In recent years, large language models (LLMs) have made significant advancements in neuro-symbolic computing. However, the combination of LLM with argumentation computation remains an underexplored domain, despite its considerable potential for real-world applications requiring defeasible reasoning. In this paper, we aim to investigate the capability of LLMs in determining the extensions of various abstract argumentation semantics. To achieve this, we develop and curate a benchmark comprising diverse abstract argumentation frameworks, accompanied by detailed explanations of algorithms for computing extensions. Subsequently, we fine-tune LLMs on the proposed benchmark, focusing on two fundamental extension-solving tasks. As a comparative baseline, LLMs are evaluated using a chain-of-thought approach, where they struggle to accurately compute semantics. In the experiments, we demonstrate that the process explanation plays a crucial role in semantics computation learning. Models trained with explanations show superior generalization accuracy compared to those trained solely with question-answer pairs. Furthermore, by leveraging the self-explanation capabilities of LLMs, our approach provides detailed illustrations that mitigate the lack of transparency typically associated with neural networks. Our findings contribute to the broader understanding of LLMs' potential in argumentation computation, offering promising avenues for further research in this domain.

The visualization of argumentation frameworks (AFs) is crucial for enabling a wide applicability of argumentative tools. However, their visualization is often considered only as an accompanying part of tools for computing semantics and standard graphical representations are used. We introduce a new visualization technique that draws an AF, together with an extension (as part of the input), as a 3-layer graph layout. Our technique supports the user to more easily explore the visualized AF, better understand extensions, and verify algorithms for computing semantics. To optimize the visual clarity and aesthetics of this layout, we propose to minimize edge crossings in our 3-layer drawing. We do so by an exact ILP-based approach, but also propose a fast heuristic pipeline. Via a quantitative evaluation, we show that the heuristic is feasible even for large instances, while producing at most twice as many crossings as an optimal drawing in most cases.

A framework with sets of attacking arguments(SETAF) is an extension of the well-known Dung's Abstract Argumentation Frameworks (AAF s) that allows joint attacks on arguments. In this paper, we provide a translation from Normal Logic Programs (NLPs) to SETAFs and vice versa, from SETAFs to NLPs. We show that there is pairwise equivalence between their semantics, including the equivalence between L-stable and semi-stable semantics. Furthermore, for a class of NLPs called Redundancy-Free Atomic Logic Programs (RFALPs), there is also a structural equivalence as these back-and-forth translations are each other's inverse. Then, we show that RFALPs are as expressive as NLPs by transforming any NLP into an equivalent RFALP through a series of program transformations already known in the literature. We also show that these program transformations are confluent, meaning that every NLP will be transformed into a unique RFALP. The results presented in this paper enhance our understanding that NLPs and SETAFs are essentially the same formalism.

When engaging in argumentative discourse, skilled human debaters tailor claims to the beliefs of the audience, to construct effective arguments. Recently, the field of computational argumentation witnessed extensive effort to address the automatic generation of arguments. However, existing approaches do not perform any audience-specific adaptation. In this work, we aim to bridge this gap by studying the task of belief-based claim generation: Given a controversial topic and a set of beliefs, generate an argumentative claim tailored to the beliefs. To tackle this task, we model the people's prior beliefs through their stances on controversial topics and extend state-of-the-art text generation models to generate claims conditioned on the beliefs. Our automatic evaluation confirms the ability of our approach to adapt claims to a set of given beliefs. In a manual study, we additionally evaluate the generated claims in terms of informativeness and their likelihood to be uttered by someone with a respective belief. Our results reveal the limitations of modeling users' beliefs based on their stances, but demonstrate the potential of encoding beliefs into argumentative texts, laying the ground for future exploration of audience reach.

Labelling-based formal argumentation relies on labelling functions that typically assign one of 3 labels to indicate either acceptance, rejection, or else undecided-to-be-either, to each argument. While a classical labelling-based approach applies globally uniform conditions as to how an argument is to be labelled, they can be determined more locally per argument. Abstract dialectical frameworks (ADF) is a well-known argumentation formalism that belongs to this category, offering a greater labelling flexibility. As the size of an argumentation increases in the numbers of arguments and argument-to-argument relations, however, it becomes increasingly more costly to check whether a labelling function satisfies those local conditions or even whether the conditions are as per the intention of those who had specified them. Some compromise is thus required for reasoning about a larger argumentation. In this context, there is a more recently proposed formalism of may-must argumentation (MMA) that enforces still local but more abstract labelling conditions. We identify how they link to each other in this work. We prove that there is a Galois connection between them, in which ADF is a concretisation of MMA and MMA is an abstraction of ADF. We explore the consequence of abstract interpretation at play in formal argumentation, demonstrating a sound reasoning about the judgement of acceptability/rejectability in ADF from within MMA. As far as we are aware, there is seldom any work that incorporates abstract interpretation into formal argumentation in the literature, and, in the stated context, this work is the first to demonstrate its use and relevance.

Generalizing the attack structure in argumentation frameworks (AFs) has been studied in different ways. Most prominently, the binary attack relation of Dung frameworks has been extended to the notion of collective attacks. The resulting formalism is often termed SETAFs. Another approach is provided via abstract dialectical frameworks (ADFs), where acceptance conditions specify the relation between arguments; restricting these conditions naturally allows for so-called support-free ADFs. The aim of the paper is to shed light on the relation between these two different approaches. To this end, we investigate and compare the expressiveness of SETAFs and support-free ADFs under the lens of 3-valued semantics. Our results show that it is only the presence of unsatisfiable acceptance conditions in support-free ADFs that discriminate the two approaches.

The semantics as to which set of arguments in a given argumentation graph may be acceptable (acceptability semantics) can be characterised in a few different ways. Among them, labelling-based approach allows for concise and flexible determination of acceptability statuses of arguments through assignment of a label indicating acceptance, rejection, or undecided to each argument. In this work, we contemplate a way of broadening it by accommodating may- and must- conditions for an argument to be accepted or rejected, as determined by the number(s) of rejected and accepted attacking arguments. We show that the broadened label-based semantics can be used to express more mild indeterminacy than inconsistency for acceptability judgement when, for example, it may be the case that an argument is accepted and when it may also be the case that it is rejected. We identify that finding which conditions a labelling satisfies for every argument can be an undecidable problem, which has an unfavourable implication to semantics. We propose to address this problem by enforcing a labelling to maximally respect the conditions, while keeping the rest that would necessarily cause non-termination labelled undecided.

Bipolar Argumentation Frameworks (BAFs) admit several interpretations of the support relation and diverging definitions of semantics. Recently, several classes of BAFs have been captured as instances of bipolar Assumption-Based Argumentation, a class of Assumption-Based Argumentation (ABA). In this paper, we establish the complexity of bipolar ABA, and consequently of several classes of BAFs. In addition to the standard five complexity problems, we analyse the rarely-addressed extension enumeration problem too. We also advance backtracking-driven algorithms for enumerating extensions of bipolar ABA frameworks, and consequently of BAFs under several interpretations. We prove soundness and completeness of our algorithms, describe their implementation and provide a scalability evaluation. We thus contribute to the study of the as yet uninvestigated complexity problems of (variously interpreted) BAFs as well as of bipolar ABA, and provide the lacking implementations thereof.

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.

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.