Abstract
Given an argumentation network with initial values to the arguments, we look for algorithms which can yield extensions compatible with such initial values. We find that the best way of tackling this problem is to offer an iteration formula that takes the initial values and the attack relation and iterates a sequence of intermediate values that eventually converges leading to an extension. The properties surrounding the application of the iteration formula and its connection with other numerical and non-numerical techniques proposed by others are thoroughly investigated in this paper.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Barringer, H., Gabbay, D.M., Woods, J.: Temporal dynamics of support and attack networks. In: Hutter, D., Stephan, W. (eds) Mechanizing Mathematical Reasoning. LNCS, vol. 2605 (2005)
Besnard P., Hunter A.: A logic-based theory of deductive arguments. Artif. Intell. 128(1–2), 203–235 (2001)
Brewka, G., Woltran S.: Abstract dialectical frameworks. In: Proceedings of the 12th International Conference on the Principles of Knowledge Representation and Reasoning: KR’10. pp. 102–111. AAAI Press, Menlo Park (2010)
Caminada, M.: An algorithm for computing semi-stable semantics. In: Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU ’07, pp. 222–234. Springer, Berlin (2007)
Caminada, M.: A labelling approach for ideal and stage semantics. Argum. Comput. 2(1), 1–21 (2011)
Caminada, M., Gabbay, D.M.: A logical account of formal argumentation. Stud. Log. 93(2–3), 109–145 (2009)
Caminada, M., Pigozzi, G.: On judgment aggregation in abstract argumentation. Auton. Agents Multi Agent Syst. 22(1), 64–102 (2011)
Cayrol, C., Lagasquie-Schiex, M.-C.: Graduality in argumentation. J. Artif. Intell. Res. 23, 245–297 (2005)
da Costa Pereira, C., Tettamanzi, A.G.B., Villata S.: Changing one’s mind: erase or rewind? Possibilistic belief revision with fuzzy argumentation based on trust. In: Proceedings of the 22nd International joint conference on artificial intelligence, IJCAI’11, pp. 164–171. AAAI Press, Menlo Park (2011)
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)
Eǧilmez, S., Leite, J., Martins, J.: Extending social abstract argumentation with votes on attacks. In: Proceedings of the 2nd International Workshop on Theory and Applications of Formal Argumentation (TAFA’13) (2014, to appear)
Gabbay D., Rodrigues O.: Probabilistic argumentation. An equational approach (to appear)
Gabbay D.M.: Introducing equational semantics for argumentation networks. doi:10.1007/978-3-642-22152-1_2 (2011)
Gabbay, D.M.: Equational approach to argumentation networks. Argum. Comput. 3, 87–142 (2012). doi:10.1080/19462166.2012.704398
Gabbay, D.M.: Meta-Logical Investigations in Argumentation Networks. Studies in Logic: Mathematical Logic and Foundations, vol. 44. College Publications (2013). ISBN: 978-1-84890-103-2
Gabbay, D.M., Rodrigues, O.: A equational approach to the merging of argumentation networks. J. Log. Comput. 24(6), 1253–1277 (2014). doi:10.1093/logcom/ext060
Gabbay, D.M., Rodrigues, O.: A numerical approach to the merging of argumentation networks. In: Fisher, M., van der Torre, L., Dastani, M., Governatori, G. (eds.) Proceedings of CLIMA XIII, pp. 195–212. Springer, Berlin (2012)
Hassell, M.P.: The Dynamics of Arthropod Predator–Prey Systems. Princeton University Press, New Jersey (1978)
Leite, J., Martins, J.: Social abstract argumentation. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence, (2011, to appear)
Prakken, H.: An abstract framework for argumentation with structured arguments. Argum. Comput. 1, 93–124 (2010)
Süli, E., Mayers, D.F.: An Introduction to Numerical Analysis. Cambridge University Press, London (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gabbay, D.M., Rodrigues, O. Equilibrium States in Numerical Argumentation Networks. Log. Univers. 9, 411–473 (2015). https://doi.org/10.1007/s11787-015-0119-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11787-015-0119-7