The concept of strong admissibility plays an important rolein some of the dialectical proof procedures that have been stated forgrounded semantics. As the grounded extension is the (unique) biggeststrongly admissible set, to show that an argument is in the groundedextension it suffices to show that it is in a strongly admissible set. Weare interested in identifying a strongly admissible set that minimizes thenumber of steps needed in the associated dialectical proof procedure. Inthe current work, we look at the computational complexity of doing so.

In this work, we explain how Assumption-Based Argumentation (ABA) is subsumed by Logic Programming (LP). The translation from ABA to LP (with a few restrictions on the ABA framework) results in a normal logic program whose semantics coincide with the semantics of the underlying ABA framework. Although the precise technicalities are beyond the current extended abstract (these can be found in the associated full paper) we provide a number of examples to illustrate the general idea.

Assumption-Based Argumentation (ABA) has been shown to subsume various other non-monotonic reasoning formalisms, among them normal logic programming (LP). We re-examine the relationship between ABA and LP and show that normal LP also subsumes (flat) ABA. More precisely, we specify a procedure that given a (flat) ABA framework yields an associated logic program with almost the same syntax whose semantics coincide with those of the ABA framework. That is, the 3-valued stable (respectively well-founded, regular, 2-valued stable, and ideal) models of the associated logic program coincide with the complete (respectively grounded, preferred, stable, and ideal) assumption labellings and extensions of the ABA framework. Moreover, we show how our results on the translation from ABA to LP can be reapplied for a reverse translation from LP to ABA, and observe that some of the existing results in the literature are in fact special cases of our work. Overall, we show that (flat) ABA frameworks can be seen as normal logic programs with a slightly different syntax. This implies that methods developed for one of these formalisms can be equivalently applied to the other by simply modifying the syntax.

An inconsistent knowledge base can be abstracted as a set of arguments and a defeat relation among them. There can be more than one consistent way to evaluate such an argumentation graph. Collective argument evaluation is the problem of aggregating the opinions of multiple agents on how a given set of arguments should be evaluated. It is crucial not only to ensure that the outcome is logically consistent, but also satisfies measures of social optimality and immunity to strategic manipulation. This is because agents have their individual preferences about what the outcome ought to be. In the current paper, we analyze three previously introduced argument-based aggregation operators with respect to Pareto optimality and strategy-proofness under different general classes of agent preferences. We highlight fundamental trade-offs between strategic manipulability and social optimality on one hand, and classical logical criteria on the other. Our results motivate further investigation into the relationship between social choice and argumentation theory. The results are also relevant for choosing an appropriate aggregation operator given the criteria that are considered more important, as well as the nature of agents’ preferences.

On the Web, there is always a need to aggregate opinions from the crowd (as in posts, social networks, forums, etc.). Different mechanisms have been implemented to capture these opinions such as Like in Facebook, Favorite in Twitter, thumbs-up/-down, flagging, and so on. However, in more contested domains (e.g., Wikipedia, political discussion, and climate change discussion), these mechanisms are not sufficient, since they only deal with each issue independently without considering the relationships between different claims. We can view a set of conflicting arguments as a graph in which the nodes represent arguments and the arcs between these nodes represent the defeat relation. A group of people can then collectively evaluate such graphs. To do this, the group must use a rule to aggregate their individual opinions about the entire argument graph. Here we present the first experimental evaluation of different principles commonly employed by aggregation rules presented in the literature. We use randomized controlled experiments to investigate which principles people consider better at aggregating opinions under different conditions. Our analysis reveals a number of factors, not captured by traditional formal models, that play an important role in determining the efficacy of aggregation. These results help bring formal models of argumentation closer to real-world application.

The current paper provides a dialectical interpretation of the argumentation-based judgment aggregation operators of Caminada and Pigozzi. In particular, we define discussion-based proof procedures for the foundational concepts of down-admissible and up-complete. We then show how these proof procedures can be used as the basis of dialectical proof procedures for the sceptical, credulous and super credulous judgment aggregation operators.

