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A Model-Based Theorem Prover for Epistemic Graphs for Argumentation

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11726))

Abstract

Epistemic graphs are a recent proposal for probabilistic argumentation that allows for modelling an agent’s degree of belief in an argument and how belief in one argument may influence the belief in other arguments. These beliefs are represented by probability distributions and how they affect each other is represented by logical constraints on these distributions. Within the full language of epistemic constraints, we distinguish a restricted class which offers computational benefits while still being powerful enough to allow for handling of many other argumentation formalisms and that can be used in applications that, for instance, rely on Likert scales. In this paper, we propose a model-based theorem prover for reasoning with the restricted epistemic language.

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Notes

  1. 1.

    We note that this is a simpler, but still equivalent version of the notion in [8].

References

  1. http://www0.cs.ucl.ac.uk/staff/A.Hunter/papers/autoepigraphextra.pdf

  2. http://www0.cs.ucl.ac.uk/staff/A.Hunter/papers/autoepigraph.py

  3. Baroni, P., Giacomin, M., Vicig, P.: On rationality conditions for epistemic probabilities in abstract argumentation. In: Parsons, S., Oren, N., Reed, C., Cerutti, F. (eds.) COMMA 2014. FAIA, vol. 266, pp. 121–132. IOS Press (2014)

    Google Scholar 

  4. Bistarelli, S., Mantadelis, T., Santini, F., Taticchi, C.: Probabilistic argumentation frameworks with MetaProbLog and ConArg. In: Tsoukalas, L.H., Grégoire, É., Alamaniotis, M. (eds.) ICTAI 2018, pp. 675–679. IEEE (2018)

    Google Scholar 

  5. Doder, D., Woltran, S.: Probabilistic argumentation frameworks – a logical approach. In: Straccia, U., Calì, A. (eds.) SUM 2014. LNCS (LNAI), vol. 8720, pp. 134–147. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11508-5_12

    Chapter  Google Scholar 

  6. Fazzinga, B., Flesca, S., Furfaro, F.: Complexity of fundamental problems in probabilistic abstract argumentation: beyond independence. Artif. Intell. 268, 1–29 (2018)

    Article  MathSciNet  Google Scholar 

  7. Feller, W.: An Introduction to Probability Theory and Its Applications, vol. 1, 2nd edn. Wiley, London (1950)

    MATH  Google Scholar 

  8. Hunter, A., Polberg, S., Thimm, M.: Epistemic graphs for representing and reasoning with positive and negative influences of arguments. arXiv CoRR (2018). abs/1802.07489

    Google Scholar 

  9. Hunter, A.: Some foundations for probabilistic abstract argumentation. In: Verheij, B., Szeider, S., Woltran, S. (eds.) COMMA 2012. FAIA, vol. 245, pp. 117–128. IOS Press (2012)

    Google Scholar 

  10. Hunter, A.: A probabilistic approach to modelling uncertain logical arguments. Int. J. Approximate Reasoning 54(1), 47–81 (2013)

    Article  MathSciNet  Google Scholar 

  11. Hunter, A.: Probabilistic qualification of attack in abstract argumentation. Int. J. Approximate Reasoning 55, 607–638 (2014)

    Article  MathSciNet  Google Scholar 

  12. Hunter, A., Polberg, S., Potyka, N.: Updating belief in arguments in epistemic graphs. In: Thielscher, M., Toni, F., Wolter, F. (eds.) KR 2018, pp. 138–147. AAAI Press (2018)

    Google Scholar 

  13. Hunter, A., Thimm, M.: Probabilistic reasoning with abstract argumentation frameworks. J. Artif. Intell. Res. 59, 565–611 (2017)

    Article  MathSciNet  Google Scholar 

  14. Li, H., Oren, N., Norman, T.J.: Probabilistic argumentation frameworks. In: Modgil, S., Oren, N., Toni, F. (eds.) TAFA 2011. LNCS (LNAI), vol. 7132, pp. 1–16. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29184-5_1

    Chapter  Google Scholar 

  15. Likert, R.: A technique for the measurement of attitudes. Arch. Psychol. 140, 1–55 (1931)

    Google Scholar 

  16. Polberg, S., Doder, D.: Probabilistic abstract dialectical frameworks. In: Fermé, E., Leite, J. (eds.) JELIA 2014. LNCS (LNAI), vol. 8761, pp. 591–599. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11558-0_42

    Chapter  Google Scholar 

  17. Polberg, S., Hunter, A.: Empirical evaluation of abstract argumentation: supporting the need for bipolar and probabilistic approaches. Int. J. Approximate Reasoning 93, 487–543 (2018)

    Article  MathSciNet  Google Scholar 

  18. Polberg, S., Hunter, A., Thimm, M.: Belief in attacks in epistemic probabilistic argumentation. In: Moral, S., Pivert, O., Sánchez, D., Marín, N. (eds.) SUM 2017. LNCS (LNAI), vol. 10564, pp. 223–236. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67582-4_16

    Chapter  Google Scholar 

  19. Thimm, M.: A probabilistic semantics for abstract argumentation. In: De Raedt, L., Bessiere, C., Dubois, D., Doherty, P., Frasconi, P., Heintz, F., Lucas, P. (eds.) ECAI 2012. FAIA, vol. 242, pp. 750–755. IOS Press (2012)

    Google Scholar 

  20. Thimm, M., Polberg, S., Hunter, A.: Epistemic attack semantics. In: Modgil, S., Budzynska, K., Lawrence, J. (eds.) COMMA 2018. FAIA, vol. 305, pp. 37–48. IOS Press (2018)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University College London, London, UK

    Anthony Hunter

  2. School of Computer Science and Informatics, Cardiff University, Cardiff, UK

    Sylwia Polberg

Authors
  1. Anthony Hunter
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  2. Sylwia Polberg
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Correspondence to Anthony Hunter or Sylwia Polberg .

Editor information

Editors and Affiliations

  1. Technische Universität Dortmund, Dortmund, Germany

    Gabriele Kern-Isberner

  2. Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Zoran Ognjanović

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Hunter, A., Polberg, S. (2019). A Model-Based Theorem Prover for Epistemic Graphs for Argumentation. In: Kern-Isberner, G., Ognjanović, Z. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science(), vol 11726. Springer, Cham. https://doi.org/10.1007/978-3-030-29765-7_5

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  • DOI: https://doi.org/10.1007/978-3-030-29765-7_5

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