It is often necessary and reasonable to justify preferences before reasoning from them. Moreover, justifying a preference ordering is reduced to justifying the criterion that produces the ordering. This paper builds on the well-known ASPIC+ formalism to develop a model that integrates justifying qualitative preferences with reasoning from the justified preferences. We first introduce a notion of preference criterion in order to model the way in which preferences are justified by an argumentation framework. We also adapt the notion of argumentation (...) theory to build a sequence of argumentation frameworks, in which an argumentation framework justifies preferences that are to underlie the next framework. That is, in our formalism, preferences become not only an input of an argumentation framework, but also an output of it. This kind of input-output process can be applied in the further steps of argumentation. We also explore some interesting properties of our formalism. (shrink)

While the philosophical literature has extensively studied how decisions relate to arguments, reasons and justifications, decision theory almost entirely ignores the latter notions. In this article, we elaborate a formal framework to introduce in decision theory the stance that decision-makers take towards arguments and counter-arguments. We start from a decision situation, where an individual requests decision support. We formally define, as a commendable basis for decision-aid, this individual’s deliberated judgment, a notion inspired by Rawls’ contributions to the philosophical literature, and (...) embodying the requirement that the decision-maker should carefully examine arguments and counter-arguments. We explain how models of deliberated judgment can be validated empirically. We then identify conditions upon which the existence of a valid model can be taken for granted, and analyze how these conditions can be relaxed. We then explore the significance of our framework for the practice of decision analysis. Our framework opens avenues for future research involving both philosophy and decision theory, as well as empirical implementations. (shrink)

This research explores the relationship between the bounded in-degree and out-degree of an argumentation framework and the computational complexity of the problems of Credulous Acceptance ( CredA ) and Skeptical Acceptance ( SkepA ) under preferred extensions. Researchers have studied the complexity of these problems when the in-degree [Formula: see text] and out-degree [Formula: see text] of the arguments are restricted to [Formula: see text]. Despite this restriction, the computational complexities of CredA and SkepA persist. Based on these results, we (...) presents new results that provide deeper insights into the impact of additional constraints on the argumentation framework. Specifically, we show that when “[Formula: see text]” or “[Formula: see text]” is restricted to [Formula: see text], both problems CredA and SkepA can be solved in polynomial time. Subsequently, we impose additional constraints on the argumentation framework by analyzing the quantities “[Formula: see text],” “[Formula: see text],” and “[Formula: see text].” For an argumentation framework [Formula: see text] and all arguments “[Formula: see text]” of [Formula: see text], the parameter “[Formula: see text]” indicates the maximum number of attackers that any argument “[Formula: see text]” can have among all those that are not attacked by “[Formula: see text]” [Formula: see text], “[Formula: see text]” indicates the maximum number of arguments that any argument “[Formula: see text]” attacks among all those that do not attack “[Formula: see text]”, and “[Formula: see text]” denotes the maximum number of arguments that any argument “[Formula: see text]” attacks among those that attack “[Formula: see text]”. Surprisingly, even when all these quantities are restricted to [Formula: see text], the computational complexity of CredA persists. Furthermore, we explore the influence of symmetric attacks by fixing “[Formula: see text]” to zero, while setting “[Formula: see text]” and “[Formula: see text]” to [Formula: see text]. Remarkably, the complexity of CredA persists under this restriction as well. (shrink)