Summary Report for the Third International Competition On Computational Models of Argumentation

The Third International Competition on Computational Models of Argumentation (ICCMA’19) focused on reasoning tasks in abstract argumentation frameworks. Submitted solvers were tested on a selected collection of benchmark instances, including artificially generated argumentation frameworks and some frameworks formalizing real-world problems. This competition introduced two main novelties over the two previous editions: the first one is the use of the Docker platform for packaging the participating solvers into virtual “light” containers; the second novelty consists of a new track for dynamic frameworks.

Yes, no, maybe, I don’t know: Complexity and application of abstract argumentation with incomplete knowledge

argumentation, as originally defined by Dung, is a model that allows the description of certain information about arguments and relationships between them: in an abstract argumentation framework (AF), the agent knows for sure whether a given argument or attack exists. It means that the absence of an attack between two arguments can be interpreted as “we know that the first argument does not attack the second one”. But the question of uncertainty in abstract argumentation has received much attention in the last years. In this paper, we survey approaches that allow to express information like “There may (or may not) be an attack between these arguments”. We describe the main models that incorporate qualitative uncertainty (or ignorance) in abstract argumentation, as well as some applications of these models. We also highlight some open questions that deserve some attention in the future.

On Probabilistic Logical Argumentation

In this paper, we introduce a framework for probabilistic logic-based argumentation inspired on the DeLP formalism and an extensive use of conditional probability. We define probabilistic arguments built from possibly inconsistent probabilistic knowledge bases and study the notions of attack, defeat and preference between these arguments. Finally, we discuss consistency properties of admissible extensions of the Dung’s abstract argumentation graphs obtained from sets of probabilistic arguments and the attack relations between them.

Strong admissibility for abstract dialectical frameworks

dialectical frameworks (ADFs) have been introduced as a formalism for modeling argumentation allowing general logical satisfaction conditions and the relevant argument evaluation. Different criteria used to settle the acceptance of arguments are called semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. However, the notion of strongly admissible semantics studied for abstract argumentation frameworks has not yet been introduced for ADFs. In the current work we present the concept of strong admissibility of interpretations for ADFs. Further, we show that strongly admissible interpretations of ADFs form a lattice with the grounded interpretation as the maximal element. We also present algorithms to answer the following decision problems: (1) whether a given interpretation is a strongly admissible interpretation of a given ADF, and (2) whether a given argument is strongly acceptable/deniable in a given interpretation of a given ADF. In addition, we show that the strongly admissible semantics of ADFs forms a proper generalization of the strongly admissible semantics of AFs.

Reasoning over Attack-incomplete AAFs in the Presence of Correlations

Attack-Incomplete Abstract Argumentation Frameworks (att- iAAFs) are a popular extension of AAFs where attacks are marked as uncertain when they are not unanimously per- ceived by different agents reasoning on the same arguments. We here extend att-iAAFs with the possibility of specifying correlations involving the uncertain attacks. This feature sup- ports a unified and more precise representation of the differ- ent scenarios for the argumentation, where, for instance, it can be stated that an attack α has to be considered only if an attack β is considered, or that α and β are alternative, and so on. In order to provide a user-friendly language for spec- ifying the correlations, we allow the argumentation analyst to express them in terms of a set of elementary dependen- cies, using common logical operators (namely, OR , NAND , CHOICE , ⇒). In this context, we focus on the problem of verifying extensions under the possible perspective, and study the sensitivity of its computational complexity to the forms of correlations expressed and the semantics of the extensions.

On the Maximal Number of Complete Extensions in Abstract Argumentation Frameworks

argumentation frameworks are by now a major research area in knowledge representation and reasoning. Various aspects of AFs have been extensively studied over the last 25 years. Contributing to understanding the expressive power of AFs, researchers found lower and upper bounds for the maximal number of extensions, that is, acceptable points of view, in AFs. One of the classical and most important concepts in AFs are so-called complete extensions. Surprisingly, the exact bound for the maximal number of complete extensions in an AF has not yet been formally established, although there is a reasonable conjecture tracing back at least to 2015. Recently the notion of modularization was introduced and it was shown that this concept plays a key role for the understanding of relations between semantics as well as intrinsic properties. In this paper, we will use this property to give a formal proof of the conjecture regarding complete semantics.