Solving Semantic Problems with Odd-Length Cycles in Argumentation

  • Pietro Baroni
  • Massimiliano Giacomin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2711)


In the context of Dung’s abstract framework for argumentation, two main semantics have been considered to assign a defeat status to arguments: the grounded semantics and the preferred semantics. While the two semantics agree in most situations, there are cases where the preferred semantics appears to be more powerful. However, we notice that the preferred semantics gives rise to counterintuitive results in some other cases, related to the presence of odd-length cycles in the attack relation between arguments. To solve these problems, we propose a new semantics which preserves the desirable properties of the preferred semantics, while correctly dealing with odd-length cycles. We check the behavior of the proposed semantics in a number of examples and discuss its relationships with both grounded and preferred semantics.




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  1. 1.
    Pollock, J.L.: How to reason defeasibly. Artificial Intelligence 57, 1–42 (1992)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Parsons, S., Sierra, C., Jennings, N.: Agents that reason and negotiate by arguing. Journal of Logic and Computation 8, 261–292 (1998)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Baroni, P., Giacomin, M., Guida, G.: Extending abstract argumentation systems theory. Artificial Intelligence 120, 251–270 (2000)MATHCrossRefMathSciNetGoogle 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 77, 321–357 (1995)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Prakken, H., Vreeswijk, G.A.W.: Logics for defeasible argumentation. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn. Kluwer Academic Publishers, Dordrecht (2001)Google Scholar
  6. 6.
    Pollock, J.L.: Justification and defeat. Artificial Intelligence 67, 377–407 (1994)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Vreeswijk, G.A.W.: Abstract argumentation systems. Artificial Intelligence 90, 225–279 (1997)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Makinson, D., Sclechta, K.: Floating conclusions and zombie paths: Two deep difficulties in the ‘directly skeptical’ approach to defeasible inheritance networks. Artificial Intelligence 48, 199–209 (1991)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Schlechta, K.: Directly sceptical inheritance cannot capture the intersection of extensions. Journal of Logic and Computation 3, 455–467 (1993)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Pollock, J.L.: Defeasible reasoning with variable degrees of justification. Artificial Intelligence 133, 233–282 (2001)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Walton, D., Krabbe, E.: Commitment in Dialogue: Basic concept of interpersonal reasoning. State University of New York Press, Albany (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Pietro Baroni
    • 1
  • Massimiliano Giacomin
    • 1
  1. 1.Dipartimento di Elettronica per l’AutomazioneUniversità di BresciaBresciaItaly

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