Instantiating Knowledge Bases in Abstract Dialectical Frameworks

  • Hannes Strass
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8143)

Abstract

We present a translation from defeasible theory bases to abstract dialectical frameworks, a recent generalisation of abstract argumentation frameworks. Using several problematic examples from the literature, we first show how our translation addresses important issues of existing approaches. We then prove that the translated frameworks satisfy the rationality postulates closure and direct/indirect consistency. Furthermore, the frameworks can detect inconsistencies in the set of strict inference rules and cyclic (strict and defeasible) supports amongst literals. We also show that the translation involves at most a quadratic blowup and is therefore effectively and efficiently computable.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dung, P.M.: On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games. Artificial Intelligence 77, 321–358 (1995)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Caminada, M., Amgoud, L.: On the evaluation of argumentation formalisms. Artificial Intelligence 171(5-6), 286–310 (2007)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Wyner, A., Bench-Capon, T., Dunne, P.: Instantiating knowledge bases in abstract argumentation frameworks. In: Proceedings of the AAAI Fall Symposium – The Uses of Computational Argumentation (2009)Google Scholar
  4. 4.
    Brewka, G., Woltran, S.: Abstract Dialectical Frameworks. In: Proceedings of the Twelfth International Conference on the Principles of Knowledge Representation and Reasoning (KR), pp. 102–111 (2010)Google Scholar
  5. 5.
    Strass, H.: Approximating operators and semantics for Abstract Dialectical Frameworks. Technical Report 1, Institute of Computer Science, Leipzig University (January 2013)Google Scholar
  6. 6.
    Brewka, G., Ellmauthaler, S., Strass, H., Wallner, J.P., Woltran, S.: Abstract Dialectical Frameworks Revisited. In: Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence. AAAI Press (to appear, August 2013)Google Scholar
  7. 7.
    Denecker, M., Theseider-Dupré, D., Van Belleghem, K.: An Inductive Definition Approach to Ramifications. Linköping Electronic Articles in Computer and Information Science 3(7), 1–43 (1998)Google Scholar
  8. 8.
    Brewka, G., Gordon, T.F.: Carneades and Abstract Dialectical Frameworks: A Reconstruction. In: Computational Models of Argument: Proceedings of COMMA 2010, Desenzano del Garda, Italy, September 8-10. Frontiers in Artificial Intelligence and Applications, vol. 216, pp. 3–12. IOS Press (2010)Google Scholar
  9. 9.
    Gordon, T.F., Prakken, H., Walton, D.: The Carneades model of argument and burden of proof. Artificial Intelligence 171(10-15), 875–896 (2007)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Van Gijzel, B., Prakken, H.: Relating Carneades with Abstract Argumentation. In: Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, vol. 2, pp. 1113–1119. AAAI Press (2011)Google Scholar
  11. 11.
    Prakken, H.: An abstract framework for argumentation with structured arguments. Argument & Computation 1(2), 93–124 (2010)CrossRefGoogle Scholar
  12. 12.
    Baroni, P., Giacomin, M., Guida, G.: SCC-recursiveness: A general schema for argumentation semantics. Artificial Intelligence 168(1-2), 162–210 (2005)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Baroni, P., Dunne, P.E., Giacomin, M.: On the resolution-based family of abstract argumentation semantics and its grounded instance. Artificial Intelligence 175(3-4), 791–813 (2011)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hannes Strass
    • 1
  1. 1.Computer Science InstituteLeipzig UniversityGermany

Personalised recommendations