Expansion and Equivalence Relations on Argumentation Frameworks Based on Logic Programs

  • Juan Carlos NievesEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10207)


Expansion and equivalence relations have been explored in the settings of abstract argumentation. However, in terms of structured arguments, expansion and equivalence relations have not been explored in the settings of structured arguments based on logic programs. In this paper, we draw connections between resulting argumentation frameworks from logic programs considering expansion and equivalence relations. We show that by considering different methods for constructing arguments and defining attack relations, one can define different expansion and equivalence relations between the resulting argumentation frameworks from logic programs. Moreover, we extended results from abstract argumentation into structured arguments based on logic programs.


  1. 1.
    Amgoud, L., Besnard, P., Vesic, S.: Equivalence in logic-based argumentation. J. Appl. Non-Class. Log. 24(3), 181–208 (2014)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Amgoud, L., Prade, H.: Using arguments for making and explaining decisions. Artif. Intell. 173, 413–436 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)CrossRefzbMATHGoogle Scholar
  4. 4.
    Baumann, R., Woltran, S.: The role of self-attacking arguments in characterizations of equivalence notions. J. Log. Comput. 26(4), 1293–1313 (2016). doi: 10.1093/logcom/exu010 MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bondarenko, A., Dung, P.M., Kowalski, R.A., Toni, F.: An abstract, argumentation-theoretic approach to default reasoning. Artif. Intell. 93, 63–101 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Caminada, M.: Semi-stable semantics. In: Dunne, P.E., Bench-Capon, T.J. (eds.) Proceedings of COMMA, vol. 144, pp. 121–130. IOS Press, Amsterdam (2006)Google Scholar
  7. 7.
    Caminada, M., Amgoud, L.: On the evaluation of argumentation formalisms. Artif. Intell. 171, 286–310 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Charwat, G., Dvorák, W., Gaggl, S.A., Wallner, J.P., Woltran, S.: Methods for solving reasoning problems in abstract argumentation - a survey. Artif. Intell. 220, 28–63 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Chesñevar, C.I., Simari, G.R., Godo, L., Alsinet, T.: Expansion operators for modelling agent reasoning in possibilistic defeasible logic programming. In: EUMAS 2005 - Proceedings of the Third European Workshop on Multi-Agent Systems, Brussels, Belgium, December 7–8, 2005, pp. 474–475 (2005)Google Scholar
  10. 10.
    Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77(2), 321–358 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Dung, P.M., Mancarella, P., Toni, F.: Computing ideal sceptical argumentation. Artif. Intell. 171(10–15), 642–674 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Elvang-Gøransson, M., Krause, P., Fox, J.: Acceptability of arguments as ‘logical uncertainty’. In: ECSQARU, pp. 85–90 (1993)Google Scholar
  13. 13.
    Gelder, A.V., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. J. ACM 38(3), 620–650 (1991)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., Bowen, K. (eds.) 5th Conference on Logic Programming, pp. 1070–1080. MIT Press, Cambridge (1988)Google Scholar
  15. 15.
    Gorogiannis, N., Hunter, A.: Instantiating abstract argumentation with classical logic arguments: postulates and properties. Artif. Intell. 175(9–10), 1479–1497 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Guerrero, E., Nieves, J.C., Lindgren, H.: Semantic-based construction of arguments: an answer set programming approach. Int. J. Approx. Reason. 64, 54–74 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Modgil, S., Prakken, H.: The ASPIC\(^{+}\) framework for structured argumentation: a tutorial. Argum. Comput. 5(1), 31–62 (2014)CrossRefGoogle Scholar
  18. 18.
    Nieves, J.C., Lindgren, H.: Deliberative argumentation for service provision in smart environments. In: Bulling, N. (ed.) Multi-Agent Systems. LNCS, vol. 8953, pp. 388–394. Springer, Cham (2015)Google Scholar
  19. 19.
    Oikarinen, E., Woltran, S.: Characterizing strong equivalence for argumentation frameworks. Artif. Intell. 175(14–15), 1985–2009 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Osorio, M., Nieves, J.C.: Range-based argumentation semantics as two-valued models. Theor. Pract. Log. Program. 17(1), 75–90 (2017)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Prakken, H., Sartor, G.: Argument-based extended logic programming with defeasible priorities. J. Appl. Non-Class. Log. 7(1), 25–75 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Prakken, H., Vreeswijk, G.A.W.: Logics for defeasible argumentation. In: Gabbay, D., Günthner, F. (eds.) Handbook of Philosophical Logic, vol. 4, 2nd edn, pp. 219–318. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  23. 23.
    Verheij, B.: Two approaches to dialectical argumentation: admissible sets and argumentation stages. In: Proceedings of the Eighth Dutch Conference on Artificial Intelligence (NAIC 1996) (1996)Google Scholar
  24. 24.
    Wu, Y., Caminada, M., Gabbay, D.M.: Complete extensions in argumentation coincide with 3-valued stable models in logic programming. Stud. Log. 93(2–3), 383–403 (2009)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computing ScienceUmeå UniversityUmeåSweden

Personalised recommendations