Correct Grounded Reasoning with Presumptive Arguments

  • Bart Verheij
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10021)


We address the semantics and normative questions for reasoning with presumptive arguments: How are presumptive arguments grounded in interpretations; and when are they evaluated as correct? For deductive and uncertain reasoning, classical logic and probability theory provide canonical answers to these questions. Staying formally close to these, we propose case models and their preferences as formal semantics for the interpretation of presumptive arguments. Arguments are evaluated as presumptively valid when they make a case that is maximally preferred. By qualitative and quantitative representation results, we show formal relations between deductive, uncertain and presumptive reasoning. In this way, the work is a step to the connection of logical and probabilistic approaches in AI.


Bayesian Network Classical Logic Case Model Crime Scene Valid Argument 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Amgoud, L.: Postulates for logic-based argumentation systems. Int. J. Intell. Syst. 55(9), 2028–2048 (2014)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Amgoud, L., Caminada, M.: On the evaluation of argumentation formalisms. Artif. Intell. 172, 286–310 (2007)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Baroni, P., Caminada, M., Giacomin, M.: Review: an introduction to argumentation semantics. Knowl. Eng. Rev. 26(4), 365–410 (2011)CrossRefGoogle Scholar
  4. 4.
    Benthem, J. van: Foundations of conditional logic. J. Philos. Logic 13, 303–349 (1984)Google Scholar
  5. 5.
    Besnard, P., García, A.J., Hunter, A., Modgil, S., Prakken, H., Simari, G.R., Toni, F.: Introduction to structured argumentation. Argument Comput. 5, 1–4 (2014)CrossRefGoogle Scholar
  6. 6.
    Besnard, P., Hunter, A.: A logic-based theory of deductive arguments. Artif. Intell. 128, 203–235 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bochman, A.: A Logical Theory of Nonmonotonic Inference and Belief Change. Springer, Berlin (2001)CrossRefzbMATHGoogle Scholar
  8. 8.
    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
  9. 9.
    Dawid, A.P.: Beware of the DAG! In: Guyon, I., Janzing, D., Schölkopf, B. (eds.) JMLR Workshop and Conference Proceedings. Causality: Objectives and Assessment (NIPS 2008 Workshop), vol. 6, pp. 59–86 (2010).
  10. 10.
    Dubois, D., Prade, H.: Possibility theory, probability theory and multiple-valued logics: a clarification. Ann. Math. Artif. Intell. 32(1), 35–66 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Eemeren, F. H. van, Garssen, B., Krabbe, E.C.W., Henkemans, A.F.S., Verheij, B., Wagemans, J.H.M.: Argumentation in artificial intelligence. In: Eemeren, F. H. van, et al. (eds.) Handbook of Argumentation Theory. Springer, Berlin (2014)Google Scholar
  13. 13.
    García, A.J., Simari, G.R.: Defeasible logic programming: an argumentative approach. Theory Pract. Logic Program. 4(2), 95–138 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Hunter, A.: A probabilistic approach to modelling uncertain logical arguments. Int. J. Approx. Reason. 54, 47–81 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Hunter, A.: Probabilistic qualification of attack in abstract argumentation. Int. J. Approx. Reason. 55, 607–638 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44, 167–207 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Li, H., Oren, N., Norman, T.J.: Probabilistic argumentation frameworks. In: Modgil, S., Oren, N., Toni, F. (eds.) TAFA 2011. LNCS, vol. 7132, pp. 1–16. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  18. 18.
    Makinson, D.: General patterns in nonmonotonic reasoning. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, Nonmonotonic Reasoning and Uncertain Reasoning, vol. 3, pp. 35–110. Clarendon Press, Oxford (1994)Google Scholar
  19. 19.
    Modgil, S., Prakken, H.: A general account of argumentation with preferences. Artif. Intell. 195, 361–397 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Pollock, J.L.: Defeasible reasoning. Cogn. Sci. 11(4), 481–518 (1987)CrossRefGoogle Scholar
  21. 21.
    Pollock, J.L.: Cognitive Carpentry: A Blueprint for How to Build a Person. The MIT Press, Cambridge (1995)Google Scholar
  22. 22.
    Prakken, H.: An abstract framework for argumentation with structured arguments. Argument Comput. 1(2), 93–124 (2010)CrossRefGoogle Scholar
  23. 23.
    Roberts, F.S.: Measurement Theory with Applications to Decisionmaking, Utility, and the Social Sciences. Cambridge University Press, Cambridge (1985)Google Scholar
  24. 24.
    Russell, S.: Unifying logic and probability. Commun. ACM 58(7), 88–97 (2015)CrossRefGoogle Scholar
  25. 25.
    Simari, G.R.: On the properties of the relation between argumentation semantics and argumentation inference operators. In: Parsons, S., Oren, N., Reed, C., Cerutti, F. (eds.) Computational Models of Argument, Proceedings of COMMA 2014, pp. 3–8. IOS Press, Amsterdam (2014)Google Scholar
  26. 26.
    Thimm, M.: A probabilistic semantics for abstract argumentation. In: Proceedings of the European Conference on Artificial Intelligence (ECAI 2012), pp. 750–755. IOS Press, Amsterdam (2012)Google Scholar
  27. 27.
    Toulmin, S.E.: The Uses of Argument. Cambridge University Press, Cambridge (1958)Google Scholar
  28. 28.
    Verheij, B.: Argumentation and rules with exceptions. In: Computational Models of Argument: Proceedings of COMMA 2010, Desenzano del Garda, Italy, 8–10 September 2010, pp. 455–462. IOS Press, Amsterdam (2010)Google Scholar
  29. 29.
    Verheij, B.: Jumping to conclusions. In: del Cerro, L.F., Herzig, A., Mengin, J. (eds.) JELIA 2012. LNCS, vol. 7519, pp. 411–423. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  30. 30.
    Verheij, B.: Arguments and their strength: revisiting Pollock’s anti-probabilistic starting points. In: Parsons, S., Oren, N., Reed, C., Cerutti, F. (eds.) Computational Models of Argument. Proceedings of COMMA 2014, pp. 433–444. IOS Press, Amsterdam (2014)Google Scholar
  31. 31.
    Verheij, B.: To catch a thief with and without numbers: arguments, scenarios and probabilities in evidential reasoning. Law Probab. Risk 13, 307–325 (2014)CrossRefGoogle Scholar
  32. 32.
    Verheij, B., Bex, F.J., Timmer, S.T., Vlek, C.S., Meyer, J.J., Renooij, S., Prakken, H.: Arguments, scenarios and probabilities: connections between three normative frameworks for evidential reasoning. Law Probab. Risk 15, 35–70 (2016)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Artificial IntelligenceUniversity of GroningenGroningenThe Netherlands

Personalised recommendations