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Link to original content: https://doi.org/10.1007/s10472-011-9271-9
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A new approach for preference-based argumentation frameworks

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Abstract

Dung’s argumentation framework consists of a set of arguments and an attack relation among them. Arguments are evaluated and acceptable sets of them, called extensions, are computed using a given semantics. Each extension represents a coherent position. In the literature, several proposals have extended this framework in order to take into account the strength of arguments. The basic idea is to ignore an attack if the attacked argument is stronger than (or preferred to) its attacker. Semantics are then applied using only the remaining attacks. In this paper, we show that those proposals behave correctly when the attack relation is symmetric. However, when it is asymmetric, conflicting extensions may be computed leading to unintended conclusions. We propose an approach that guarantees conflict-free extensions. This approach presents two novelties: the first one is that it takes into account preferences at the semantics level rather than the attack level. The idea is to extend existing semantics with preferences. In case preferences are not available or do not conflict with the attacks, the extensions of the new semantics coincide with those of the basic ones. The second novelty of our approach is that a semantics is defined as a dominance relation on the powerset of the set of arguments. The extensions (under a semantics) are the maximal elements of the dominance relation. Such an approach makes it possible not only to compute the extensions of a framework but also to compare its non-extensions. We start by proposing three dominance relations that generalize respectively stable, preferred and grounded semantics with preferences. Then, we focus on stable semantics and provide full characterizations of its dominance relations and those of its generalized versions. Complexity results are provided. Finally, we show that an instance of the proposed framework retrieves the preferred sub-theories which were proposed in the context of handling inconsistency in weighted knowledge bases.

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References

  1. Amgoud, L., Besnard, Ph.: Bridging the gap between abstract argumentation systems and logic. In: International Conference on Scalable Uncertainty Management (SUM’09), pp. 12–27 (2009)

  2. Amgoud, L., Besnard, Ph.: A formal analysis of logic-based argumentation systems. In: International Conference on Scalable Uncertainty Management (SUM’10), pp. 42–55 (2010)

  3. Amgoud, L., Cayrol, C.: Inferring from inconsistency in preference-based argumentation frameworks. J. Autom. Reason. 29(2), 125–169 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Amgoud, L., Cayrol, C.: A reasoning model based on the production of acceptable arguments. Ann. Math. Artif. Intell. 34, 197–216 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Amgoud, L., Prade, H.: Using arguments for making and explaining decisions. Artif. Intell. J. 173, 413–436 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Amgoud, L., Serrurier, M.: Agents that argue and explain classifications. J. Auton. Agents Multi-Agents Syst. 16, 187–209 (2008)

    Article  Google Scholar 

  7. Amgoud, L., Vesic, S.: Repairing preference-based argumentation systems. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI’09), pp. 665–670 (2009)

  8. Amgoud, L., Vesic, S.: Generalizing stable semantics by preferences. In: Proceedings of the 3rd International Conference on Computational Models of Argument (COMMA’10), pp. 39–50 (2010)

  9. Amgoud, L., Vesic, S.: On the role of preferences in argumentation frameworks. In: Proceedings of the 22nd International Conference on Tools with Artificial Intelligence (ICTAI’10), pp. 219–222 (2010)

  10. Amgoud, L., Cayrol, C., LeBerre, D.: Comparing arguments using preference orderings for argument-based reasoning. In: Proceedings of the 8th International Conference on Tools with Artificial Intelligence (ICTAI’96), pp. 400–403 (1996)

  11. Amgoud, L., Maudet, N., Parsons, S.: Modelling dialogues using argumentation. In: Proceedings of the 4th International Conference on Multi-Agent Systems (ICMAS’00), pp. 31–38 (2000)

  12. Amgoud, L., Caminada, M., Cayrol, C., Lagasquie, M.C., Prakken, H.: Towards a consensual formal model: inference part. Technical report. In: Deliverable D2.2: Draft Formal Semantics for Inference and Decision-Making. ASPIC Project (2004)

  13. Amgoud, L., Dimopoulos, Y., Moraitis, P.: Making decisions through preference-based argumentation. In: Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning (KR’08), pp. 113–123 (2008)

  14. Amgoud, L., Besnard, Ph., Vesic, S.: Identifying the core of logic-based argumentation systems. In: Proceedings of the International Conference on Tools with Artificial Intelligence (ICTAI’11) (2011)

  15. Baroni, P., Giacomin, M.: On principle-based evaluation of extension-based argumentation semantics. Artif. Intell. J. 171, 675–700 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Baroni, P., Giacomin, M., Guida, G.: Scc-recursiveness: a general schema for argumentation semantics. Artif. Intell. J. 168, 162–210 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  17. Bench-Capon, T.J.M.: Persuasion in practical argument using value-based argumentation frameworks. J. Log. Comput. 13(3), 429–448 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  18. Benferhat, S., Dubois, D., Prade, H.: Argumentative inference in uncertain and inconsistent knowledge bases. In: Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence (UAI’93), pp. 411–419 (1993)

  19. Besnard, Ph., Hunter, A.: Elements of Argumentation. MIT Press (2008)

  20. Bonet, B., Geffner, H.: Arguing for decisions: a qualitative model of decision making. In: Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence (UAI’96), pp. 98–105 (1996)

