On the Acceptability of Incompatible Arguments

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4724)


In this paper we study the acceptability of incompatible arguments within Dung’s abstract argumentation framework. As an example we introduce an instance of Dung’s framework where arguments are represented by propositional formulas and an argument attacks another one when the conjunction of their representations is inconsistent, which we characterize as a kind of symmetric attack. Since symmetric attack is known to have the drawback to collapse the various argumentation semantics, we consider also two variations. First, we consider propositional arguments distinguishing support and conclusion. Second, we introduce a preference ordering over the arguments and we define the attack relation in terms of a symmetric incompatibility relation and the preference relation. We show how to characterize preference-based argumentation using a kind of acyclic attack relation.


Propositional Logic Propositional Atom Propositional Formula Argumentation Framework Complete Extension 
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  1. 1.
    Amgoud, L., Cayrol, C.: Inferring from inconsistency in preference-based argumentation frameworks. International Journal of Approximate Reasoning 29(1), 125–169 (2002)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Amgoud, L., Cayrol, C.: A reasoning model based on the production of acceptable arguments. Annals of Mathematics and Artificial Intelligence 34, 197–216 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Amgoud, L., Cayrol, C., LeBerre, D.: Comparing arguments using preference orderings for argument-based reasoning. In: 8th International Conference on Tools with Artificial Intelligence (ICTAI 1996), pp. 400–403 (1996)Google Scholar
  4. 4.
    Amgoud, L., Parsons, S., Perrussel, L.: An argumentation framework based on contextual preferences. In: Proceedings of the 3rd International Conference on Formal and Applied Practical Reasoning (FAPR 2000), pp. 59–67 (2000)Google Scholar
  5. 5.
    Bench-Capon, T.: Persuasion in practical argument using value based argumentation framework. Journal of Logic and Computation 13(3), 429–448 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Benferhat, S., Dubois, D., Prade, H.: Argumentative inference in uncertain and inconsistent knowledge base. In: 9th Int. Conf. on Uncertainty in AI (UAI 1993), pp. 411–419 (1993)Google Scholar
  7. 7.
    Besnard, P., Hunter, A.: A logic-based theory of deductive arguments. Artificial Intelligence 128, 203–235 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Bochman, A.: Propositional Argumentation and Causal Reasoning. In: 11th International Joint Conference on Artificial Intelligence (IJCAI 2005), pp. 388–393 (2005)Google Scholar
  9. 9.
    Coste-Marquis, S., Devred, C., Marquis, P.: Symmetric argumentation frameworks. In: Godo, L. (ed.) ECSQARU 2005. LNCS (LNAI), vol. 3571, pp. 317–328. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Kaci, S., van der Torre, L., Weydert, E.: Acyclic Argumentation: Attack = Conflict + Preference. In: Proceedings of the 17th European Conference on Artificial Intelligence (ECAI 2006), pp. 725–726 (2006)Google Scholar
  12. 12.
    Pollock, J.L.: Defeasible reasoning. Cognitive Science 11(4), 481–518 (1987)CrossRefGoogle Scholar
  13. 13.
    Prakken, H., Sartor, G.: Argument-based extended logic programming with defeasible priorties. Journal of Applied Non-Classical Logics 7, 25–75 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Simari, G.R., Loui, R.P.: A mathematical treatment of defeasible reasoning and its implementation. Artificial Intelligence 53, 125–157 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Stolzenburg, F., García, A.J., Chesñevar, C.I., Simari, G.R.: Computing generalized specificity. Journal of Applied Non-Classical Logics 13(1), 87–113 (2003)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.CRILLens CedexFrance
  2. 2.Computer Science and CommunicationUniversity of LuxembourgLuxembourg

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