Abstract
Argumentation frameworks with collective attacks are a prominent extension of Dung’s abstract argumentation frameworks, where an attack can be drawn from a set of arguments to another argument. These frameworks are often abbreviated as SETAFs. Although SETAFs have received increasing interest recently, the notion of strong equivalence, which is fundamental in nonmonotonic formalisms to characterize equivalent replacements, has not yet been investigated. In this paper, we study how strong equivalence between SETAFs can be decided with respect to the most important semantics and also consider variants of strong equivalence.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
\(\textit{sem}\) and \(\textit{stage}\) are not considered in [14] but the result immediately extends to those semantics.
References
Baumann, R.: Normal and strong expansion equivalence for argumentation frameworks. Artif. Intell. 193, 18–44 (2012)
Baumann, R.: Characterizing equivalence notions for labelling-based semantics. In: Baral, C., Delgrande, J.P., Wolter, F. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the Fifteenth International Conference, KR 2016, 25–29 April 2016, Cape Town, South Africa, pp. 22–32. AAAI Press (2016)
Baumann, R., Brewka, G.: The equivalence zoo for Dung-style semantics. J. Log. Comput. 28(3), 477–498 (2018)
Baumann, R., Dvořák, W., Linsbichler, T., Woltran, S.: A general notion of equivalence for abstract argumentation. In: Sierra, C. (ed.) Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, 19–25 August 2017, Melbourne, Australia, pp. 800–806 (2017)
Brewka, G., Polberg, S., Woltran, S.: Generalizations of Dung frameworks and their role in formal argumentation. IEEE Intell. Syst. 29(1), 30–38 (2014)
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)
Dvořák, W., Fandinno, J., Woltran, S.: On the expressive power of collective attacks. In: Modgil, S., Budzynska, K., Lawrence, J. (eds.) Computational Models of Argument - Proceedings of COMMA 2018, 12–14 September 2018, Warsaw, Poland. Frontiers in Artificial Intelligence and Applications, vol. 305, pp. 49–60. IOS Press (2018)
Dvořák, W., Greßler, A., Woltran, S.: Evaluating SETAFs via answer-set programming. In: Thimm, M., Cerutti, F., Vallati, M. (eds.) Proceedings of the Second International Workshop on Systems and Algorithms for Formal Argumentation (SAFA 2018) Co-located with the 7th International Conference on Computational Models of Argument (COMMA 2018), 11 September 2018, Warsaw, Poland. CEUR Workshop Proceedings, vol. 2171, pp. 10–21. CEUR-WS.org (2018)
Dvořák, W., Järvisalo, M., Linsbichler, T., Niskanen, A., Woltran, S.: Preprocessing argumentation frameworks via replacement patterns. In: Calimeri, F., Leone, N., Manna, M. (eds.) JELIA 2019. LNCS (LNAI), vol. 11468, pp. 116–132. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-19570-0_8
Flouris, G., Bikakis, A.: A comprehensive study of argumentation frameworks with sets of attacking arguments. Int. J. Approx. Reason. 109, 55–86 (2019)
Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Trans. Comput. Logic 2(4), 526–541 (2001)
Nielsen, S.H., Parsons, S.: A generalization of Dung’s abstract framework for argumentation: arguing with sets of attacking arguments. In: Maudet, N., Parsons, S., Rahwan, I. (eds.) ArgMAS 2006. LNCS (LNAI), vol. 4766, pp. 54–73. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75526-5_4
Oikarinen, E., Woltran, S.: Characterizing strong equivalence for argumentation frameworks. Artif. Intell. 175(14–15), 1985–2009 (2011)
Polberg, S.: Developing the abstract dialectical framework. Ph.D. thesis, TU Wien, Institute of Information Systems (2017)
Truszczynski, M.: Strong and uniform equivalence of nonmonotonic theories - an algebraic approach. Ann. Math. Artif. Intell. 48(3–4), 245–265 (2006)
Turner, H.: Strong equivalence for causal theories. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 289–301. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-24609-1_25
Yun, B., Vesic, S., Croitoru, M.: Toward a more efficient generation of structured argumentation graphs. In: Modgil, S., Budzynska, K., Lawrence, J. (eds.) Computational Models of Argument - Proceedings of COMMA 2018, 12–14 September 2018, Warsaw, Poland. Frontiers in Artificial Intelligence and Applications, vol. 305, pp. 205–212. IOS Press (2018)
Acknowledgments
This research has been supported by FWF through projects I2854, P30168 and W1255-N23.
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
Dvořák, W., Rapberger, A., Woltran, S. (2019). Strong Equivalence for Argumentation Frameworks with Collective Attacks. In: Benzmüller, C., Stuckenschmidt, H. (eds) KI 2019: Advances in Artificial Intelligence. KI 2019. Lecture Notes in Computer Science(), vol 11793. Springer, Cham. https://doi.org/10.1007/978-3-030-30179-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-30179-8_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-30178-1
Online ISBN: 978-3-030-30179-8
eBook Packages: Computer ScienceComputer Science (R0)