  21. Brewka, G.: Preferred subtheories: an extended logical framework for default reasoning. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI’89), pp. 1043–1048 (1989)

  22. Brewka, G., Eiter, T.: Preferred answer sets for extended logic programs. Artif. Intell. J. 109, 297–356 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  23. Brewka, G., Niemela, I., Truszczynski, M.: Preferences and nonmonotonic reasoning. AI Mag. 29(4), 69–78 (2008)

    Google Scholar 

  24. Caminada, M., Amgoud, L.: On the evaluation of argumentation formalisms. Artif. Intell. J. 171(5–6), 286–310 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Caminada, M.W.A.: Semi-stable semantics. In: Proceedings of the 1st International Conference on Computational Models of Argument (COMMA’06), pp. 121–130 (2006)

  26. Cayrol, C.: On the relation between argumentation and non-monotonic coherence-based entailment. In: Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI’95), pp. 1443–1448 (1995)

  27. Cayrol, C., Royer, V., Saurel, C.: Management of preferences in assumption-based reasoning. Lect. Notes Comput. Sci. 682, 13–22 (1993)

    Google Scholar 

  28. Dimopoulos, Y., Moraitis, P., Amgoud, L.: Extending argumentation to make good decisions. In: Proceedings of the 1st International Conference on Algorithmic Decision Theory (ADT’09). LNCS 5783, pp. 225–236 (2009)

  29. Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. J. 77, 321–357 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  30. Dung, P.M., Mancarella, P., Toni, F.: Computing ideal skeptical argumentation. Artif. Intell. J. 171, 642–674 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  31. Dunne, P.: Computational properties of argument systems satisfying graph-theoretic constraints. Artif. Intell. J. 171(10–15), 701–729 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  32. Elvang-Gøransson, M., Fox, J., Krause, P.: Acceptability of arguments as ‘logical uncertainty’. In: Proceedings of the 2nd European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU’93), pp. 85–90 (1993)

  33. Kaci, S.: Refined preference-based argumentation frameworks. In: Proceedings of the 3rd International Conference on Computational Models of Argument (COMMA’10), pp. 299–310 (2010)

  34. Kaci, S., van der Torre, L.: Preference-based argumentation: arguments supporting multiple values. J. of Approx. Reas. 48(3), 730–751 (2008)

    Article  MATH  Google Scholar 

  35. Kaci, S., van der Torre, L., Weydert, E.: Acyclic argumentation: attack = conflict + preference. In: Proceedings of the European Conference on Artificial Intelligence (ECAI’06), pp. 725–726 (2006)

  36. Kraus, S., Sycara, K., Evenchik, A.: Reaching agreements through argumentation: a logical model and implementation. J. Artif. Intell. 104, 1–69 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  37. Martinez, G., Garcia, A., Simari, G.: On defense strength of blocking defeaters in admissible sets. In: Proceedings of KSEM’07. LNAI 4798, pp. 140–152 (2007)

  38. Modgil, S.: Reasoning about preferences in argumentation frameworks. Artif. Intell. J. 173(9–10), 901–934 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  39. Modgil, S., Prakken, H.: Revisiting preferences and argumentation. In: Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI’11), pp. 1021–1026 (2011)

  40. Mozina, M., Zabkar, J., Bratko, I.: Argument based machine learning. Artif. Intell. J. 171(10–15), 922–937 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  41. Pollock, J.: How to reason defeasibly. Artif. Intell. J. 57, 1–42 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  42. Prakken, H.: Coherence and flexibility in dialogue games for argumentation. J. Log. Comput. 15, 1009–1040 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  43. Prakken, H.: An abstract framework for argumentation with structured arguments. J. of Arg. and Comp. 1, 93–124 (2010)

    Article  Google Scholar 

  44. Prakken, H., Sartor, G.: Argument-based extended logic programming with defeasible priorities. J. Appl. Non-class. Log. 7, 25–75 (1997)

    MathSciNet  MATH  Google Scholar 

  45. Rescher, N., Manor, R.: On inference from inconsistent premises. J. Theory Decis. 1, 179–219 (1970)

    Article  MATH  Google Scholar 

  46. Simari, G.R., Loui, R.P.: A mathematical treatment of defeasible reasoning and its implementation. Artif. Intell. J. 53, 125–157 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  47. Sycara, K.: Persuasive argumentation in negotiation. Theory Decis. 28, 203–242 (1990)

    Article  Google Scholar 

  48. Tarski, A.: On Some Fundamental Concepts of Metamathematics. Logic, Semantics, Metamathematic. Edited and Translated by J. H. Woodger. Oxford University Press (1956)

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  1. IRIT - CNRS, 118 route de Narbonne, 31062, Toulouse Cedex 9, France

    Leila Amgoud & Srdjan Vesic

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  1. Leila Amgoud
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  2. Srdjan Vesic
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Correspondence to Leila Amgoud.

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Amgoud, L., Vesic, S. A new approach for preference-based argumentation frameworks. Ann Math Artif Intell 63, 149–183 (2011). https://doi.org/10.1007/s10472-011-9271-9

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