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Argument graphs and assumption-based argumentation. (English) Zbl 1351.68264
Summary: Arguments in structured argumentation are usually defined as trees, and extensions as sets of such tree-based arguments with various properties depending on the particular argumentation semantics. However, these arguments and extensions may have redundancies as well as circularities, which are conceptually and computationally undesirable. Focusing on the specific case of Assumption-Based Argumentation (ABA), we propose novel notions of arguments and admissible/grounded extensions, both defined in terms of graphs. We show that this avoids the redundancies and circularities of standard accounts, and set out the relationship to standard tree-based arguments and admissible/grounded extensions (as sets of arguments). We also define new notions of graph-based admissible/grounded dispute derivations for ABA, for determining whether specific sentences hold under the admissible/grounded semantics. We show that these new derivations are superior with respect to standard dispute derivations in that they are complete in general, rather than solely for restricted classes of ABA frameworks. Finally, we present several experiments comparing the implementation of graph-based admissible/grounded dispute derivations with implementations of standard dispute derivations, suggesting that the graph-based approach is computationally advantageous.

68T27 Logic in artificial intelligence
Full Text: DOI
[1] Amgoud, L., The outcomes of logic-based argumentation systems under preferred semantics, (Hüllermeier, E.; Link, S.; Fober, T.; Seeger, B., Proceedigs of the 6th International Conference on Scalable Uncertainty Management, SUM 2012, (2012), Springer), 72-84
[2] Bench-Capon, T. J.; Dunne, P. E., Argumentation in artificial intelligence, Artif. Intell., 171, 619-641, (2007) · Zbl 1168.68560
[3] Besnard, P.; García, A. J.; Hunter, A.; Modgil, S.; Prakken, H.; Simari, G. R.; Toni, F., Introduction to structured argumentation, Argum. Comput., 5, 1-4, (2014)
[4] Besnard, P.; Hunter, A., Elements of argumentation, (2008), MIT Press
[5] Besnard, P.; Hunter, A., Constructing argument graphs with deductive arguments: a tutorial, Argum. Comput., 5, 5-30, (2014)
[6] Bondarenko, A.; Dung, P. M.; Kowalski, R. A.; Toni, F., An abstract, argumentation-theoretic approach to default reasoning, Artif. Intell., 93, 63-101, (1997) · Zbl 1017.03511
[7] Caminada, M., Semi-stable semantics, (Dunne, P. E.; Bench-Capon, T. J., Computational Models of Argument: Proceedings of COMMA, Liverpool, UK, September 11-12, 2006, (2006), IOS Press), 121-130
[8] Craven, R.; Toni, F.; Hadad, A.; Cadar, C.; Williams, M., Efficient support for medical argumentation, (Brewka, G.; Eiter, T.; McIlraith, S. A., Proc. 13th International Conference on Principles of Knowledge Representation and Reasoning, (2012), AAAI Press), 598-602
[9] Craven, R.; Toni, F.; Williams, M., Graph-based dispute derivations in assumption-based argumentation, (Black, E.; Modgil, S.; Oren, N., Theory and Applications of Formal Argumentation, (2013), Springer), 46-62 · Zbl 1405.68345
[10] Dimopoulos, Y.; Nebel, B.; Toni, F., On the computational complexity of assumption-based argumentation for default reasoning, Artif. Intell., 141, 57-78, (2002) · Zbl 1043.68097
[11] Dung, P. M., On the acceptability of arguments and its fundamental role in non-monotonic reasoning, logic programming and n-person games, Artif. Intell., 77, 321-357, (1995) · Zbl 1013.68556
