A Dung argumentation framework (AF) is a pair (A,R): A is a set of abstract arguments and R ⊆ A×A is a binary relation, so-called the attack relation, for capturing the conflicting arguments. Labeling based algorithms for enumerating extensions (i.e. sets of acceptable arguments) have been set out such that arguments (i.e. elements of A) are the only subject for labeling. In this paper we present implemented algorithms for listing extensions by labeling attacks (i.e. elements of R) along with arguments. Specifically, these algorithms are concerned with enumerating all extensions of an AF under a number of argumentation semantics: preferred, stable, complete, semi stable, stage, ideal and grounded. Our algorithms have impact, in particular, on enumerating extensions of AF-extended models that allow attacks on attacks. To demonstrate this impact, we instantiate our algorithms for an example of such models: namely argumentation frameworks with recursive attacks (AFRA), thereby we end up with unified algorithms that enumerate extensions of any AF/AFRA.

Properties like logical closure and consistency are important properties in any logical reasoning system. Caminada and Amgoud showed that not every logic-based argument system satisfies these relevant properties. But under conditions like closure under contraposition or transposition of the monotonic part of the underlying logic, ASPIC-like systems satisfy these properties. In contrast, the logical closure and consistency properties are not well-understood for other well-known and widely applied systems like logic programming or assumption based argumentation. Though conditions like closure under contraposition or transposition seem intuitive in ASPIC-like systems, they rule out many sensible ASPIC-like systems that satisfy both properties of closure and consistency. We present a new condition referred to as the self-contradiction axiom that guarantees the consistency property in both ASPIC-like and assumption-based systems and is implied by both properties of closure under contraposition or transposition. We develop a logic-associated abstract argumentation framework, by associating abstract argumentation with abstract logics to represent the conclusions of arguments. We show that logic-associated abstract argumentation frameworks capture ASPIC-like systems (without preferences) and assumption-based argumentation. We present two simple and natural properties of compactness and cohesion in logic-associated abstract argumentation frameworks and show that they capture the logical closure and consistency properties. We demonstrate that in both assumption-based argumentation and ASPIC-like systems, cohesion follows naturally from the self-contradiction axiom. We further give a translation from ASPIC-like systems (without preferences) into equivalent assumption-based systems that keeps the self-contradiction axiom invariant.

This paper presents a novel SAT-based approach for the computation of extensions in abstract argumentation, with focus on preferred semantics, and an empirical evaluation of its performances. The approach is based on the idea of reducing the problem of computing complete extensions to a SAT problem and then using a depth-first search method to derive preferred extensions. The proposed approach has been tested using two distinct SAT solvers and compared with three state-of-the-art systems for preferred extension computation. It turns out that the proposed approach delivers significantly better performances in the large majority of the considered cases.

Probabilistic abstract argumentation combines Dung's abstract argumentation framework with probability theory in order to model uncertainty in argumentation. In this setting, we address the fundamental problem of computing the probability that a set of arguments is an extension according to a given semantics. We focus on the most popular semantics (i.e., admissible, stable, complete, grounded, preferred, ideal), and show the following dichotomy result: computing the probability that a set of arguments is an extension is either PTIME or FP #P -complete depending on the semantics adopted. Our PTIME results are particularly interesting, as they hold for some semantics for which no polynomial-time technique was known so far.

My thesis work aims to study change operations for argumentation systems, especially for abstract argumentation systems à la Dung. This paper presents a first study of the AGM revision adapted to the case of argumentation. We also sketch future research works planned to complete the one already achieved.

We present various new concepts and results related to abstract dialectical frameworks (ADFs), a powerful generalization of Dung's argumentation frameworks (AFs). In particular, we show how the existing definitions of stable and preferred semantics which are restricted to the subcase of so-called bipolar ADFs can be improved and generalized to arbitrary frameworks. Furthermore, we introduce preference handling methods for ADFs, allowing for both reasoning with and about preferences. Finally, we present an implementation based on an encoding in answer set programming.

This paper deals with the issue of strategic argumentation in the setting of Dung-style abstract argumentation theory. Such reasoning takes place through the use of opponent models—recursive representations of an agent’s knowledge and beliefs regarding the opponent’s knowledge. Using such models, we present three approaches to reasoning. The first directly utilises the opponent model to identify the best move to advance in a dialogue. The second extends our basic approach through the use of quantitative uncertainty over the opponent’s model. The final extension introduces virtual arguments into the opponent’s reasoning process. Such arguments are unknown to the agent, but presumed to exist and interact with known arguments. They are therefore used to add a primitive notion of risk to the agent’s reasoning. We have implemented our models and we have performed an empirical analysis that shows that this added expressivity improves the performance of an agent in a dialogue.

Dungs abstract argumentation theory can be seen as a general framework for non-monotonic reasoning. An important question is then: what is the class of logics that can be subsumed as instantiations of this theory? The goal of this paper is to identify and study the large class of logic-based instantiations of Dungs theory which correspond to the maxi-consistent operator, i.e. to the function which returns maximal consistent subsets of an inconsistent knowledge base. In other words, we study the class of instantiations where very extension of the argumentation system corresponds to exactly one maximal consistent subset of the knowledge base. We show that an attack relation belonging to this class must be conflict-dependent, must not be valid, must not be conflict-complete, must not be symmetric etc. Then, we show that some attack relations serve as lower or upper bounds of the class (e.g. if an attack relation contains canonical undercut then it is not a member of this class). By using our results, we show for all existing attack relations whether or not they belong to this class. We also define new attack relations which are members of this class. Finally, we interpret our results and discuss more general questions, like: what is the added value of argumentation in such a setting? We believe that this work is a first step towards achieving our long-term goal, which is to better understand the role of argumentation and, particularly, the expressivity of logic-based instantiations of Dung-style argumentation frameworks.

We present a new approach to reasoning about the outcome of an argumentation framework, where an agent's reasoning with a framework and semantics is represented by an inference relation defined over a logical labeling language. We first study a monotonic type of inference which is, in a sense, more general than an acceptance function, but equally expressive. In order to overcome the limitations of this expressiveness, we study a non-monotonic type of inference which allows counterfactual inferences. We precisely characterize the classes of frameworks distinguishable by the non-monotonic inference relation for the admissible semantics.

In this paper we incorporate integrity constraints in Dung-style abstract argumentation frameworks. We show that even for constraints of a very simple form standard conflict-free semantics for argumentation frameworks are not adequate, as conflicts among arguments should sometimes be accepted and tolerated. For this, we use conflict-tolerant semantics and show how corresponding extensions may be represented in terms of propositional formulas.