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In preference-based argumentation theory, an argument may be preferred to another one when, for example, it is more specific, its beliefs have a higher probability or certainty, or it promotes a higher value. In this paper we generalize Bench-Capon's value-based argumentation theory such that arguments can promote multiple values, and preferences among values or arguments can be specified in various ways. We assume in addition that there is default knowledge about the preferences over the arguments, and we use an algorithm to derive the most likely preference order. In particular, we show how to use non-monotonic preference reasoning to compute preferences among arguments, and subsequently the acceptable arguments, from preferences among values. We show also how the preference ordering can be used to optimize the algorithm to construct the grounded extension by proceeding from most to least preferred arguments.

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Abstract. In this paper we consider the dynamics of abstract argumentation in Baroni and Giacomin's framework for the evaluation of extension based argumentation semantics. Following Baroni and Giacomin, we do not consider individual approaches, but we define general principles or postulates that individual approaches may satisfy. In particular, we define abstraction principles for the attack relation, and for the arguments in the framework. We illustrate the principles on the grounded extension. In this paper we consider only principles for the single extension case, and leave the multiple extension case to further research.