Algorithms for Acceptance in Argument Systems

Samer Nofal, Paul Dunne, Katie Atkinson


We introduce algorithms that decide arguments’ acceptance in Dung’s system of argumentation. Under \emph{preferred} semantics, there might be various extensions of acceptable arguments, and hence, the acceptance problem is concerned with deciding whether a given argument is in an extension or in all extensions. The new algorithms decide the acceptance without truly enumerating all extensions. This is of interest in situations where the acceptance problem is confined to a specific argument while the underlying argument system changes frequently such as in a dialog setting. We analyze our algorithms in contrast to existing algorithms. Consistent with experimental results, we argue that the new algorithms are more efficient with respect to running time.


  1. Amgoud, L. and Devred, C. (2011). Argumentation frameworks as constraint satisfaction problems. In SUM, pages 110-122.
  2. Amgoud, L. and Prade, H. (2009). Using arguments for making and explaining decisions. Artificial Intelligence Journal, 173:413-436.
  3. Baroni, P., Caminada, M., and Giacomin, M. (2011). An introduction to argumentation semantics. The Knowledge Engineering Review, 26(4):365-410.
  4. Baumann, R., Brewka, G., and Wong, R. (2011). Splitting argumentation frameworks: An empirical evaluation. In TAFA, pages 17-31.
  5. Bench-Capon, T. (2003). Persuasion in practical argument using value-based argumentation frameworks. Logic and Computation, 13(3):429-448.
  6. Besnard, P. and Doutre, S. (2004). Checking the acceptability of a set of arguments. In NMR, pages 59-64.
  7. Caminada, M. (2007). An algorithm for computing semistable semantics. In ECSQARU, pages 222 - 234.
  8. Caminada, M. (2010). An algorithm for stage semantics. In COMMA, pages 147-158.
  9. Cayrol, C., Doutre, S., and Mengin, J. (2003). On decision problems related to the preferred semantics for argumentation frameworks. Logic and Computation, 13(3):377-403.
  10. Dimopoulos, Y., Nebel, B., and Toni, F. (2000). Finding admissible and preferred arguments can be very hard. In KR, pages 53-61.
  11. Doutre, S. and Mengin, J. (2001). Preferred extensions of argumentation frameworks: Query, answering, and computation. In IJCAR, pages 272-288.
  12. Doutre, S. and Mengin, J. (2004). On sceptical versus credulous acceptance for abstract argument systems. In JELIA, pages 462-473.
  13. Dung, P. (1995). On the acceptability of arguments and its fundamental role in non monotonic reasoning, logic programming and n-person games. Artificial Intelligence, 77(2):321-357.
  14. Dung, P., Mancarella, P., and Toni, F. (2007). Computing ideal skeptical argumentation. Artificial Intelligence, 171(10-15):642-674.
  15. Dunne, P. (2007). Computational properties of argument systems satisfying graph-theoretic constraints. Artificial Intelligence, 171:701-729.
  16. Dunne, P. E. and Bench-Capon, T. J. M. (2003). Two party immediate response disputes: Properties and efficiency. Artificial Intelligence, 149(2):221-250.
  17. Dvorak, W., Jarvisalo, M., Wallner, J., and Woltran, S. (2012). Complexity-sensitive decision procedures for abstract argumentation. In KR.
  18. Dvorák, W., Pichler, R., and Woltran, S. (2012). Towards fixed-parameter tractable algorithms for abstract argumentation. Artificial Intelligence, 186:1-37.
  19. Egly, U., Gaggl, S. A., and Woltran, S. (2008). Aspartix: Implementing argumentation frameworks using answer-set programming. In ICLP, pages 734-738.
  20. Gaertner, D. and Toni, F. (2007). Casapi: a system for credulous and sceptical argumentation. In NMR, pages 80- 95.
  21. Jakobovits, H. and Vermeir, D. (1999). Dialectic semantics for argumentation frameworks. In ICAIL, pages 53- 62.
  22. Li, H., Oren, N., and Norman, T. (2011). Probabilistic argumentation frameworks. In TAFA, pages 1-16.
  23. Liao, B. S., Jin, L., and Koons, R. C. (2011). Dynamics of argumentation systems: A division-based method. Artif. Intell., 175(11):1790-1814.
  24. Martinez, D., Garcia, A., and Simari, G. (2008). An abstract argumentation framework with varied-strength attacks. In KR, pages 135-143.
  25. McBurney, P. and Parsons, S. (2009). Dialogue games for agent argumentation. In Simari, G. and Rahwan, I., editors, Argumentation in Artificial Intelligence, pages 261-280. Springer.
  26. Modgil, S. (2009). Labellings and games for extended argumentation frameworks. In IJCAI, pages 873-878.
  27. Modgil, S. and Caminada, M. (2009). Proof theories and algorithms for abstract argumentation frameworks. In Rahwan, I. and Simari, G. R., editors, Argumentation in AI, pages 105-129. Springer.
  28. Mozina, M., Zabkar, J., and Bratko, I. (2007). Argument based machine learning. Artificial Intelligence, 171:922-937.
  29. Nieves, J., Cortes, U., and Osorio, M. (2008). Preferred extensions as stable models. Theory and Practice of Logic Programming, 8(4):527-543.
  30. Nofal, S., Dunne, P., and Atkinson, K. (2012). On preferred extension enumeration in abstract argumentation. In COMMA, to appear.
  31. Ordyniak, S. and Szeider, S. (2011). Augmenting tractable fragments of abstract argumentation. In IJCAI, pages 1033-1038.
  32. South, M., Vreeswijk, G., and Fox, J. (2008). Dungine: A java dung reasoner. In COMMA, pages 360-368.
  33. Thang, P., Dung, P., and Hung, N. (2009). Towards a common framework for dialectical proof procedures in abstract argumentation. Logic and Computation, pages 1071-1109.
  34. Verheij, B. (1996). Two approaches to dialectical argumentation: admissible sets and argumentation stages. In The Eighth Dutch Conference on AI, pages 357-368.
  35. Verheij, B. (2007). A labeling approach to the computation of credulous acceptance in argumentation. In IJCAI, pages 623-628.
  36. Vreeswijk, G. (2006). An algorithm to compute minimally grounded and admissible defence sets in argument systems. In COMMA, pages 109-120.
  37. Vreeswijk, G. and Prakken, H. (2000). Credulous and sceptical argument games for preferred semantics. In JELIA, pages 239-253.

Paper Citation

in Harvard Style

Nofal S., Dunne P. and Atkinson K. (2013). Algorithms for Acceptance in Argument Systems . In Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-8565-39-6, pages 34-43. DOI: 10.5220/0004192400340043

in Bibtex Style

author={Samer Nofal and Paul Dunne and Katie Atkinson},
title={Algorithms for Acceptance in Argument Systems},
booktitle={Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

in EndNote Style

JO - Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - Algorithms for Acceptance in Argument Systems
SN - 978-989-8565-39-6
AU - Nofal S.
AU - Dunne P.
AU - Atkinson K.
PY - 2013
SP - 34
EP - 43
DO - 10.5220/0004192400340043