Abstract
In this paper we investigate the links between instantiated argumentation systems and the axioms for non-monotonic reasoning described in [15] with the aim of characterising the nature of argument based reasoning. In doing so, we consider two possible interpretations of the consequence relation, and describe which axioms are met by \({{\textsc {aspic}}^\mathbf {+}}\) under each of these interpretations. We then consider the links between these axioms and the rationality postulates. Our results indicate that argument based reasoning as characterised by \({{\textsc {aspic}}^\mathbf {+}}\) is—according to the axioms of [15]—non-cumulative and non-monotonic, and therefore weaker than the weakest non-monotonic reasoning systems considered in [15]. This weakness underpins \({{\textsc {aspic}}^\mathbf {+}}\)’s success in modelling other reasoning systems. We conclude by considering the relationship between \({{\textsc {aspic}}^\mathbf {+}}\) and other weak logical systems.
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Notes
- 1.
\({{\textsc {aspic}}^\mathbf {+}}\) was selected for this study due to its popularity, and its ability to model a variety of other structured systems [20].
- 2.
While additional rationality postulates have been proposed [24], we do not consider them in this paper.
- 3.
This position was doubtless a side-effect of the fact that at that time there were no logics that did not obey cumulativity. The subsequent discovery of logics of causality that are not cumulative suggests that this view should be revised.
- 4.
This is exactly how defeasible logic [2] satisfies Ref.
References
Baroni, P., Caminada, M., Giacomin, M.: An introduction to argumentation semantics. Knowl. Eng. Rev. 26(4), 365–410 (2011)
Billington, D.: Defeasible logic is stable. J. Log. Comput. 3(4), 379–400 (1993)
Bondarenko, A., Dung, P.M., Kowalski, R.A., Toni, F.: An abstract, argumentation-theoretic approach to default reasoning. Artif. Intell. 93(1), 63–101 (1997)
Caminada, M., Amgoud, L.: On the evaluation of argumentation formalisms. Artif. Intell. 171(5), 286–310 (2007)
Caminada, M., Modgil, S., Oren, N.: Preferences and unrestricted rebut. In: Proceedings of 5th International Conference on Computational Models of Argument, pp. 209–220 (2014)
Croitoru, M., Vesic, S.: What can argumentation do for inconsistent ontology query answering? In: Liu, W., Subrahmanian, V.S., Wijsen, J. (eds.) SUM 2013. LNCS (LNAI), vol. 8078, pp. 15–29. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40381-1_2
Čyras, K., Toni, F.: Non-monotonic inference properties for assumption-based argumentation. In: Black, E., Modgil, S., Oren, N. (eds.) TAFA 2015. LNCS (LNAI), vol. 9524, pp. 92–111. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-28460-6_6
Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-persons games. Artif. Intell. 77(2), 321–358 (1995)
Dung, P.M.: An axiomatic analysis of structured argumentation for prioritized default reasoning. In: European Conference on Artificial Intelligence, pp. 267–272 (2014)
Dung, P.M.: An axiomatic analysis of structured argumentation with priorities. Artif. Intell. 231, 107–150 (2016)
Gabbay, D.M.: Theoretical foundations for non-monotonic reasoning in expert systems. In: Apt, K.R. (ed.) Proceedings of the NATO Advanced Study Institute on Logics and Models. NATO ASI Series, vol. 13, pp. 439–457. Springer, Heidelberg (1985). https://doi.org/10.1007/978-3-642-82453-1_15
García, A.J., Simari, G.R.: Defeasible logic programming: an argumentative approach. Theory Pract. Log. Prog. 4(1+2), 95–138 (2004)
Governatori, G., Maher, M.J., Antoniou, G., Billington, D.: Argumentation semantics for defeasible logic. J. Log. Comput. 14(5), 675–702 (2004)
Hunter, A.: Base logics in argumentation. In: COMMA, pp. 275–286 (2010)
Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44(1), 167–207 (1990)
Li, Z., Parsons, S.: On argumentation with purely defeasible rules. In: Beierle, C., Dekhtyar, A. (eds.) SUM 2015. LNCS (LNAI), vol. 9310, pp. 330–343. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23540-0_22
Lin, F., Shoham, Y.: Argument systems: a uniform basis for nonmonotonic reasoning. KR 89, 245–255 (1989)
McCarthy, J.: Circumscription, a form of nonmonotonic reasoning. Artif. Intell. 13, 27–39 (1980)
Modgil, S., Prakken, H.: A general account of argumentation with preferences. Artif. Intell. 195, 361–397 (2012)
Modgil, S., Prakken, H.: The \(ASPIC^{+}\) framework for structured argumentation: a tutorial. Argum. Comput. 5(1), 31–62 (2014)
Moore, R.C.: Semantical considerations on nonmonotonic logic. Artif. Intell. 25(1), 75–94 (1985)
Nute, D.: Defeasible logic. In: Bartenstein, O., Geske, U., Hannebauer, M., Yoshie, O. (eds.) INAP 2001. LNCS (LNAI), vol. 2543, pp. 151–169. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36524-9_13
Reiter, R.: A logic for default reasoning. Artif. Intell. 13(1), 81–132 (1980)
Wu, Y.: Between argument and conclusion - argument-based approaches to discussion, inference and uncertainty. Ph.D. thesis (2012)
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This work was partially supported by EPSRC grant EP/P010105/1.
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Li, Z., Oren, N., Parsons, S. (2018). On the Links Between Argumentation-Based Reasoning and Nonmonotonic Reasoning. In: Black, E., Modgil, S., Oren, N. (eds) Theory and Applications of Formal Argumentation. TAFA 2017. Lecture Notes in Computer Science(), vol 10757. Springer, Cham. https://doi.org/10.1007/978-3-319-75553-3_5
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