Capturing Bipolar Argumentation in Non-flat Assumption-Based Argumentation

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10621)

Abstract

Bipolar Argumentation Frameworks (BAFs) encompass both attacks and supports among arguments. We study different semantic interpretations of support in BAFs, particularly necessary and deductive support, as well as argument coalitions and a recent proposal by Gabbay. We analyse the relationship of these different notions of support in BAFs with the semantics of a well established structured argumentation formalism, Assumption-Based Argumentation (ABA), which predates BAFs. We propose natural mappings from BAFs into a restricted class of (non-flat) ABA frameworks, which we call bipolar, and prove that the admissible and preferred semantics of these ABA frameworks correspond to the admissible and preferred semantics of the various approaches to BAFs. Motivated by the definition of stable semantics for BAFs, we introduce a novel set-stable semantics for ABA frameworks, and prove that it corresponds to the stable semantics of the various approaches to BAFs. Finally, as a by-product of modelling various approaches to BAFs in bipolar ABA, we identify precise semantic relationships amongst all approaches we consider.

References

  1. 1.
    Amgoud, L., Ben-Naim, J.: Axiomatic foundations of acceptability semantics. In: Baral, C., Delgrande, J.P., Wolter, F. (eds.) 15th International Conference on Principles of Knowledge Representation and Reasoning, pp. 2–11. AAAI Press (2016)Google Scholar
  2. 2.
    Amgoud, L., Cayrol, C., Lagasquie-Schiex, M., Livet, P.: On bipolarity in argumentation frameworks. Int. J. Intell. Syst. 23(10), 1062–1093 (2008)CrossRefMATHGoogle Scholar
  3. 3.
    Besnard, P., García, A.J., Hunter, A., Modgil, S., Prakken, H., Simari, G.R., Toni, F.: Introduction to structured argumentation. Argum. Comput. 5(1), 1–4 (2014)CrossRefGoogle Scholar
  4. 4.
    Boella, G., Gabbay, D.M., van der Torre, L., Villata, S.: Support in abstract argumentation. In: Baroni, P., Cerutti, F., Giacomin, M., Simari, G.R. (eds.) Computational Models of Argument. Frontiers in AI and Applications, vol. 216, pp. 111–122. IOS Press, Amsterdam (2010)Google Scholar
  5. 5.
    Bondarenko, A., Dung, P.M., Kowalski, R., Toni, F.: An abstract, argumentation-theoretic approach to default reasoning. Artif. Intell. 93(97), 63–101 (1997)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Boudhar, I., Nouioua, F., Risch, V.: Handling preferences in argumentation frameworks with necessities. In: Filipe, J., Fred, A.L.N. (eds.) 4th International Conference on Agents and Artificial Intelligence, pp. 340–345. SciTePress (2012)Google Scholar
  7. 7.
    Cabrio, E., Villata, S.: A natural language bipolar argumentation approach to support users in online debate interactions. Argum. Comput. 4(3), 209–230 (2013)CrossRefGoogle Scholar
  8. 8.
    Cayrol, C., Lagasquie-Schiex, M.C.: Gradual valuation for bipolar argumentation frameworks. In: Godo, L. (ed.) ECSQARU 2005. LNCS (LNAI), vol. 3571, pp. 366–377. Springer, Heidelberg (2005). doi:10.1007/11518655_32 CrossRefGoogle Scholar
  9. 9.
    Cayrol, C., Lagasquie-Schiex, M.C.: On the acceptability of arguments in bipolar argumentation frameworks. In: Godo, L. (ed.) ECSQARU 2005. LNCS (LNAI), vol. 3571, pp. 378–389. Springer, Heidelberg (2005). doi:10.1007/11518655_33 CrossRefGoogle Scholar
  10. 10.
    Cayrol, C., Lagasquie-Schiex, M.C.: Coalitions of arguments: a tool for handling bipolar argumentation frameworks. Int. J. Intell. Syst. 25(1), 83–109 (2010)CrossRefMATHGoogle Scholar
  11. 11.
