Probabilistic Argumentation Frameworks

  • Hengfei Li
  • Nir Oren
  • Timothy J. Norman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7132)


In this paper, we extend Dung’s seminal argument framework to form a probabilistic argument framework by associating probabilities with arguments and defeats. We then compute the likelihood of some set of arguments appearing within an arbitrary argument framework induced from this probabilistic framework. We show that the complexity of computing this likelihood precisely is exponential in the number of arguments and defeats, and thus describe an approximate approach to computing these likelihoods based on Monte-Carlo simulation. Evaluating the latter approach against the exact approach shows significant computational savings. Our probabilistic argument framework is applicable to a number of real world problems; we show its utility by applying it to the problem of coalition formation.


Bayesian Network Multiagent System Coalition Formation Argumentation Framework Exact Approach 
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.
    Agresti, A., Coull, B.A.: Approximate is better than “exact” for interval estimation of binomial proportions. The American Statistician 52(2), 119–126 (1998)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Amgoud, L., Cayrol, C.: Inferring from inconsistency in preference-based argumentation frameworks. Journal of Automated Reasoning 29, 125–169 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Baroni, P., Dunne, P.E., Giacomin, M.: On extension counting problems in argumentation frameworks. In: Proceeding of the 2010 Conference on Computational Models of Argument: Proceedings of COMMA 2010, pp. 63–74. IOS Press, Amsterdam (2010)Google Scholar
  4. 4.
    Baroni, P., Giacomin, M.: Semantics of abstract argument systems. In: Simari, G., Rahwan, I. (eds.) Argumentation in Artificial Intelligence, pp. 25–44. Springer, US (2009)CrossRefGoogle Scholar
  5. 5.
    Bench-Capon, T.: Value based argumentation frameworks. In: Proceedings of the 9th International Workshop on Nonmonotonic Reasoning, Toulouse, France, pp. 444–453 (2002)Google Scholar
  6. 6.
    Burnett, C., Norman, T.J., Sycara, K.: Stereotypical trust and bias in dynamic multi-agent systems. ACM Transactions on Intelligent Systems and Technology (in press)Google Scholar
  7. 7.
    Cayrol, C., Lagasquie-Schiex, M.C.: Bipolar Abstract Argumentation Systems. In: Rahwan, I., Simari, G. (eds.) Argumentation in Artificial Intelligence, ch. 4, pp. 65–84. Springer, Heidelberg (2009), CrossRefGoogle Scholar
  8. 8.
    Coulom, R.: Efficient Selectivity and Backup Operators in Monte-Carlo Tree Search. In: van den Herik, H.J., Ciancarini, P., Donkers, H.H.L.M(J.) (eds.) CG 2006. LNCS, vol. 4630, pp. 72–83. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence 77(2), 321–357 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Dunne, P.E., Hunter, A., McBurney, P., Parsons, S., Wooldridge, M.: Weighted argument systems: Basic definitions, algorithms, and complexity results. Artificial Intelligence 175(2), 457–486 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Dunne, P.E., Wooldridge, M.: Complexity of abstract argumentation. In: Simari, G., Rahwan, I. (eds.) Argumentation in Artificial Intelligence, pp. 85–104. Springer, US (2009)CrossRefGoogle Scholar
  12. 12.
    Emele, C.D., Norman, T.J., Parsons, S.: Argumentation strategies for plan resourcing. In: Proceedings of the Tenth International Conference on Autonomous Agents and Multiagent Systems (2011)Google Scholar
  13. 13.
    Erriquez, E., van der Hoek, W., Wooldridge, M.: An abstract framework for reasoning about trust. In: Proceedings of AAMAS 2011 (to appear, 2011)Google Scholar
  14. 14.
