Modelling qualitative uncertainty in formal argumentation is essential both for practical applications and theoretical understanding. Yet, most of the existing works focus on \textit{abstract} models for arguing with uncertainty. Following a recent trend in the literature, we tackle the open question of studying plausible instantiations of these abstract models. To do so, we ground the uncertainty of arguments in their components, structured within rules and premises. Our main technical contributions are: i) the introduction of a notion of expressivity that can handle abstract and structured formalisms, and ii) the presentation of both negative and positive expressivity results, comparing the expressivity of abstract and structured models of argumentation with uncertainty. These results affect incomplete abstract argumentation frameworks, and their extension with dependencies, on the abstract side, and ASPIC+, on the structured side.

We augment Assumption Based Argumentation (ABA for short) with weighted argumentation. In a nutshell, we assign weights to arguments and then derive the weight of attacks between ABA arguments. We illustrate our proposal through running examples in the field of ethical reasoning, and present an implementation based on Answer Set Programming.

The rule $\mathrm{Defeated}(x) \leftarrow \mathrm{Attacks}(y,x),\, \neg \, \mathrm{Defeated}(y)$, evaluated under the well-founded semantics (WFS), yields a unique 3-valued (skeptical) solution of an abstract argumentation framework (AF). An argument $x$ is defeated ($\mathrm{OUT}$) if there exists an undefeated argument $y$ that attacks it. For 2-valued (stable) solutions, this is the case iff $y$ is accepted ($\mathrm{IN}$), i.e., if all of $y$'s attackers are defeated. Under WFS, arguments that are neither accepted nor defeated are undecided ($\mathrm{UNDEC}$). As shown in prior work, well-founded solutions (a.k.a. grounded labelings) "explain themselves": The provenance of arguments is given by subgraphs (definable via regular path queries) rooted at the node of interest. This provenance is closely related to winning strategies of a two-player argumentation game. We present a novel approach for extending this provenance to stable AF solutions. Unlike grounded solutions, which can be constructed via a bottom-up alternating fixpoint procedure, stable models often involve non-deterministic choice as part of the search for models. Thus, the provenance of stable solutions is of a different nature, and reflects a more expressive generate & test paradigm. Our approach identifies minimal sets of critical attacks, pinpointing choices and assumptions made by a stable model. These critical attack edges provide additional insights into the provenance of an argument's status, combining well-founded derivation steps with choice steps. Our approach can be understood as a form of diagnosis that finds minimal "repairs" to an AF graph such that the well-founded solution of the repaired graph coincides with the desired stable model of the original AF graph.

An abstract argumentation framework is a commonly used formalism to provide a static representation of a dialogue. However, the order of enunciation of the arguments in an argumentative dialogue is very important and can affect the outcome of this dialogue. In this paper, we propose a new framework for modelling abstract argumentation graphs, a model that incorporates the order of enunciation of arguments. By taking this order into account, we have the means to deduce a unique outcome for each dialogue, called an extension. We also establish several properties, such as termination and correctness, and discuss two notions of completeness. In particular, we propose a modification of the previous transformation based on a "last enunciated last updated" strategy, which verifies the second form of completeness.

In recent years, there has been a lot of research in artificial intelligence, focusing on leveraging argumentation theory for non-monotonic reasoning [1, 2]. Starting with Dung's seminal work [3], many researchers have considered abstract argumentation frameworks, composed of a set of arguments and a binary attack relation between them, and created many semantics for tasks such as computing accepted sets of arguments [4, 5] or rank arguments [6, 7, 8]. This abstract argumentation framework was extended with many features such as supports [9, 10, 11], sets of attacking arguments [12, 13], or probabilities [14] among others. However, one important question that remained was: "Where do argumentation frameworks come from in real-life settings?". While there are some pieces of evidence that the fundamental aspects of abstract argumentation frameworks have links with human reasoning [15, 16], humans debates or natural language texts are not always written as arguments and the relation between arguments is not always clear, even for experts [17]. The question of the origin of argumentation frameworks is crucial to facilitate the application of argumentation theory semantics in real-world contexts.

We present an extension-based approach for computing and verifying preferences in an abstract argumentation system. Although numerous argumentation semantics have been developed previously for identifying acceptable sets of arguments from an argumentation framework, there is a lack of justification behind their acceptability based on implicit argument preferences. Preference-based argumentation frameworks allow one to determine what arguments are justified given a set of preferences. Our research considers the inverse of the standard reasoning problem, i.e., given an abstract argumentation framework and a set of justified arguments, we compute what the possible preferences over arguments are. Furthermore, there is a need to verify (i.e., assess) that the computed preferences would lead to the acceptable sets of arguments. This paper presents a novel approach and algorithm for exhaustively computing and enumerating all possible sets of preferences (restricted to three identified cases) for a conflict-free set of arguments in an abstract argumentation framework. We prove the soundness, completeness and termination of the algorithm. The research establishes that preferences are determined using an extension-based approach after the evaluation phase (acceptability of arguments) rather than stated beforehand. In this work, we focus our research study on grounded, preferred and stable semantics. We show that the complexity of computing sets of preferences is exponential in the number of arguments, and thus, describe an approximate approach and algorithm to compute the preferences. Furthermore, we present novel algorithms for verifying (i.e., assessing) the computed preferences. We provide details of the implementation of the algorithms (source code has been made available), various experiments performed to evaluate the algorithms and the analysis of the results.

The pyglaf reasoner takes advantage of circumscription to solve computational problems of abstract argumentation frameworks. In fact, many of these problems are reduced to circumscription by means of linear encodings, and a few others are solved by means of a sequence of calls to an oracle for circumscription. Within pyglaf, Python is used to build the encodings and to control the execution of the external circumscription solver, which extends the SAT solver glucose and implements algorithms taking advantage of unsatisfiable core analysis and incremental computation.

argumentation [16] is an important topic in the Knowledge Representation and Reasoning community. Intuitively, an abstract argumentation framework (AF) is a directed graph where nodes are arguments and edges are relations (usually attacks) between these arguments. The outcome of such an AF is an evaluation of the arguments' acceptance (through extensions [16, 3], labellings [7] or rankings [1]). In such an AF, the assumption of complete information is made: an argument that appears in the graph is sure to actually exist, and similarly, an edge (or the absence of an edge) in the graph means that the attack between arguments certainly exists (or certainly does not). The question of how to incorporate uncertainty in AFs has then arisen. Two kinds of approaches have been proposed. If a quantitative evaluation of the uncertainty is available, it seems natural to use it in the definition of reasoning mechanisms.

We study invariant local expansion operators for conflict-free and admissible sets in Abstract Argumentation Frameworks (AFs). Such operators are directly applied on AFs, and are invariant with respect to a chosen "semantics" (that is w.r.t. each of the conflict free/admissible set of arguments). Accordingly, we derive a definition of robustness for AFs in terms of the number of times such operators can be applied without producing any change in the chosen semantics.

We review the First International Competition on Computational Models of Argumentation (ICCMA'15). The competition evaluated submitted solvers' performance on four different computational tasks related to solving abstract argumentation frameworks. Each task evaluated solvers in ways that pushed the edge of existing performance by introducing new challenges. Despite being the first competition in this area, the high number of competitors entered, and differences in results, suggest that the competition will help shape the landscape of ongoing developments in argumentation theory solvers. While still a young field when compared to areas such as SAT solving and logic programming, the argumentation community is very active, with a conference series (COMMA, which began in 2006) and a variety of workshops and special issues of journals.