[en] In this paper, we introduce a new definition of weakest link attack relation assignment based on lookahead, and compare this new lookahead definition with two existing ones in the literature using a principle-based analysis. We adopt a formal framework for such attack relation assignments that was introduced by Dung in 2016. We show that our lookahead definition does not satisfy context independence, we introduce a new principle called weak context independence, and we show that lookahead weakest link satisfies weak context independence. We also show that lookahead weakest link is the closest approximation to Brewka’s prioritised default logic PDL, also known as the greedy approach. For PDL, we prove an impossibility result under Dung’s axioms. Our results generalise earlier findings restricted to total orders to the more general case of modular orders.
Disciplines :
Computer science
Author, co-author :
Chen, Chen ; Zhejiang University, Hangzhou, China
PARDO VENTURA, Pere ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
VAN DER TORRE, Leon ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
YU, Liuwen ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS) ; University of Bologna, Bologna, Italy
External co-authors :
yes
Language :
English
Title :
Weakest Link in Formal Argumentation: Lookahead and Principle-Based Analysis
Publication date :
2023
Event name :
Logic and Argumentation - 5th International Conference (CLAR 2023)
Event place :
Hangzhou, Chn
Event date :
10-09-2023 => 12-09-2023
Audience :
International
Main work title :
Logic and Argumentation - 5th International Conference, CLAR 2023, Proceedings
Author, co-author :
Jieting, Luo
PARDO VENTURA, Pere ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
Editor :
Herzig, Andreas
Publisher :
Springer Science and Business Media Deutschland GmbH
FNR14776480 - Deontic Logic For Epistemic Rights, 2020 (01/09/2021-31/08/2024) - Leon Van Der Torre
Funding text :
Acknowledgements. The authors are thankful to the three anonymous reviewers for their helpful comments and suggestions. L. van der Torre is financially supported by FNR through the project OPEN O20/14776480, the G.A. INTER/CHIST/19/14589586 Horizon 2020 grant, and EU’s Justice programme under grant 101007420 (ADELE).
Arrow, K.J.: A difficulty in the concept of social welfare. J. Polit. Econ. 54(4), 328–346 (1950)
Beirlaen, M., Heyninck, J., Pardo, P., Straßer, C.: Argument strength in formal argumentation. J. Log. Their Appl. 5(3), 629–676 (2018)
Besnard, P., Hunter, A.: Elements of Argumentation. MIT Press, Cambridge (2008)
Bondarenko, A., Dung, P., Kowalski, R., Toni, F.: An abstract, argumentation-theoretic approach to default reasoning. Artif. Intell. 93(1), 63–101 (1997)
Brewka, G., Eiter, T.: Preferred answer sets for extented logic programs. Artif. Intell. 109, 297–356 (1999)
Brewka, G.: Reasoning about priorities in default logic. In: Hayes-Roth, B., Korf, R.E. (eds.) Proceedings of the 12th National Conference on AI, vol. 2, pp. 940–945. AAAI Press/The MIT Press (1994)
Brewka, G., Eiter, T.: Prioritizing default logic. In: Hölldobler, S. (ed.) Intellectics and Computational Logic. Applied Logic Series, vol. 19, pp. 27–45. Kluwer (2000)
Caminada, M.: Rationality postulates: applying argumentation theory for nonmonotonic reasoning. FLAP 4(8), 2707–2734 (2017)
Delgrande, J.P., Schaub, T.: Expressing preferences in default logic. Artif. Intell. 123(1–2), 41–87 (2000)
Delgrande, J.P., Schaub, T., Tompits, H., Wang, K.: A classification and survey of preference handling approaches in nonmonotonic reasoning. Comput. Intell. 20(2), 308–334 (2004)