    Gómez Lucero, M.J., Chesñevar, C.I., Simari, G.R.: Modelling Argument Accrual in Possibilistic Defeasible Logic Programming. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS, vol. 5590, pp. 131–143. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  15. 15.
    Janssen, J., Cock, M.D., Vermeir, D.: Fuzzy argumentation frameworks. In: Proceedings of IMPU 2008 (12th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems), pp. 513–520 (2008)Google Scholar
  16. 16.
    Kohlas, J., Haenni, R.: Assumption-based reasoning and probabilistic argumentation systems. Tech. Rep. 96–07, Institute of Informatics, University of Fribourg, Switzerland (1996)Google Scholar
  17. 17.
    Krause, P., Ambler, S., Elvang-Goransson, M., Fox, J.: A logic of argumentation for reasoning under uncertainty. Computational Intelligence 11(1), 113–131 (1995)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Lewicki, P., Hill, T.: Statistics: Methods and Applications. StatSoft Inc. (2005)Google Scholar
  19. 19.
    Mitchell, T.M.: Machine Learning. McGraw-Hill Higher Education (1997)Google Scholar
  20. 20.
    Oren, N., Norman, T.J.: Semantics for evidence-based argumentation. In: Computational Models of Argument: Proceedings of COMMA 2008, Toulouse, France, May 28-30, pp. 276–284 (2008)Google Scholar
  21. 21.
    Oren, N., Norman, T.J.: Arguing Using Opponent Models. In: McBurney, P., Rahwan, I., Parsons, S., Maudet, N. (eds.) ArgMAS 2009. LNCS, vol. 6057, pp. 160–174. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  22. 22.
    Oren, N., Norman, T.J., Preece, A.: Arguing with confidential information. In: Proceedings of the 18th European Conference on Artificial Intelligence, Riva del Garda, Italy, pp. 280–284 (August 2006)Google Scholar
  23. 23.
    Parsons, S.: Normative Argumentation and Qualitative Probability. In: Gabbay, D.M., Kruse, R., Nonnengart, A., Ohlbach, H.J. (eds.) FAPR 1997 and ECSQARU 1997. LNCS, vol. 1244, pp. 466–480. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  24. 24.
    Patel, J., Teacy, W.T.L., Jennings, N.R., Luck, M., Chalmers, S., Oren, N., Norman, T.J., Preece, A., Gray, P.M.D., Shercliff, G., Stockreisser, P.J., Shao, J., Gray, W.A., Fiddian, N.J., Thompson, S.: Agent-based virtual organisations for the grid. Multiagent and Grid Systems 1(4), 237–249 (2006)Google Scholar
  25. 25.
    Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann Publishers Inc., San Francisco (1988)Google Scholar
  26. 26.
    Pechoucek, M., Marík, V., Bárta, J.: A knowledge-based approach to coalition formation. IEEE Intelligent Systems 17, 17–25 (2002)Google Scholar
  27. 27.
    Pollock, J.L.: Cognitive Carpentry. Bradford/MIT Press (1995)Google Scholar
  28. 28.
    Rahwan, T.: Algorithms for Coalition Formation in Multi-Agent Systems. Ph.D. thesis, University of Southampton (2007)Google Scholar
  29. 29.
    Riveret, R., Prakken, H., Rotolo, A., Sartor, G.: Heuristics in argumentation: A game theory investigation. In: Computational Models of Argument: Proceedings of COMMA 2008, Toulouse, France, May 28-30, pp. 324–335 (2008)Google Scholar
  30. 30.
    Rotstein, N., Oren, N., Norman, T.J.: Resource bounded argumentation frameworks. Tech. rep., University of Aberdeen (2011)Google Scholar
  31. 31.
    Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction (Adaptive Computation and Machine Learning). The MIT Press (March 1998)Google Scholar
  32. 32.
    Teacy, W.T.L., Patel, J., Jennings, N.R., Luck, M.: Travos: Trust and reputation in the context of inaccurate information sources. Autonomous Agents and Multi-Agent Systems 12(2), 183–198 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hengfei Li
    • 1
  • Nir Oren
    • 1
  • Timothy J. Norman
    • 1
  1. 1.Department of Computing ScienceUniversity of AberdeenAberdeenUK

Personalised recommendations