Advertisement

Two Forms of Minimality in ASPIC\(^+\)

  • Zimi Li
  • Andrea Cohen
  • Simon Parsons
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10767)

Abstract

Many systems of structured argumentation explicitly require that the facts and rules that make up the argument for a conclusion be the minimal set required to derive the conclusion. \(\textsc {aspic}^{\mathsf {+}}\) does not place such a requirement on arguments, instead requiring that every rule and fact that are part of an argument be used in its construction. Thus \(\textsc {aspic}^{\mathsf {+}}\) arguments are minimal in the sense that removing any element of the argument would lead to a structure that is not an argument. In this paper we discuss these two types of minimality and show how the first kind of minimality can, if desired, be recovered in \(\textsc {aspic}^{\mathsf {+}}\).

Notes

Acknowledgements

This work was partially funded by EPSRC EP/P010105/1 Collaborative Mobile Decision Support for Managing Multiple Morbidities.

References

  1. 1.
    Amgoud, L., Cayrol, C.: A reasoning model based on the production of acceptable arguments. Ann. Math. Artif. Intell. 34(3), 197–215 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Besnard, P., Hunter, A.: A logic-based theory of deductive arguments. Artif. Intell. 128, 203–235 (2001)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cohen, A., Parsons, S., Sklar, E., McBurney, P.: A characterization of types of support between structured arguments and their relationship with support in abstract argumentation. Int. J. Approx. Reason. 94, 76–104 (2018)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Dung, P.M., Kowalski, R.A., Toni, F.: Dialectic proof procedures for assumption-based, admissable argumentation. Artif. Intell. 170(2), 114–159 (2006)CrossRefGoogle Scholar
  5. 5.
    García, A.J., Simari, G.: Defeasible logic programming: an argumentative approach. Theory Pract. Logic Program. 4(1), 95–138 (2004)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Krause, P., Ambler, S., Elvang-Gørannson, M., Fox, J.: A logic of argumentation for reasoning under uncertainty. Comput. Intell. 11(1), 113–131 (1995)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Loui, R.P.: Defeat among arguments: a system of defeasible inference. Comput. Intell. 3(3), 100–106 (1987)CrossRefGoogle Scholar
  8. 8.
    Modgil, S., Prakken, H.: A general account of argumentation with preferences. Artif. Intell. 195, 361–397 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Pollock, J.: Cognitive Carpentry. MIT Press, Cambridge (1995)Google Scholar
  10. 10.
    Pollock, J.L.: Defeasible reasoning. Cogn. Sci. 11, 481–518 (1987)CrossRefGoogle Scholar
  11. 11.
    Pollock, J.L.: OSCAR–a general-purpose defeasible reasoner. J. Appl. Non-Classical Logics 6, 89–113 (1996)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Prakken, H.: An abstract framework for argumentation with structured arguments. Argum. Comput. 1, 93–124 (2010)CrossRefGoogle Scholar
  13. 13.
    Prakken, H., Sartor, G.: Argument-based logic programming with defeasible priorities. J. Appl. Non-classical Logics 7, 25–75 (1997)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Sinnott-Armstrong, W.: Begging the question. Australas. J. Philos. 77(2), 174–191 (1999)CrossRefGoogle Scholar
  15. 15.
    Walton, D.N.: Plausible Argument in Everyday Conversation. State University of New York Press, Albany (1992)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Computer Science, Graduate CenterCity University of New YorkNew York CityUSA
  2. 2.Institute for Computer Science and Engineering, CONICET-UNS, Department of Computer Science and EngineeringUniversidad Nacional del SurBahía BlancaArgentina
  3. 3.Department of InformaticsKing’s College LondonLondonUK

Personalised recommendations