Abstract
Some abstract argumentation approaches consider that arguments have a degree of uncertainty, which impacts on the degree of uncertainty of the extensions obtained from a abstract argumentation framework (AAF) under a semantics. In these approaches, both the uncertainty of the arguments and of the extensions are modeled by means of precise probability values. However, in many real life situations the exact probabilities values are unknown and sometimes there is a need for aggregating the probability values of different sources. In this paper, we tackle the problem of calculating the degree of uncertainty of the extensions considering that the probability values of the arguments are imprecise. We use credal sets to model the uncertainty values of arguments and from these credal sets, we calculate the lower and upper bounds of the extensions. We study some properties of the suggested approach and illustrate it with an scenario of decision making.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Amgoud, L., Cayrol, C., Lagasquie-Schiex, M.C., Livet, P.: On bipolarity in argumentation frameworks. Int. J. Intell. Syst. 23(10), 1062–1093 (2008)
Cozman, F.G.: Credal networks. Artif. Intell. 120(2), 199–233 (2000)
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)
Dung, P.M., Thang, P.M.: Towards (probabilistic) argumentation for jury-based dispute resolution. In: International Conference on Computational Models of Argument, vol. 216, pp. 171–182 (2010)
Gabbay, D.M.: Equational approach to argumentation networks. Argument Comput. 3(2–3), 87–142 (2012)
Gabbay, D.M., Rodrigues, O.: Probabilistic argumentation: an equational approach. Logica Universalis 9(3), 345–382 (2015)
Hunter, A.: Some foundations for probabilistic abstract argumentation. In: International Conference on Computational Models of Argument, vol. 245, pp. 117–128 (2012)
Hunter, A.: A probabilistic approach to modelling uncertain logical arguments. Int. J. Approx. Reasoning 54(1), 47–81 (2013)
Hunter, A.: Probabilistic qualification of attack in abstract argumentation. Int. J. Approx. Reasoning 55(2), 607–638 (2014)
Levi, I.: The Enterprise of Knowledge: An Essay on Knowledge, Credal Probability, and Chance. MIT Press, Cambridge (1983)
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
Riveret, R., Korkinof, D., Draief, M., Pitt, J.: Probabilistic abstract argumentation: an investigation with boltzmann machines. Argument Comput. 6(2), 178–218 (2015)
Thimm, M.: A probabilistic semantics for abstract argumentation. In: European Conference on Artificial Intelligence, vol. 12, pp. 750–755 (2012)
Thimm, M., Baroni, P., Giacomin, M., Vicig, P.: Probabilities on extensions in abstract argumentation. In: Black, E., Modgil, S., Oren, N. (eds.) TAFA 2017. LNCS (LNAI), vol. 10757, pp. 102–119. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75553-3_7
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Morveli-Espinoza, M., Nieves, J.C., Tacla, C.A. (2019). An Imprecise Probability Approach for Abstract Argumentation Based on Credal Sets. 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_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-29765-7_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-29764-0
Online ISBN: 978-3-030-29765-7
eBook Packages: Computer ScienceComputer Science (R0)