Abstract
Some semantics for argumentation, including the newly introduced weakly admissible semantics, allow us to ignore attacks from arguments that are perceived as problematic. A key intuition motivating such semantics is that arguments that indirectly attack themselves may be problematic in such a way that this is justified. In this paper, we formalise this intuition and provide a class of semantics that are weakly admissible, coincide with the stable semantics on a large class of argumentation frameworks that admit stable sets, and only ignore attacks from arguments on unsafe cycles of odd length. We also show that no member of our class of semantics coincide with the semantics that takes all \(\subseteq \)-maximal weakly admissible sets as extensions. However, we show that this semantics satisfies an even stronger property, if the following conjecture is true: if an argumentation framework has no non-empty weakly admissible sets, then every argument lies on an unsafe odd cycle.
Thanks to the anonymous reviewers for pointing out some relevant references and making suggestions that greatly improved the presentation of the paper.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
The notion of a perfect extension could be made more general by explicitly taking the principle that is perfectly extended as a parameter, defining an AF to be perfectly X if all induced subdigraphs of the AF has an extension satisfying X. Then we could say that a semantics perfectly extends X, or that it satisfies the perfect extension principle for X, whenever it satisfies X for all AFs that are perfectly X. However, we only consider perfect extensions of the stable semantics in this paper, so we prefer to avoid the additional notation and terminology that the generalisation entails.
References
Baroni, P., Giacomin, M.: On principle-based evaluation of extension-based argumentation semantics. Artif. Intell. 171(10–15), 675–700 (2007)
Baroni, P., Giacomin, M., Guida, G.: SCC-recursiveness: a general schema for argumentation semantics. Artif. Intell. 168(1–2), 162–210 (2005)
Baumann, R., Brewka, G., Ulbricht, M.: Revisiting the foundations of abstract argumentation - semantics based on weak admissibility and weak defense. In: The Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20), pp. 2742–2749. AAAI Press (2020)
Baumann, R., Brewka, G., Ulbricht, M.: Shedding new light on the foundations of abstract argumentation: Modularization and weak admissibility. Artif. Intell. 310, 103742 (2022)
Caminada, M.W.A., Carnielli, W.A., Dunne, P.E.: Semi-stable semantics. J. Log. Comput. 22(5), 1207–1254 (2012)
Cramer, M., van der Torre, L.: SCF2 - an argumentation semantics for rational human judgments on argument acceptability. In: Beierle, C., Ragni, M., Stolzenburg, F., Thimm, M. (eds.) Proceedings of the 8th Workshop on Dynamics of Knowledge and Belief (DKB-2019) and the 7th Workshop KI & Kognition (KIK-2019)co-located with 44nd German Conference on Artificial Intelligence (KI 2019), Kassel, Germany, September 23, 2019. CEUR Workshop Proceedings, vol. 2445, pp. 24–35. CEUR-WS.org (2019). https://ceur-ws.org/Vol-2445/paper_3.pdf
Dauphin, J., Rienstra, T., van der Torre, L.: A principle-based analysis of weakly admissible semantics. In: Prakken, H., Bistarelli, S., Santini, F., Taticchi, C. (eds.) Computational Models of Argument - Proceedings of COMMA 2020, Perugia, Italy, September 4–11, 2020. Frontiers in Artificial Intelligence and Applications, vol. 326, pp. 167–178. IOS Press (2020)
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)
Dvorák, W., Rienstra, T., van der Torre, L., Woltran, S.: Non-admissibility in abstract argumentation. In: Toni, F., Polberg, S., Booth, R., Caminada, M., Kido, H. (eds.) Computational Models of Argument - Proceedings of COMMA 2022, Cardiff, Wales, UK, 14–16 September 2022. Frontiers in Artificial Intelligence and Applications, vol. 353, pp. 128–139. IOS Press (2022)
Dyrkolbotn, S.K., Walicki, M.: Propositional discourse logic. Synthese 191(5), 863–899 (2014)
Galeana-Sánchez, H., Neumann-Lara, V.: On kernels and semikernels of digraphs. Discret. Math. 48(1), 67–76 (1984)
Kampik, T., Gabbay, D.M., Sartor, G.: A comprehensive account of the burden of persuasion in abstract argumentation. J. Log. Comput. 33(2), 257–288 (2023)
Richardson, M.: Solutions of irreflexive relations. Ann. Math. 58(3), 573–590 (1953). http://www.jstor.org/stable/1969755
Thimm, M.: Revisiting initial sets in abstract argumentation. Argument Comput. 13(3), 325–360 (2022)
Thimm, M.: On undisputed sets in abstract argumentation. In: The Thirty-Seventh AAAI Conference on Artificial Intelligence (AAAI-23), pp. 6550–6557. AAAI Press (2023)
Xu, Y., Cayrol, C.: Initial sets in abstract argumentation frameworks. In: Ågotnes, T., Liao, B., Wáng, Y.N. (eds.) Proceedings of the 1st Chinese Conference on Logic and Argumentation (CLAR 2016), Hangzhou, China, April 2–3, 2016. CEUR Workshop Proceedings, vol. 1811, pp. 72–85. CEUR-WS.org (2016). https://ceur-ws.org/Vol-1811/paper6.pdf
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Dyrkolbotn, S.K. (2023). Weak Argumentation Semantics and Unsafe Odd Cycles: Results and a Conjecture. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_12
Download citation
DOI: https://doi.org/10.1007/978-3-031-43619-2_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-43618-5
Online ISBN: 978-3-031-43619-2
eBook Packages: Computer ScienceComputer Science (R0)