation in Artificial Intelligence. Springer, Heidelberg (2009)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Remi Brochenin
    • 1
  • Thomas Linsbichler
    • 2
  • Marco Maratea
    • 1
  • Johannes Peter Wallner
    • 3
  • Stefan Woltran
    • 2
  1. 1.University of GenoaGenoaItaly
  2. 2.TU WienViennaAustria
  3. 3.HIIT, Department of Computer ScienceUniversity of HelsinkiHelsinkiFinland

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