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The issue of formalizing skepticism relations between argumentation semantics has been considered only recently in the literature. In this paper, we contribute to this kind of analysis by providing a systematic comparison of a significant set of literature semantics (namely grounded, complete, preferred, stable, semi-stable, ideal, prudent, and 2 semantics) using both a weak and a strong skepticism relation.

The semi-stable semantics for formal argumentation has been introduced as a way of approximating stable semantics in situations where no stable extensions exist. Semi-stable semantics can be located between stable semantics and preferred semantics in the sense that every stable extension is a semi-stable extension and every semi-stable extension is a preferred extension. Moreover, in situations where at least one stable extension exists, the semi-stable extensions are equal to the stable extensions. In this paper we provide an outline of an algorithm for computing the semi-stable extensions, given an argumentation framework. We show that with a few modifications, the algorithm can also be used for computing stable and preferred semantics.

Previous logic-based handling of arguments has mainly focused on explanation or justification in presence of inconsistency. As a consequence, only one type of argument has been considered, namely the explanatory type; several argumentation frameworks have been proposed for generating and evaluating explanatory arguments. However, recent investigations of argument-based negotiation have emphasized other types of arguments, such as , and . In parallel, cognitive psychologists recently started studying the characteristics of these different types of arguments, and the conditions under which they have their desired effect. Bringing together these two lines of research, we present in this article some logical definitions as well as some criteria for evaluating each type of argument. Empirical findings from cognitive psychology validate these formal results.

In this paper we study the acceptability of incompatible arguments within Dung’s abstract argumentation framework. As an example we introduce an instance of Dung’s framework where arguments are represented by propositional formulas and an argument attacks another one when the conjunction of their representations is inconsistent, which we characterize as a kind of symmetric attack. Since symmetric attack is known to have the drawback to collapse the various argumentation semantics, we consider also two variations. First, we consider propositional arguments distinguishing support and conclusion. Second, we introduce a preference ordering over the arguments and we define the attack relation in terms of a symmetric incompatibility relation and the preference relation. We show how to characterize preference-based argumentation using a kind of acyclic attack relation.

In this paper we propose semantics for acceptablity in partial argumentation frameworks (PAF). The PAF is an extension of Dung’s argumentation framework and has been introduced in [1] for merging argumentation frameworks. It consists in adding a new interaction between arguments representing the ignorance about the existence of an attack.

The proposed semantics are built following Dung’s method, so that they generalize Dung’s semantics without increasing the temporal complexity.

In Dung’s argumentation system, acceptable sets of arguments are de- fined as sets of arguments that attack all their attackers, and that do not contain any direct contradiction. However, in many applications, the presence of indirect contradictions should prevent a set from being acceptable. The family of prudent semantics has been proposed as an answer to this problem. We are interested in this paper in determining whether a given set of arguments is included in at least one acceptable set under the prudent preferred semantics. To this end, we propose a dialectical framework and several proof theories.

Many types of inter-agent dialogue, including information seeking, negotiation and deliberation can be seen as varieties of argumentation. Argumentation is especially appropriate where demonstration is not possible because the information is incomplete and uncertain or because the parties involved in the argument have different perspectives on an issue. Argumentation frameworks provide a powerful tool for evaluating the sets of conflicting arguments which emerge from such dialogues. Originally argumentation frameworks considered arguments as completely abstract entities related by a single attack relation, which always succeeded. Use of the frameworks in practical applications such as law, e-democracy and medicine has motivated a distinction between successful and unsuccessful attacks, determined by properties of the conflicting arguments. This remains insufficient to capture a range of phenomena which arise from procedural and contextual considerations. These require that a successful attack depend not only on the properties of the con- flicting arguments but also on the nature of the attack and the context in which it is made. In this paper we present an analysis of arguments, their properties and relations which can accommodate a wide range of such phenomena. Our analysis is extensible for we can add components to each system while preserving an overarching argumentation framework. We first capture the abstract notions of original argumentation frameworks, and then introduce a system which embraces properties of arguments. This system is further extended in two ways to include properties of relations between arguments. We illustrate each system with a characteristic example and discuss the particular features of argumentation which they can address.

This work addresses the problem of providing explanation capabilities to an argumentation system. Explanation in defeasible argumentation is an important, and yet undeveloped field in the area. Therefore, we move in this direction by defining a concrete argument system with explanation facilities.

We consider the structures that provide information on the warrant status of a literal. Our focus is put on argumentation systems based on a dialectical proof procedure, therefore we study . Although arguments represent a form of explanation for a literal, we study the complete set of dialectical trees that justifies the warrant status of a literal, since this set has proved to be a useful tool to comprehend, analyze, develop, and debug argumentation systems.

There has recently been many proposals to adopt an argumentative approach to decision-making. As the underlying assumptions made in these different approaches are not always clearly stated, we review these works, taking a more classical decision theory perspective, more precisely a multicriteria perspective. It appears that these approaches seem to have much to offer to decision models, because they allow a great expressivity in the specification of agents’ preferences, because they naturally cater for partial specification of preferences, and because they make explicit many aspects that are usually somewhat hidden in decision models. On the other hand, the typically intrinsic evaluation used in these approaches is not always the most appropriate, and it is not always clear how the multicriteria feature is taken into account when it comes to aggregating several arguments that may potentially interact.

The binary representation is widely used for representing focal sets of Dempster-Shafer belief functions because it allows to compute efficiently all relevant operations. However, as its space requirement grows exponentially with the number of variables involved, computations may become prohibitive or even impossible for belief functions with larger domains. This paper proposes shared ordered binary decision diagrams for representing focal sets. This not only allows to compute efficiently all relevant operations, but also turns out to be a compact representation of focal sets.