Building an Epistemic Logic for Argumentation

  • François Schwarzentruber
  • Srdjan Vesic
  • Tjitze Rienstra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7519)

Abstract

In this paper, we study a multi-agent setting in which each agent is aware of a set of arguments. The agents can discuss and persuade each other by putting forward arguments and counter-arguments. In such a setting, what an agent will do, i.e. what argument she will utter, may depend on what she knows about the knowledge of other agents. For example, an agent does not want to put forward an argument that can easily be attacked, unless she believes that she is able to defend her argument against possible attackers. We propose a logical framework for reasoning about the sets of arguments owned by other agents, their knowledge about other agents’ arguments, etc. We do this by defining an epistemic logic for representing their knowledge, which allows us to express a wide range of scenarios.

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References

  1. 1.
    Areces, C., de Rijke, M.: From description to hybrid logics, and back. Advances in Modal Logic 3, 17–36 (2001)MATHGoogle Scholar
  2. 2.
    Bennett, B., Cohn, A.G., Wolter, F., Zakharyaschev, M.: Multi-dimensional modal logic as a framework for spatio-temporal reasoning. Applied Intelligence 17(3), 239–251 (2002)CrossRefMATHGoogle Scholar
  3. 3.
    Bolander, T., Braüner, T.: Tableau-based decision procedures for hybrid logic. Journal of Logic and Computation 16(6), 737–763 (2006)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence Journal 77, 321–357 (1995)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Fagin, R., Moses, Y., Halpern, J., Vardi, M.: Reasoning about knowledge. The MIT Press (2003)Google Scholar
  6. 6.
    Gabbay, D.M.: Many-dimensional modal logics: theory and applications, vol. 148. North-Holland (2003)Google Scholar
  7. 7.
    Grossi, D.: On the logic of argumentation theory. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2010), pp. 409–416. IFAAMAS (2010)Google Scholar
  8. 8.
    Halpern, J.Y., Moses, Y.: A guide to completeness and complexity for modal logics of knowledge and belief. Artificial intelligence 54(3), 319–379 (1992)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Halpern, J.Y., Vardi, M.Y.: The complexity of reasoning about knowledge and time. i. lower bounds. Journal of Computer and System Sciences 38(1), 195–237 (1989)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Pollock, J.: How to reason defeasibly. Artificial Intelligence Journal 57, 1–42 (1992)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Rahwan, I., Larson, K.: Argumentation and game theory, pp. 321–339. Springer (2009)Google Scholar
  12. 12.
    Riveret, R., Prakken, H., Rotolo, A., Sartor, G.: Heuristics in argumentation: A game theory investigation. In: COMMA, pp. 324–335 (2008)Google Scholar
  13. 13.
    Simari, G.R., Loui, R.P.: A mathematical treatment of defeasible reasoning and its implementation. Artificial Intelligence Journal 53, 125–157 (1992)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Thimm, M., Garcia, A.J.: Classification and strategical issues of argumentation games on structured argumentation frameworks. In: Proceedings of the Ninth International Joint Conference on Autonomous Agents and Multi-Agent Systems 2010, AAMAS 2010 (2010)Google Scholar
  15. 15.
    van Ditmarsch, H., French, T.: Becoming aware of propositional variables. In: Logic and Its Applications, pp. 204–218 (2011)Google Scholar
  16. 16.
    Vreeswijk, G.: Abstract argumentation systems. Artificial Intelligence Journal 90, 225–279 (1997)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • François Schwarzentruber
    • 1
  • Srdjan Vesic
    • 2
  • Tjitze Rienstra
    • 2
  1. 1.IRISA / ENS CachanFrance
  2. 2.Computer Science and CommunicationUniversity of LuxembourgLuxembourg

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