I don’t care, I don’t know … I know too much! On Incompleteness and Undecidedness in Abstract Argumentation

  • Pietro Baroni
  • Massimiliano Giacomin
  • Beishui Liao

Abstract

Incompleteness and undecidedness are pervasively present in human reasoning activities and make the definition of the relevant computational models challenging. In this discussion paper we focus on one such model, namely abstract argumentation frameworks, and examine several flavours of incompleteness and undecidedness thereof, by providing a conceptual analysis, a critical literature review, and some new ideas with pointers to future research.

Keywords

Argumentation frameworks Argumentation semantics Incompleteness Undecidedness 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arieli, O.: On the acceptance of loops in argumentation frameworks. J. of Logic and Computation (to appear, 2014)Google Scholar
  2. 2.
    Arieli, O., Avron, A.: The value of the four values. Artif. Intell. 102, 97–141 (1998)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Baroni, P., Boella, G., Cerutti, F., Giacomin, M., van der Torre, L.W.N., Villata, S.: On input/output argumentation frameworks. In: Proc. of the 4th Int. Conf. on Computational Models of Argument (COMMA 2012), pp. 358–365 (2012)Google Scholar
  4. 4.
    Baroni, P., Boella, G., Cerutti, F., Giacomin, M., Torre, L.W.N.v.d., Villata, S.: On the input/output behavior of argumentation frameworks. Artif. Intell. 217, 144–197 (2014)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Baroni, P., Caminada, M., Giacomin, M.: An introduction to argumentation semantics. Knowledge Engineering Review 26(4), 365–410 (2011)CrossRefGoogle Scholar
  6. 6.
    Baroni, P., Giacomin, M.: On principle-based evaluation of extension-based argumentation semantics. Artif. Intell. 171(10/15), 675–700 (2007)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Baroni, P., Giacomin, M., Guida, G.: SCC-recursiveness: a general schema for argumentation semantics. Artif. Intell. 168(1-2), 165–210 (2005)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Baroni, P., Giacomin, M., Liao, B.: On topology-related properties of abstract argumentation semantics. A correction and extension to Dynamics of argumentation systems: A division-based method. Artif. Intell. 212, 104–115 (2014)CrossRefMATHGoogle Scholar
  9. 9.
    Baumann, R.: Splitting an argumentation framework. In: Delgrande, J.P., Faber, W. (eds.) LPNMR 2011. LNCS, vol. 6645, pp. 40–53. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Baumann, R., Brewka, G.: Expanding argumentation frameworks: Enforcing and monotonicity results. In: Proc. of the 3rd Int. Conf. on Computational Models of Argument (COMMA 2010), pp. 75–86 (2010)Google Scholar
  11. 11.
    Baumann, R., Brewka, G., Dvořák, W., Woltran, S.: Parameterized splitting: A simple modification-based approach. In: Erdem, E., Lee, J., Lierler, Y., Pearce, D. (eds.) Correct Reasoning. LNCS, vol. 7265, pp. 57–71. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  12. 12.
    Belnap, N.D.: How a computer should think. In: Ryle, G. (ed.) Contemporary aspects of philosophy, pp. 30–56. Oriel Press (1977)Google Scholar
  13. 13.
    Besnard, P., Garcia, A., Hunter, A., Modgil, S., Prakken, H., Simari, G., Toni, F.: Special issue: Tutorials on structured argumentation. Argument & Computation 5(1) (2014)Google Scholar
  14. 14.
    Brewka, G., Woltran, S.: Abstract dialectical frameworks. In: Proc. of the 12th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR 2010), pp. 102–111 (2010)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(2), 321–357 (1995)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Dunn, J.M.: Contradictory information: Too much of a good thing. J. of Philosophical Logic 39, 425–452 (2010)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Gabbay, D.M.: Fibring argumentation frames. Studia Logica 93(2-3), 231–295 (2009)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Ginsberg, M.L.: Multivalued logics: a uniform approach to reasoning in AI. Computer Intelligence 4, 256–316 (1988)Google Scholar
  19. 19.
    Jakobovits, H., Vermeir, D.: Robust semantics for argumentation frameworks. J. of Logic and Computation 9(2), 215–261 (1999)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Liao, B.: Toward incremental computation of argumentation semantics: A decomposition-based approach. Ann. Math. Artif. Intell. 67(3-4), 319–358 (2013)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Liao, B., Huang, H.: Partial semantics of argumentation: basic properties and empirical results. J. of Logic and Computation 23(3), 541–562 (2013)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Liao, B., Jin, L., Koons, R.C.: Dynamics of argumentation systems: A division-based method. Artif. Intell. 175(11), 1790–1814 (2011)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Pollock, J.: How to reason defeasibly. Artif. Intell. 57, 1–42 (1992)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Rienstra, T., Perotti, A., Villata, S., Gabbay, D.M., van der Torre, L.: Multi-sorted argumentation. In: Modgil, S., Oren, N., Toni, F. (eds.) TAFA 2011. LNCS, vol. 7132, pp. 215–231. Springer, Heidelberg (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Pietro Baroni
    • 1
  • Massimiliano Giacomin
    • 1
  • Beishui Liao
    • 2
  1. 1.Dip. Ingegneria dell’InformazioneUniv. of BresciaBresciaItaly
  2. 2.Center for the Study of Language and CognitionZhejiang Univ.HangzhouChina

Personalised recommendations