Valid attacks in argumentation frameworks with recursive attacks. (English) Zbl 07355086

Summary: The purpose of this work is to study a generalisation of Dung’s abstract argumentation frameworks that allows representing recursive attacks, that is, a class of attacks whose targets are other attacks. We do this by developing a theory of argumentation where the classic role of attacks in defeating arguments is replaced by a subset of them, which is “extension-dependent” and which, intuitively, represents a set of “valid attacks” with respect to the extension. The studied theory displays a conservative generalisation of Dung’s semantics (complete, preferred, stable and grounded) and also of its principles (conflict-freeness, acceptability and admissibility). Furthermore, despite its conceptual differences, we are also able to show that our theory agrees with the AFRA interpretation of recursive attacks for the complete, preferred, stable and grounded semantics and with a recent flattening method.


68-XX Computer science


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[1] Amgoud, L.; Cayrol, C., A reasoning model based on the production of acceptable arguments, Ann. Math. Artif. Intell., 34, 197-216 (2002) · Zbl 1002.68172
[2] Amgoud, L., Maudet, N., Parsons, S.: Modelling dialogues using argumentation. In: Proc. of ICMAS, pp. 31-38 (2000)
[3] Arisaka, R., Satoh, K.: Voluntary manslaughter? a case study with meta-argumentation with supports. In: New Frontiers in Artificial Intelligence. JSAI-isAI 2016. LNCS 10247, pp. 241-252. Springer (2017)
[4] Baroni, P.; Cerutti, F.; Giacomin, M.; Guida, G., AFRA: Argumentation framework with recursive attacks, Int. J. Approx. Reasoning, 52, 1, 19-37 (2011) · Zbl 1211.68433
[5] Barringer, H., Gabbay, D., Woods, J.: Temporal dynamics of support and attack networks : From argumentation to zoology. In: Mechanizing Mathematical Reasoning. LNAI 2605, pp. 59-98. Springer Verlag (2005) · Zbl 1098.68122
[6] Besnard, P., Doutre, S.: Checking the acceptability of a set of arguments. In: Proc. of NMR, pp. 59-64 (2004)
[7] Carballido, JL; Nieves, JC; Osorio, M., Inferring preferred extensions by pstable semantics, Inteligencia artificial: Revista Iberoamericana de Inteligencia Artificial, 13, 41, 38-53 (2009)
[8] Cayrol, C., Cohen, A., Lagasquie-Schiex, M.C.: Towards a new framework for recursive interactions in abstract bipolar argumentation. In: Proc. of COMMA, pp. 191-198 (2016)
[9] Cayrol, C., Fandinno, J., Fariñas del Cerro, L., Lagasquie-Schiex, M.C.: Valid attacks in argumentation frameworks with recursive attacks. In: International symposium on commonsense reasoning, vol. 2052. CEUR-WS : Workshop proceedings (2017) · Zbl 06894598
[10] Cayrol, C., Fandinno, J., Fariñas del Cerro, L., Lagasquie-Schiex, M.C.: Argumentation frameworks with recursive attacks and evidence-based support. In: Proc. of FoIKS. Springer-Verlag (2018) · Zbl 06894598
[11] Cayrol, C., Fandinno, J., Fariñas del Cerro, L., Lagasquie-Schiex, M.C.: Structure-based semantics of argumentation frameworks with higher-order attacks and supports. In: Proc. of COMMA. IOS Press (2018) · Zbl 1440.68261
[12] Cayrol, C., Lagasquie-Schiex, M.C.: Logical encoding of argumentation frameworks with higher-order attacks. In: Alamaniotis, M. (ed.) Proc. of ICTAI 2018, pp. 667-674. IEEE (2018)
[13] Cohen, A.; Gottifredi, S.; García, AJ; Simari, GR, An approach to abstract argumentation with recursive attack and support, J. Applied Logic, 13, 4, 509-533 (2015) · Zbl 1386.68156
[14] Cohen, A., Gottifredi, S., García, A.J., Simari, G.R.: On the acceptability semantics of argumentation frameworks with recursive attack and support. In: Proc. of COMMA, pp. 231-242 (2016) · Zbl 1451.68262
[15] Dung, PM, 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) · Zbl 1013.68556
[16] Dunne, P.; Bench-Capon, T., Coherence in finite argument system, Artif. Intell., 141, 1-2, 187-203 (2002) · Zbl 1043.68098
[17] Dunne, PE, Computational properties of argument systems satisfying graph-theoretic constraints, Artif. Intell., 171, 10-15, 701-729 (2007) · Zbl 1168.68565
[18] Egly, U.; Gaggl, SA; Woltran, S., Answer-set programming encodings for argumentation frameworks, Argument Comput., 1, 2, 147-177 (2010) · Zbl 1226.68018
[19] Gabbay, DM, Semantics for higher level attacks in extended argumentation frames part 1: Overview, Stud. Logica., 93, 2, 357 (2009) · Zbl 1185.68669
[20] Hanh, DD; Dung, PM; Hung, ND; Thang, PM, Inductive defense for sceptical semantics of extended argumentation, J. Log. Comput., 21, 2, 307-349 (2010) · Zbl 1214.68383
[21] Modgil, S., Reasoning about preferences in argumentation frameworks, Artif. Intell., 173, 9-10, 901-934 (2009) · Zbl 1192.68663
[22] Osorio, M., Nieves, J.C., Santoyo, A.: Complete extensions as clark’s completion semantics. In: Proc. of the Mexican international conference on computer science, pp. 81-88 (2013)
[23] Villata, S.; Boella, G.; Gabbay, DM; van der Torre, L., Modelling defeasible and prioritized support in bipolar argumentation, Ann. Math. AI, 66, 1-4, 163-197 (2012) · Zbl 1280.68255
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