Abstract This paper proposes novel semantics based on solid admissibility, which strengthens Dung’s admissibility by incorporating a condition that an argument requires all defenders for it to be successfully defended. These solid semantics provide a better approach to handling controversial scenarios in Dung’s argumentation framework compared to Dung’s semantics. Specifically, if two arguments are such that one of them indirectly attacks a third argument while the other one indirectly defends the third one, then the three arguments cannot be included in the same solid extension. Furthermore, an argument that is indirectly attacked and indirectly defended by another argument (controversial arguments) cannot be an element of any solid extension. Additionally, applying solid semantics to judgment aggregation yields more positive aggregation outcomes than Dung’s semantics; notably, any quota rule higher than or equal to the strict majority rule preserves solid admissibility for all argumentation frameworks but fails to preserve Dung’s admissibility.

We have developed a system, based on prioritized default logic, for representing legal rules and their exceptions. Our system can help the law practitioner’s reasoning in presence of scenarios that induce an exception to a rule. When there is no known exception to the rule r1 for a scenario, the system can help the user to adapt the exception r′2 to a general rule r2.

Abstract Argumentation has become an essential tool in AI, allowing the representation of knowledge with only a set of arguments and a binary relation between arguments, the attack relation. Since the seminal work presented in 1995 by Dung, many extensions have been proposed in order to enrich this very simple framework by the addition of a second type of interaction, the support relation, and by the use of higher-order or collective interactions. In parallel, several links have been exhibited and studied between Logics and Abstract Argumentation, showing that these two domains are closely interrelated. Among these works, one can find several logical encodings of abstract argumentation frameworks. Nevertheless, these encodings are very often built ad hoc and only for some given frameworks. The aim of this paper is to propose a generic logical encoding covering several families of abstract argumentation frameworks, from Dung’s framework to the most enriched framework using higher-order and collective evidential supports and attacks.

Computation and decision problems related to argumentation frameworks with higher-order attacks have not received a lot of attention so far. This paper is a step towards these issues: first, it provides a labelling counterpart for the structure semantics of Recursive Argumentation Frameworks (RAF); second, it investigates the complexity of decision problems associated with RAF. This investigation shows that, for the higher expressiveness offered by these enriched systems, the complexity is the same as for classical argumentation frameworks. As a side contribution, a new semantics for RAF, the semi-stable semantics, and a new process for translating RAF into Argumentation Frameworks without higher-order attacks (AF), are introduced.

Ranking-based semantics are a way of assessing the acceptability of arguments in an abstract argumentation framework, by providing a ranking on arguments. This paper aims at going towards a generalization of the construction of such semantics, by investigating subsumption and incompatibility cases that may arise when principles that may enter into their composition are combined.

Properties of argumentation semantics have been widely studied in the last decades. However, there has been no investigation on the question of difference measures between semantics. Such measures turn helpful when the semantics associated to an argumentation framework may have to be changed, in a way that ensures that the new semantics is not too dissimilar from the old one. Three main notions of difference measures between semantics are defined in this paper. Some of these measures are shown to be distances or semi-distances.

GRAFIX is a graphical tool for handling abstract argumentation graphs. GRAFIX allows the edition and the presentation of argumentation graphs (or sets of graphs), and the execution of some “predefined treatments” (called “server treatments”) on the current graph(s) such as, for instance, computing various acceptability semantics, or computing the strength of arguments. GRAFIX also allows the user to introduce her own treatments (“client treatments”).

Constrained argumentation frameworks (CAF) generalize Dung's frameworks by allowing additional constraints on arguments to be taken into account in the definition of acceptability of arguments. These constraints are expressed by means of a logical formula which is added to Dung's framework. The resulting system captures several other extensions of Dung's original system. To determine if a set of arguments is credulously inferred from a CAF, the notion of dialectical proof (alternating pros and cons arguments) is extended for Dung's frameworks in order to respect the additional constraint. The new constrained dialectical proofs are computed by using Answer Set Programming.

Argumentation is a form of reasoning, in which two agents cooperate in order to establish the validity of a given argument; this argument could be used to deduce some conclusion of interest. In this article, we look at the credulous and the sceptical decision problems under Dung's preferred semantics, that is, the problems of deciding if an argument belongs to one or to every preferred extension of an argumentation framework. We present two proof theories for the credulous decision problem and an algorithm which computes one of them. We show how these proof theories can be used for the sceptical decision problem in two particular cases of argumentation frameworks and we give an algorithm which answers that problem in the general case.