In abstract argumentation theory, preferred semantics has become one of the most popular approaches for determining the sets of arguments that can collectively be accepted. However, the description of preferred semantics, as it was originally stated by Dung, has a mainly technical and mathematical nature, making it difficult for lay persons to understand what the concept of preferred semantics is essentially about. In the current article, we aim to bridge the gap between mathematics and philosophy by providing a reformulation of (credulous) preferred semantics in terms of Socratic discussion. In order to do so, we first provide a (semi-)formal treatment of some of the concepts in Socratic dialogue.

M.W.A. Caminada, M. Giacomin; Introducing the Special Issue on 20 Years of Argument-Based Inference, Journal of Logic and Computation, Volume 25, Issue 2, 1 Apr

In an abstract argumentation framework, there are often multiple plausible ways to evaluate (or label) the status of each argument as accepted, rejected, or undecided. But often there exists a critical set of arguments whose status is sufficient to determine uniquely the status of every other argument. Once an agent has decided its position on a critical set of arguments, then essentially the entire frame-work has been evaluated. Likewise, once a group, e.g. a jury, agrees on the status of a critical set of arguments, all of their different views over all other arguments are resolved. Thus, critical sets of arguments are important both for efficient evaluation by individual agents and for collective agreement by groups of such. To exploit this idea in practice, however, a number of computational questions must be considered. In particular, how much computational effort is needed to verify that a set is, indeed, a critical set or a minimal critical set. In this paper we determine exact bounds on the computational complexity of these and related questions. In addition we provide similar analyses of issues: a concept closely related to critical set and derived in terms of (equivalence) classes of arguments related through “common” labelling behaviours.

In the current paper, we re-examine the concept of strong admissibility, as was originally introduced by Baroni and Giacomin. We examine the formal properties of strong admissibility, both in its extension-based and in its labelling-based form. Moreover, we show that strong admissibility plays a vital role in discussion-based proof procedures for grounded semantics. In particular it allows one to compare the performance of alternative dialectical proof procedures for grounded semantics, and obtain some remarkable differences between the Standard Grounded Game and the Grounded Persuasion Game.

The work of Caminada & Amgoud presents two possible ways of satisfying the rationality postulates: one using restricted rebut, and one using unrestricted rebut. Subsequent work on ASPIC+ has extended the work of Caminada & Amgoud, for instance by allowing preferences over arguments. However, such extensions have utilised restricted rebut only. In the current paper, we make the case for unrestricted rebut, and provide a formalism (called ASPIC−) that implements preferences between the defeasible rules, in the context of unrestricted rebut while still satisfying the rationality postulates of Caminada & Amgoud.

We introduce a unified logical approach, based on signed theories and Quantified Boolean Formulas (QBFs), that can serve as a basis for representing and reasoning with various argumentation-based decision problems. By this, we are able to represent, in a uniform and simple way, a wide range of extension-based semantics for argumentation theory, including complete, grounded, preferred, semi-stable, stage, ideal and eager semantics. Furthermore, our approach involves only propositional languages and quantifications over propositional variables, making decision problems like skeptical and credulous acceptance of arguments simply a matter of logical entailment and satisfiability, which can be verified by existing QBF-solvers.

In the current work, we provide a formal Mackenzie-style persuasion dialogue for grounded semantics. We show that an argument is in the grounded extension iff the proponent is able to persuade a maximally sceptical opponent in the dialogue.

In this article, we examine an argument-based semantics called semi-stable semantics. Semi-stable semantics is quite close to traditional stable semantics in the sense that every stable extension is also a semi-stable extension. One of the advantages of semi-stable semantics is that for finite argumentation frameworks there always exists at least one semi-stable extension. Furthermore, if there also exists at least one stable extension, then the semi-stable extensions coincide with the stable extensions. Semi-stable semantics can be seen as a general approach that can be applied to abstract argumentation, as well as to fields like default logic and answer set programming, yielding an interpretation with properties very similar to those of paraconsistent logic, including the properties of crash resistance and backward compatibility.

In the current paper, we re-examine the concept of stage semantics, which is one of the oldest semantics for abstract argumentation. Using a formal treatment of its properties, we explain how the intuition behind stage semantics differs from the intuition behind the admissibility based semantics that most scholars in argumentation theory are familiar with. We then provide a labelling-based algorithm for computing all stage extensions, based on earlier algorithms for computing all preferred, stable and semi-stable extensions.