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), 321–358 (1995)
Dung, P.M.: An axiomatic analysis of structured argumentation for prioritized default reasoning. In: Frontiers in Artificial Intelligence and Applications, vol. 263, pp. 267–272. IOS Press (2014)
Dung, P.M.: An axiomatic analysis of structured argumentation with priorities. Artif. Intell. 231, 107–150 (2016)
Dung, P.M.: A canonical semantics for structured argumentation with priorities. In: Baroni, P., Gordon, T.F., Scheffler, T., Stede, M. (eds.) Computational Models of Argument-Proceedings of COMMA. Frontiers in Artificial Intelligence and Applications, vol. 287, pp. 263–274. IOS Press (2016)
Dung, P.M., Kowalski, R.A., Toni, F.: Assumption-based argumentation. In: Simari, G.R., Rahwan, I. (eds.) Argumentation in Artificial Intelligence, pp. 199– 218. Springer, Boston (2009). https://doi.org/10.1007/978-0-387-98197-0 10
Dung, P.M., Thang, P.M.: Fundamental properties of attack relations in structured argumentation with priorities. Artif. Intell. 255, 1–42 (2018)
Dung, P.M., Thang, P.M., Son, T.C.: On structured argumentation with conditional preferences. In: The Thirty-Third AAAI Conference on Artificial Intelligence, AAAI, pp. 2792–2800. AAAI Press (2019)
Goodman, N.: Fact, Fiction, and Forecast. Harvard University Press, Cambridge (1955)
Gorogiannis, N., Hunter, A.: Instantiating abstract argumentation with classical logic arguments: postulates and properties. Artif. Intell. 175(9–10), 1479–1497 (2011)
Governatori, G., Maher, M.J., Antoniou, G., Billington, D.: Argumentation semantics for defeasible logic. J. Log. Comput. 14(5), 675–702 (2004)
Lehtonen, T., Wallner, J.P., Järvisalo, M.: Computing stable conclusions under the weakest-link principle in the ASPIC+ argumentation formalism. In: Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning, vol. 19 (1), pp. 215–225 (2022)
Liao, B., Oren, N., van der Torre, L., Villata, S.: Prioritized norms in formal argumentation. J. Log. Comput. 29(2), 215–240 (2019)
Modgil, S., Prakken, H.: A general account of argumentation with preferences. Artif. Intell. 195, 361–397 (2013)
Modgil, S., Prakken, H.: The ASP IC+ framework for structured argumentation: a tutorial. Argument Comput. 5(1), 31–62 (2014)
Modgil, S., Prakken, H.: Abstract rule-based argumentation. In: Baroni, P., et al. (eds.) Handbook of Formal Argumentation, vol. 1, pp. 287–364. College Publications, Norcross (2018)
Pardo, P., Straßer, C.: Modular orders on defaults in formal argumentation. J. Logic Comput. (2022)
Pollock, J.L.: How to reason defeasibly. Artif. Intell. 57(1), 1–42 (1992)
Pollock, J.L.: Justification and defeat. Artif. Intell. 67(2), 377–407 (1994)
Pollock, J.L.: Cognitive Carpentry: A Blueprint for How to Build a Person. MIT Press, Cambridge (1995)
Pollock, J.L.: Defeasible reasoning with variable degrees of justification. Artif. Intell. 133(1–2), 233–282 (2001)
Pollock, J.L.: Defeasible reasoning and degrees of justification. Argument Comput. 1(1), 7–22 (2010)
Prakken, H., Vreeswijk, G.: Logics for defeasible argumentation. In: Handbook of Philosophical Logic, pp. 219–318 (2002)
Young, A.P., Modgil, S., Rodrigues, O.: Prioritised default logic as rational argumentation. In: Jonker, C.M., Marsella, S., Thangarajah, J., Tuyls, K. (eds.) Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems, pp. 626–634. ACM (2016)
Young, A.P., Modgil, S., Rodrigues, O.: On the interaction between logic and preference in structured argumentation. In: Black, E., Modgil, S., Oren, N. (eds.) TAFA 2017. LNCS (LNAI), vol. 10757, pp. 35–50. Springer, Cham (2018). https://doi. org/10.1007/978-3-319-75553-3 3
