Proof Theories and Algorithms for Abstract Argumentation Frameworks

  • Sanjay Modgil
  • Martin Caminada

Previous chapters have focussed on abstract argumentation frameworks and properties of sets of arguments defined under various extension-based semantics. The main focus of this chapter is on more procedural, proof-theoretic and algorithmic aspects of argumentation. In particular, Chapter 11 describes properties of extensions of a Dung argumentation framework.


Winning Strategy Proof Theory Transition Step Argumentation Framework Argument System 
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.


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The authors would like to thank Gerard Vreeswijk for his contributions to the contents of this chapter. Thanks also to Nir Oren for commenting on a draft of the chapter.


  1. 1.
    L. Amgoud and C. Cayrol. A Reasoning Model Based on the Production of Acceptable Arguments. Annals of Mathematics and Artificial Intelligence, 34(1–3),197–215, 2002.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    H. Barringer, D. M. Gabbay and J. Woods. Temporal Dynamics of Support and Attack Networks: From Argumentation to Zoology. Mechanizing Mathematical Reasoning, 59–98, 2005.Google Scholar
  3. 3.
    A. Bondarenko and P.M. Dung and R.A. Kowalski and F. Toni. An abstract, argumentation-theoretic approach to default reasoning. Artificial Intelligence, 93:63–101, 1997.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    M. Caminada. For the sake of the Argument. Explorations into argument-based reasoning. Doctoral dissertation Free University Amsterdam, 2004.Google Scholar
  5. 5.
    M. Caminada. On the Issue of Reinstatement in Argumentation. In European Conference on Logic in Artificial Intelligence (JELIA), 111–123, 2006.Google Scholar
  6. 6.
    M. Caminada. An Algorithm for Computing Semi-stable Semantics. In European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU), 222–234, 2007.Google Scholar
  7. 7.
    M. Caminada and Y. Wu. Towards an Argument Game for Stable Semantics. InComputational Models of Natural Argument, to appear, 2008.Google Scholar
  8. 8.
    C. Cayrol, S. Doutre and J. Mengin. Dialectical Proof Theories for the Credulous Preferred Semantics of Argumentation Frameworks. In European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU), 668–679, 2001.Google Scholar
  9. 9.
    C. Cayrol, S. Doutre and J. Mengin. On Decision Problems related to the preferred semantics for argumentation frameworks. Journal of Logic and Computation, 13(3), 377–403, 2003.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    C. Cayrol and M. Lagasquie-Schiex. On the Acceptability of Arguments in Bipolar Argumentation Frameworks. In European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU), 378–389, 2005.Google Scholar
  11. 11.
    C. Cayrol and M.-Ch. Lagasquie-Schiex. Graduality in argumentation. Journal of Artificial Intelligence Research, 23:245–297, 2005.MATHMathSciNetGoogle Scholar
  12. 12.
    S. Doutre and J. Mengin. On sceptical vs credulous acceptance for abstract argument systems. In Ninth European Conference on Logics in Artificial Intelligence (JELIA 2004), 462–473, 2004.Google Scholar
  13. 13.
    P. M. Dung. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence, 77:321–357, 1995.MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    P.M. Dung, P. Mancarella and F. Toni. Computing ideal sceptical argumentation. Artificial Intelligence Journal, 171(10–15):642–674, 2007.CrossRefMathSciNetGoogle Scholar
  15. 15.
    P.M. Dung and P.M. Thang. A Sound and Complete Dialectical Proof Procedure for Sceptical Preferred Argumentation. In Proc. of the LPNMR-Workshop on Argumentation and Nonmonotonic Reasoning (ArgNMR07), 49–63, 2007.Google Scholar
  16. 16.
    P.E. Dunne and T.J.M. Bench-Capon. Two Party Immediate Response Disputes: Properties and Efficiency. Artificial Intelligence Journal, 149(2),221–250, 2003.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    H. Jakobovits and D. Vermeir. Dialectic Semantics for Argumentation Frameworks. Journal of Logic and Computation, 53–62, 1999.Google Scholar
  18. 18.
    P. Lorenzen. Dialectical foundations of logical calculi. Constructive Philosophy, Univ. of Massachusetts Press, 1987.Google Scholar
  19. 19.
    P. Lorenzen and K.Lorenz”. Dialogische Logik. Wissenschaftliche Buchgesellschaft, Darmstadt, 1978.Google Scholar
  20. 20.
    S. Modgil. An Abstract Theory of Argumentation That Accommodates Defeasible Reasoning About Preferences. In European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU), 648–659, 2007.Google Scholar
  21. 21.
    S. Modgil and M. Caminada. Proof Theories and Algorithms for Abstract Argumentation Frameworks. Technical Report, Department of Computer Science, King’s College London,, 2008.
  22. 22.
    S. Nielsen and S. Parsons. A generalization of Dung’s abstract framework for argumentation: Arguing with sets of attacking arguments. In Proc. Third International Workshop on Argumentation in Multiagent Systems (ArgMAS 2006), 54–73, 2006.Google Scholar
  23. 23.
    J. L. Pollock. Cognitive Carpentry. A Blueprint for How to Build a Person. MIT Press, Cambridge, MA, 1995.Google Scholar
  24. 24.
    H. Prakken and G. Sartor. Argument-based extended logic programming with defeasible priorities. Journal of Applied Non-Classical Logics, 7:25–75, 1997.MATHMathSciNetGoogle Scholar
  25. 25.
    B. Verheij. A Labeling Approach to the Computation of Credulous Acceptance in Argumentation. In International Joint Conference on Aritificial Intelligence (IJCAI), 623–628, 2007.Google Scholar
  26. 26.
    G. A. W. Vreeswijk. Defeasible dialectics: A controversy-oriented approach towards defeasible argumentation. Journal of Logic and Computation, 3:3–27, 1993.CrossRefMathSciNetGoogle Scholar
  27. 27.
    G. A. W. Vreeswijk. An algorithm to compute minimally grounded and admissible defence sets in argument systems. In Proc. 1st International Conference on Computational Models of Argument, 109–120, 2006.Google Scholar
  28. 28.
    G. A. W. Vreeswijk and H. Prakken. Credulous and sceptical argument games for preferred semantics. In Proc. 7th European Workshop on Logic for Artificial Intelligence, 239–253, 2000.Google Scholar

Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Department of Computer ScienceKing’s College LondonLondonUK

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