Skip to main content
SpringerLink
Log in

Toward incremental computation of argumentation semantics: A decomposition-based approach

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

Currently, except some classes of argumentation frameworks (with special topologies or fixed parameters, such as acyclic, symmetric, and bounded tree-width, etc.) that have been clearly identified as tractable, for a generic argumentation framework (also called a defeat graph), how to efficiently compute its semantics is still a challenging problem. Inspired by the local tractability of an argumentation framework, we first propose a decomposition-based approach, and then conduct an empirical investigation. Given a generic argumentation framework, it is firstly decomposed into a set of sub-frameworks that are located in a number of layers. Then, the semantics of an argumentation framework are computed incrementally, from the lowest layer in which each sub-framework is not restricted by other sub-frameworks, to the highest layer in which each sub-framework is most restricted by the sub-frameworks located in the lower layers. In each iteration, the semantics of each sub-framework is computed locally, while the combination of semantics of a set of sub-frameworks is performed in two dimensions: horizontally and vertically. The average results show that when the ratio of the number of edges to the number of nodes of a defeat graph is less than 1.5:1, the decomposition-based approach is obviously efficient.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Liao, B., Huang, H.: Computing the extensions of an argumentation framework based on its strongly connected components. In: Proceedings of ICTAI (2012)

  2. Bench-Capon, T., Dunne, P.E.: Argumentation in artificial intelligence. Artif. Intell. 171, 619–641 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dunne, P.: Computational properties of argument systems satisfying graph-theoretic constraints. Artif. Intell. 171, 701–729 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dunne, 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)

    Article  Google Scholar 

  5. Coste-Marquis, S., Devred, C., Marquis, P.: Symmetric argumentation frameworks. In: Proceedings of the ECSQARU 2005, LNAI, vol. 3571, pp. 317–328. Springer (2005)

  6. Dvořák, W., Pichler, R., Woltran, S.: Towards fixed-parameter tractable algorithms for argumentation. In: Proceedings of the KR 2010, pp. 112–122. AAAI Press (2010)

  7. Cayrol, C., Doutre, S., Mengin, J.: On decision problems related to the preferred semantics for argumentation frameworks. J. Logic Comput. 13, 377–403 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Caminada, M.: An algorithm for computing semi-stable semantics. In: Proceedings of the ECSQARU 2007, LNAI, vol. 4724, pp. 222–234. Springer (2007)

  9. Dung, P., Kowalski, R., Toni, F.: Dialectic proof procedures for assumption-based, admissible argumentation. Artif. Intell. 170, 114–159 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dung, P., Thang, P.: A sound and complete dialectical proof procedure for sceptical preferred argumentation. In: Proceedings of the ArgNMR@LPNMR, pp. 49–63 (2007)

  11. Dung, P., Mancarella, P., Toni, F.: Computing ideal sceptical argumentation. Artif. Intell. 171, 642–674 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Modgil, S., Caminada, M.: Proof theories and algorithms for abstract argumentation frameworks. In: Rahwan, I., Simari, G.R. (eds.) Argumentation in Artificial Intelligence, pp. 105–129. Springer (2009)

  13. Egly, U., Gaggl, S., Woltran, S.: Aspartix: Implementing argumentation frameworks using answer-set programming. In: Proceedings of the ICLP 2008, LNCS 5366, pp. 734–738. Springer (2009)

  14. Nieves, J., Cortés, U., Osorio, M.: Preferred extensions as stable models. Theory Pract. Log. Program. 8, 527–543 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wakaki, T., Nitta, K.: Computing argumentation semantics in answer set programming. In: Proceedings of the JSAI 2008, LNAI, vol. 5447, pp. 254–269. Springer (2009)

