Strong Equivalence for Argumentation Semantics Based on Conflict-Free Sets

  • Sarah Alice Gaggl
  • Stefan Woltran
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6717)


Argumentation can be understood as a dynamic reasoning process, i.e. it is in particular useful to know the effects additional information causes with respect to a certain semantics. Accordingly, one can identify the information which does not contribute to the results no matter which changes are performed. In other words, we are interested in so-called kernels of frameworks, where two frameworks with the same kernel are then “immune” to all kind of newly added information in the sense that they always produce an equal outcome. The concept of strong equivalence for argumentation frameworks captures this intuition and has been analyzed for several semantics which are all based on the concept of admissibility. Other important semantics have been neglected so far. To close this gap, we give strong equivalence results with respect to naive, stage and cf2 extensions, and we compare the new results with the already existing ones. Furthermore, we analyze strong equivalence for symmetric frameworks and discuss local equivalence, a certain relaxation of strong equivalence.


Abstract Argumentation Argumentation Framework Stage Extension Strong Equivalence Stable 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amgoud, L., Dimopoulos, Y., Moraitis, P.: Making Decisions through Preference-Based Argumentation. In: Proc. KR 2008, pp. 113–123. AAAI Press, Menlo Park (2008)Google Scholar
  2. 2.
    Amgoud, L., Vesic, S.: Handling Inconsistency with Preference-Based Argumentation. In: Deshpande, A., Hunter, A. (eds.) SUM 2010. LNCS, vol. 6379, pp. 56–69. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Baroni, P., Giacomin, M.: On Principle-based Evaluation of Extension-based Argumentation semantics. Artif. Intell. 171(10-15), 675–700 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Baroni, P., Giacomin, M., Guida, G.: SCC-Recursiveness: A General Schema for Argumentation Semantics. Artif. Intell. 168(1-2), 162–210 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Caminada, M.: Semi-Stable Semantics. In: Proc. COMMA 2006. FAIA, vol. 144, pp. 121–130. IOS Press, Amsterdam (2006)Google Scholar
  6. 6.
    Caminada, M., Amgoud, L.: On the Evaluation of Argumentation Formalisms. Artif. Intell. 171(5-6), 286–310 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Coste-Marquis, S., Devred, C., Marquis, P.: Symmetric Argumentation Frameworks. In: Godo, L. (ed.) ECSQARU 2005. LNCS (LNAI), vol. 3571, pp. 317–328. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dung, P.M., Mancarella, P., Toni, F.: Computing Ideal Sceptical Argumentation. Artif. Intell. 171(10-15), 642–674 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Gaggl, S.A., Woltran, S.: cf2 Semantics Revisited. In: Proc. COMMA 2010. FAIA, vol. 216, pp. 243–254. IOS Press, Amsterdam (2010)Google Scholar
  11. 11.
    Gaggl, S.A., Woltran, S.: Strong Equivalence for Argumentation Semantics based on Conflict-free Sets. Tech. Report DBAI-TR-2011-68, Technische Universität Wien (2011)Google Scholar
  12. 12.
    Oikarinen, E., Woltran, S.: Characterizing Strong Equivalence for Argumentation Frameworks. In: Proc. KR 2010, pp. 123–133. AAAI Press, Menlo Park (2010)Google Scholar
  13. 13.
    Verheij, B.: Two Approaches to Dialectical Argumentation: Admissible Sets and Argumentation Stages. In: Proc. NAIC 1996, pp. 357–368 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sarah Alice Gaggl
    • 1
  • Stefan Woltran
    • 1
  1. 1.Vienna University of TechnologyAustria

Personalised recommendations