Abstract
The exact relationship between formal argumentation and nonmonotonic logics is a research topic that keeps on eluding researchers despite recent intensified efforts. We contribute to a deeper understanding of this relation by investigating characterizations of abstract dialectical frameworks in conditional logics for nonmonotonic reasoning. We first show that in general, there is a gap between argumentation and conditional semantics when applying several intuitive translations, but then prove that this gap can be closed when focusing on specific classes of translations.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Arieli, O., Heyninck, J.: Prioritized simple contrapositive assumption-based frameworks. In: Proceedings of the 24th European Conference on Artificial Intelligence (ECAI20). IOS Press. http://www2.mta.ac.il/oarieli/Papers/ecai20.pdf (2020)
Arlo-Costa, H.: The Logic of Conditionals. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, Summer 2019 edn. Metaphysics Research Lab, Stanford University (2019)
Besnard, P., Garcia, A., Hunter, A., Modgil, S., Prakken, H., Simari, G., Toni, F.: Introduction to structured argumentation. Argument & Computation 5(1), 1–4 (2014)
Besnard, P., Grégoire, É., Raddaoui, B.: A conditional logic-based argumentation framework. In: International Conference on Scalable Uncertainty Management, pp. 44–56. Springer (2013)
Besnard, P., Hunter, A.: Elements of Argumentation, vol. 47. MIT Press, Cambridge (2008)
Booth, R., Varzinczak, I.: Towards conditional inference under disjunctive rationality. In: NMR 2020 Workshop Notes, p 37 (2020)
Brewka, G., Strass, H., Ellmauthaler, S., Wallner, J.P., Woltran, S.: Abstract dialectical frameworks revisited. In: ICJAI (2013)
Čyras, K., Toni, F.: Non-monotonic inference properties for assumption-based argumentation. In: TAFA, pp. 92–111. Springer (2015)
Diller, M., Zafarghandi, A., Linsbichler, T., Woltran, S.: Investigating subclasses of abstract dialectical frameworks. Argument & Computation, pp. 1–29. https://doi.org/10.3233/AAC-190481 (2020)
Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. AI 77, 321–358 (1995)
de Finetti, B.: Theory of probability (2 vols.) (1974)
García, A.J., Simari, G.R.: Defeasible logic programming: an argumentative approach. TPLP 4(1 + 2), 95–138 (2004)
Goldszmidt, M., Pearl, J.: Qualitative probabilities for default reasoning, belief revision, and causal modeling. AI 84(1-2), 57–112 (1996)
Gottlob, G.: The power of beliefs or translating default logic into standard autoepistemic logic. In: Foundations of Knowledge Representation and Reasoning, pp. 133–144. Springer (1994)
Heyninck, J.: Relations between assumption-based approaches in non-monotonic logic and formal argumentation. Journal of Applied Logics 6(2), 317–357 (2019)
Heyninck, J., Arieli, O.: Simple contrapositive assumption-based argumentation frameworks. Int. J. Approx. Reason. 121, 103–124 (2020)
Heyninck, J.: Straßer, C.: Relations between Assumption-Based Approaches in Nonmonotonic Logic and Formal Argumentation. In: 16Th International Workshop on Non-Monotonic Reasoning, P. 65 (2016)
Heyninck, J., Straßer, C.: A comparative study of assumption-based approaches to reasoning with priorities. In: Second Chinese Conference on Logic and Argumentation (2018)
Imielinski, T.: Results on translating defaults to circumscription. Artif. Intell. 32(1), 131–146 (1987)
Kern-Isberner, G.: Conditionals in Nonmonotonic Reasoning and Belief Revision: Considering Conditionals as Agents. Springer, Berlin (2001)
Kern-Isberner, G., Simari, G.R.: A default logical semantics for defeasible argumentation. In: FLAIRS 24 (2011)
Kern-Isberner, G., Thimm, M.: Towards conditional logic semantics for abstract dialectical frameworks. In: Others, C.C. (ed.) Argumentation-Based Proofs of Endearment, Tributes, vol. 37. College Publications (2018)
Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. AI 44(1-2), 167–207 (1990)
Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? AI 55(1), 1–60 (1992)
Li, Z., Oren, N., Parsons, S.: On the links between argumentation-based reasoning and nonmonotonic reasoning. In: TAFA, pp. 67–85. Springer (2017)
Linsbichler, T., Woltran, S.: Revision of abstract dialectical frameworks: preliminary report. In: First International Workshop on Argumentation in Logic Programming and Non-Monotonic Reasoning, Arg-LPNMR 2016 (2016)
Makinson, D.: General theory of cumulative inference. In: NMR, pp. 1–18. Springer (1988)
Nute, D.: Conditional logic. In: Handbook of Philosophical Logic, pp. 387–439. Springer (1984)
Ramsey, F.P.: General propositions and causality (2007)
Rienstra, T., Sakama, C., van der Torre, L.: Persistence and monotony properties of argumentation semantics. In: TAFA, pp. 211–225. Springer (2015)
Spohn, W.: Ordinal conditional functions: a dynamic theory of epistemic states. In: Causation in Decision, Belief Change, and Statistics, pp. 105–134. Springer (1988)
Strass, H.: Approximating operators and semantics for abstract dialectical frameworks. Artif. Intell. 205, 39–70 (2013)
Strass, H.: Instantiating rule-based defeasible theories in abstract dialectical frameworks and beyond. J. Log. Comput. 28(3), 605–627 (2015)
Thimm, M., Kern-Isberner, G.: On the relationship of defeasible argumentation and answer set programming. COMMA 8, 393–404 (2008)
Weydert, E.: On the plausibility of abstract arguments. In: ECSQARU, pp. 522–533. Springer (2013)
Acknowledgements
The research reported here was supported by the Deutsche Forschungsgemeinschaft under grant KE 1413/11-1. We thank the anonymous reviewers for helpful feedback on previous versions of this paper.
Funding
Open Access funding enabled and organized by Projekt DEAL.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Heyninck, J., Kern-Isberner, G., Thimm, M. et al. On the correspondence between abstract dialectical frameworks and nonmonotonic conditional logics. Ann Math Artif Intell 89, 1075–1099 (2021). https://doi.org/10.1007/s10472-021-09758-y
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10472-021-09758-y
Keywords
- Abstract argumentation
- Abstract dialectical frameworks
- Conditional logics
- Non-monotonic logics
- Non-monotonic conditionals
- Non-monotonic reasoning
- Defeasible reasoning