[12] Dung, P. M.; Kowalski, R. A.; Toni, F., Dialectic proof procedures for assumption-based, admissible argumentation, Artif. Intell., 170, 114-159, (2006) · Zbl 1131.68103
[13] Dung, P. M.; Kowalski, R. A.; Toni, F., Assumption-based argumentation, (Rahwan, I.; Simari, G. R., Argumentation in AI, (2009), Springer), 25-44
[14] Dung, P. M.; Mancarella, P.; Toni, F., Computing ideal sceptical argumentation, Artif. Intell., 171, 642-674, (2007) · Zbl 1168.68564
[15] Dunne, P. E., The computational complexity of ideal semantics, Artif. Intell., 173, 1559-1591, (2009) · Zbl 1185.68666
[16] Efstathiou, V.; Hunter, A., Algorithms for effective argumentation in classical propositional logic: a connection graph approach, (Hartmann, S.; Kern-Isberner, G., Foundations of Information and Knowledge Systems, Lecture Notes in Computer Science, vol. 4932, (2008), Springer), 272-290 · Zbl 1138.68557
[17] Egly, U.; Gaggl, S. A.; Woltran, S., Answer-set programming encodings for argumentation frameworks, Argum. Comput., 1, 147-177, (2010)
[18] Fan, X.; Craven, R.; Singer, R.; Toni, F.; Williams, M., Assumption-based argumentation for decision-making with preferences: a medical case study, (Leite, J.; Son, T. C.; Torroni, P.; van der Torre, L.; Woltran, S., Proceedings of the 14th International Workshop on Computational Logic in Multi-Agent Systems, CLIMA XIV, Corunna, Spain, September 16-18, 2013, (2013), Springer), 374-390
[19] Fan, X.; Toni, F.; Mocanu, A.; Williams, M., Dialogical two-agent decision making with assumption-based argumentation, (Lomuscio, A.; Scerri, P.; Bazzan, A.; Huhns, M., Proceedings of the 13th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2014, (2014), IFAAMAS), 533-540
[20] García, A. J.; Simari, G. R., Defeasible logic programming: an argumentative approach, Theory Pract. Log. Program., 4, 95-138, (2004) · Zbl 1090.68015
[21] Kowalski, R., A proof procedure using connection graphs, J. ACM, 22, 572-595, (1975) · Zbl 0357.68097
[22] Matt, P. A.; Toni, F.; Stournaras, T.; Dimitrelos, D., Argumentation-based agents for eprocurement, (Berger, M.; Burg, B.; Nishiyama, S., Proceedings of the 7th International Conference on Autonomous Agents and Multiagent Systems, Industry and Applications Track, AAMAS 2008, (2008)), 71-74
[23] Modgil, S.; Prakken, H., A general account of argumentation with preferences, Artif. Intell., 195, 361-397, (2013) · Zbl 1270.68284
[24] Rahwan, I.; Simari, G. R., Argumentation in artificial intelligence, (2009), Springer
[25] Snaith, M.; Reed, C., TOAST: online \(\text{ASPIC}^+\) implementation, (Verheij, B.; Szeider, S.; Woltran, S., Proceedings of the Fourth International Conference on Computational Models of Argument, COMMA 2012, Vienna, Austria, September 10-12, 2012, (2012), IOS Press), 509-510
[26] Thang, P. M.; Dung, P. M.; Hung, N. D., Towards a common framework for dialectical proof procedures in abstract argumentation, J. Log. Comput., 19, 1071-1109, (2009) · Zbl 1185.68677
[27] Toni, F., A generalised framework for dispute derivations in assumption-based argumentation, Artif. Intell., 195, 1-43, (2013) · Zbl 1270.68289
[28] Toni, F., A tutorial on assumption-based argumentation, Argum. Comput., Special Issue: Tutorials on Structured Argumentation, 5, 89-117, (2014)
[29] Vreeswijk, G., Abstract argumentation systems, Artif. Intell., 90, 225-279, (1997) · Zbl 1017.03513
[30] Zhong, Q.; Fan, X.; Toni, F.; Luo, X., Explaining best decisions via argumentation, (Herzig, A.; Lorini, E., Proceedings of the European Conference on Social Intelligence, ECSI-2014, Barcelona, Spain, November 3-5, 2014, (2014), CEUR-WS.org), 224-237
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