  16. Kim, E., Ordyniak, S., Szeider, S.: Algorithms and complexity results for persuasive argumentation. Artif. Intell. 175, 1722–1736 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Coste-Marquis, S., Devred, C., Konieczny, S., Lagasquie-Schiex, M., Marquis, P.: On the merging of dung’s argumentation systems. Artif. Intell. 171, 730–753 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Baroni, P., Giacomin, M., Guida, G.: Scc-recursiveness: a general schema for argumentation semantics. Artif. Intell. 168, 162–210 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  19. Baroni, P., Giacomin, M.: On principle-based evaluation of extension-based argumentation semantics. Artif. Intell. 171, 675–700 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Caminada, M.: Semi-stable semantics. In: Proceedings of the COMMA 2006, pp. 121–130. IOS Press (2006)

  21. Coste-Marquis, S., Devred, C., Marquis, P.: Prudent semantics for argumentation frameworks. In: Proceedings of the ICTAI 2005, pp. 568–572. IEEE Computer Society (2005)

  22. Baroni, P., Caminada, M., Giacomin, M.: An introduction to argumentation semantics. Knowl. Eng. Rev. 26, 365–410 (2011)

    Article  Google Scholar 

  23. Jakobovits, H., Vermeir, D.: Robust semantics for argumentation frameworks. J. Logic Comput. 9, 215–261 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. Caminada, M.: On the issue of reinstatement in argumentation. In: Proceedings of the JELIA, LNCS, vol. 4160, pp. 111–123. Springer, Heidelberg (2006)

    Google Scholar 

  25. Caminada, M., Gabbay, D.: A logical account of formal argumentation. Studia Logica 93, 109–145 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. Caminada, M.: A labelling approach for ideal and stage semantics. Argument and Computation 1, 1–21 (2011)

    Article  Google Scholar 

  27. Liao, B., Jin, L., Koons, R.: Dynamics of argumentation systems: A division-based method. Artif. Intell. 175, 1790–1814 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. Tarjan, R.: Depth-first search and linear graph algorithms. SIAM J. Comput. 1, 146–160 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  29. Dasgupta, S., Papadimitriou, C.H., Vazirani, U.V.: Algorithms. McGraw-Hill, New York (2006)

    Google Scholar 

  30. Verheij, B.: Two approaches to dialectical argumentation: Admissible sets and argumentation stages. In: Proceedings of the 8th International Dutch Conference on Artificial Intelligence, pp. 357–368. Utrecht University (1996)

  31. Baumann, R., Brewka, G., Wong, R.: Splitting argumentation frameworks: An empirical evaluation. In: Proceedings of the 1st Int. Workshop on Theory and Applications of Formal Argumentation, LNAI 7132, pp. 17–31. Springer (2012)

  32. Nofal, S., Dunne, P., Atkinson, K.: On preferred extension enumeration in abstract argumentation. In: Proceedings of the COMMA 2012, pp. 205–216. IOS Press (2012)

  33. Dvořák, W., Szeider, S., Woltran, S.: Reasoning in argumentation frameworks of bounded clique-width. In: Proceedings of the COMMA 2010, pp. 219–230. IOS Press (2010)

  34. Dvořák, W., Ja̋rvisalo, M., Wallner, J.P., Woltran, S.: Complexity-sensitive decision procedures for abstract argumentation. In: Proceedings of the KR2012, pp. 54–64. AAAI Press (2012)

  35. Nofal, S., Dunne, P., Atkinson, K.: Towards experimental algorithms for abstract argumentation. In: Proceedings of the COMMA 2012, pp. 217–228. IOS Press (2012)

Download references

Author information

Authors and Affiliations

  1. Center for the Study of Language and Cognition, Department of Philosophy, Zhejiang University, Hangzhou, 310028, China

    Beishui Liao

Authors
  1. Beishui Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Beishui Liao.

Additional information

The basic idea of this paper has been introduced in [1].

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liao, B. Toward incremental computation of argumentation semantics: A decomposition-based approach. Ann Math Artif Intell 67, 319–358 (2013). https://doi.org/10.1007/s10472-013-9364-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-013-9364-8

Keywords

Search

Navigation