Probabilistic Abstract Dialectical Frameworks

  • Sylwia Polberg
  • Dragan Doder
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8761)

Abstract

Although Dung’s frameworks are widely approved tools for abstract argumentation, their abstractness makes expressing notions such as support or uncertainty very difficult. Thus, many of their generalizations were created, including the probabilistic argumentation frameworks (PrAFs) and the abstract dialectical frameworks (ADFs). While the first allow modeling uncertain arguments and attacks, the latter can handle various dependencies between arguments. Although the actual probability layer in PrAFs is independent of the chosen semantics, new relations pose new challenges and new interpretations of what is the probability of a relation. Thus, the methodology for handling uncertainties cannot be shifted to more general structures without any further thought. In this paper we show how ADFs are extended with probabilities.

Keywords

Abstract argumentation abstract dialectical frameworks probabilistic argumentation frameworks 

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References

  1. 1.
    Bench-Capon, T.J.M., Dunne, P.E.: Argumentation in artificial intelligence. Artificial Intelligence 171, 619–641 (2007)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    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
  3. 3.
    Brewka, G., Polberg, S., Woltran, S.: Generalizations of Dung frameworks and their role in formal argumentation. IEEE Intelligent Systems 29, 30–38 (2014)Google Scholar
  4. 4.
    Hunter, A.: A probabilistic approach to modelling uncertain logical arguments. International Journal of Approximate Reasoning 54, 47–81 (2013)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Li, H., Oren, N., Norman, T.J.: Probabilistic argumentation frameworks. In: Modgil, S., Oren, N., Toni, F. (eds.) TAFA 2011. LNCS, vol. 7132, pp. 1–16. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  6. 6.
    Li, H., Oren, N., Norman, T.J.: Relaxing independence assumptions in probabilistic argumentation. In: Proceedings of ArgMAS 2013 (2013) (forthcoming)Google Scholar
  7. 7.
    Brewka, G., Woltran, S.: Abstract dialectical frameworks. In: Lin, F., Sattler, U., Truszczyński, M. (eds.) Proceedings of the 12th International Conference on Principles of Knowledge Representation and Reasoning (KR 2010), pp. 780–785. AAAI Press (2010)Google Scholar
  8. 8.
    Cayrol, C., Lagasquie-Schiex, M.C.: Bipolarity in argumentation graphs: Towards a better understanding. International Journal of Approximate Reasoning 54, 876–899 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Nouioua, F.: AFs with necessities: Further semantics and labelling characterization. In: Liu, W., Subrahmanian, V.S., Wijsen, J. (eds.) SUM 2013. LNCS, vol. 8078, pp. 120–133. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    Polberg, S., Oren, N.: Revisiting support in abstract argumentation systems. In: Proceedings of COMMA 2014 (forthcoming, 2014)Google Scholar
  11. 11.
    Brewka, G., Ellmauthaler, S., Strass, H., Wallner, J.P., Woltran, S.: Abstract dialectical frameworks revisited. In: Proceedings of IJCAI 2013, pp. 803–809. AAAI Press (2013)Google Scholar
  12. 12.
    Polberg, S., Wallner, J.P., Woltran, S.: Admissibility in the abstract dialectical framework. In: Leite, J., Son, T.C., Torroni, P., van der Torre, L., Woltran, S. (eds.) CLIMA XIV 2013. LNCS, vol. 8143, pp. 102–118. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  13. 13.
    Strass, H.: Approximating operators and semantics for abstract dialectical frameworks. Artificial Intelligence 205, 39–70 (2013)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Strass, H.: Instantiating knowledge bases in abstract dialectical frameworks. In: Leite, J., Son, T.C., Torroni, P., van der Torre, L., Woltran, S. (eds.) CLIMA XIV 2013. LNCS, vol. 8143, pp. 86–101. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  15. 15.
    Strass, H., Wallner, J.P.: Analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory. In: Proceedings of KR 2014, Vienna, Austria (forthcoming, 2014)Google Scholar
  16. 16.
    Polberg, S.: Extension–based semantics of abstract dialectical frameworks. Technical Report DBAI-TR-2014-85, Institute for Information Systems, Technical University of Vienna (2014)Google Scholar
  17. 17.
    Doder, D., Woltran, S.: Probabilistic argumentation frameworks – A logical approach. In: Straccia, U., Cali, A. (eds.) SUM 2014. LNCS, vol. 8720, pp. 134–147. Springer, Heidelberg (2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sylwia Polberg
    • 1
  • Dragan Doder
    • 2
  1. 1.Institute of Information SystemsVienna University of TechnologyViennaAustria
  2. 2.Computer Science and CommunicationsUniversity of LuxembourgLuxembourg

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