    Cayrol, C., Lagasquie-Schiex, M.C.: Bipolarity in argumentation graphs: towards a better understanding. Int. J. Approx. Reason. 54(7), 876–899 (2013)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Cohen, A., Gottifredi, S., García, A.J., Simari, G.R.: A survey of different approaches to support in argumentation systems. Knowl. Eng. Rev. 29(5), 513–550 (2014)CrossRefGoogle Scholar
  13. 13.
    Cohen, A., Gottifredi, S., García, A.J., Simari, G.R.: An approach to abstract argumentation with recursive attack and support. J. Appl. Logic 13(4), 509–533 (2015)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Čyras, K., Fan, X., Schulz, C., Toni, F.: Assumption-based argumentation: disputes, explanations, preferences. In: Baroni, P., Gabbay, D.M., Giacomin, M., van der Torre, L. (eds.) Handbook of Formal Argumentation, vol. 1. College Publications (to appear)Google Scholar
  15. 15.
    Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77, 321–357 (1995)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Gabbay, D.M.: Logical foundations for bipolar and tripolar argumentation networks: preliminary results. J. Logic Comput. 26(1), 247–292 (2016)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Modgil, S., Prakken, H.: A general account of argumentation with preferences. Artif. Intell. 195, 361–397 (2013)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Nouioua, F.: AFs with necessities: further semantics and labelling characterization. In: Liu, W., Subrahmanian, V.S., Wijsen, J. (eds.) SUM 2013. LNCS (LNAI), vol. 8078, pp. 120–133. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40381-1_10 CrossRefGoogle Scholar
  19. 19.
    Nouioua, F., Risch, V.: Bipolar argumentation frameworks with specialized supports. In: 22nd IEEE International Conference on Tools with Artificial Intelligence, vol. 1, pp. 215–218. IEEE (2010)Google Scholar
  20. 20.
    Nouioua, F., Risch, V.: Argumentation frameworks with necessities. In: Benferhat, S., Grant, J. (eds.) SUM 2011. LNCS (LNAI), vol. 6929, pp. 163–176. Springer, Heidelberg (2011). doi:10.1007/978-3-642-23963-2_14 CrossRefGoogle Scholar
  21. 21.
    Polberg, S., Oren, N.: Revisiting support in abstract argumentation systems. In: Parsons, S., Oren, N., Reed, C., Cerutti, F. (eds.) Computational Models of Argument. Frontiers in AI and Applications, vol. 266, pp. 369–376. IOS Press, Amsterdam (2014)Google Scholar
  22. 22.
    Prakken, H.: On support relations in abstract argumentation as abstractions of inferential relations. In: Schaub, T., Friedrich, G., O’Sullivan, B. (eds.) 21st European Conference on Artificial Intelligence. Frontiers in AI and Applications, vol. 263, pp. 735–740. IOS Press (2014)Google Scholar
  23. 23.
    Rago, A., Toni, F., Aurisicchio, M., Baroni, P.: Discontinuity-free decision support with quantitative argumentation debates. In: Baral, C., Delgrande, J.P., Wolter, F. (eds.) 15h International Conference on Principles of Knowledge Representation and Reasoning, pp. 63–73. AAAI Press, Cape Town (2016)Google Scholar
  24. 24.
    Toni, F.: Reasoning on the web with assumption-based argumentation. In: Eiter, T., Krennwallner, T. (eds.) Reasoning Web 2012. LNCS, vol. 7487, pp. 370–386. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33158-9_10 CrossRefGoogle Scholar
  25. 25.
    Toni, F.: A tutorial on assumption-based argumentation. Argum. Comput. 5(1), 89–117 (2014)CrossRefGoogle Scholar
  26. 26.
    Villata, S., Boella, G., Gabbay, D.M., van der Torre, L.: Modelling defeasible and prioritized support in bipolar argumentation. Ann. Math. Artif. Intell. 66(1–4), 163–197 (2012)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of ComputingImperial College LondonLondonUK

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