Over the past three decades, formal argumentation has established itself as a prominent research area within Artificial Intelligence, owing to its versatility in addressing various reasoning tasks. These include nonmonotonic reasoning, multi-agent systems, rule-based systems, and the analysis of debates or dialogues. Formal argumentation provides a unifying framework for representing diverse reasoning approaches, ranging from highly skeptical to more permissive forms of inference (for a comprehensive introduction to this area, see the handbook [4]). At the heart of formal argumentation lies Dung's abstract argumentation frameworks (AFs) [15], which are modeled as directed graphs, where nodes correspond to arguments, and directed edges represent the attack relations between them. AFs serve as a common foundational core across various reasoning systems in formal argumentation, with many extensions and refinements, e.g.

In this research note, we show the relationship between two non-admissible argumentation framework semantics: cogent and weakly admissible semantics. We prove that, while cogent extensions are weakly admissible, the converse is not true.

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.

Artificial Intelligence (AI) systems are increasingly deployed in legal contexts, where their opacity raises significant challenges for fairness, accountability, and trust. The so-called ``black box problem'' undermines the legitimacy of automated decision-making, as affected individuals often lack access to meaningful explanations. In response, the field of Explainable AI (XAI) has proposed a variety of methods to enhance transparency, ranging from example-based and rule-based techniques to hybrid and argumentation-based approaches. This paper promotes computational models of arguments and their role in providing legally relevant explanations, with particular attention to their alignment with emerging regulatory frameworks such as the EU General Data Protection Regulation (GDPR) and the Artificial Intelligence Act (AIA). We analyze the strengths and limitations of different explanation strategies, evaluate their applicability to legal reasoning, and highlight how argumentation frameworks -- by capturing the defeasible, contestable, and value-sensitive nature of law -- offer a particularly robust foundation for explainable legal AI. Finally, we identify open challenges and research directions, including bias mitigation, empirical validation in judicial settings, and compliance with evolving ethical and legal standards, arguing that computational argumentation is best positioned to meet both technical and normative requirements of transparency in the law domain.

We address the issue of defining a semantics for deontic argumentation that supports weak permission. Some recent results show that grounded semantics do not support weak permission when there is a conflict between two obligations. We provide a definition of Deontic Argumentation Theory that accounts for weak permission, and we recall the result about grounded semantics. Then, we propose a new semantics that supports weak permission.

Abstract argumentation frameworks (AFs) provide a formal setting to analyze many forms of reasoning with conflicting information. While the expressiveness of general infinite AFs make them a tempting tool for modeling many kinds of reasoning scenarios, the computational intractability of solving infinite AFs limit their use, even in many theoretical applications. We investigate the complexity of computational problems related to infinite but finitary argumentations frameworks, that is, infinite AFs where each argument is attacked by only finitely many others. Our results reveal a surprising scenario. On one hand, we see that the assumption of being finitary does not automatically guarantee a drop in complexity. However, for the admissibility-based semantics, we find a remarkable combinatorial constraint which entails a dramatic decrease in complexity. We conclude that for many forms of reasoning, the finitary infinite AFs provide a natural setting for reasoning which balances well the competing goals of being expressive enough to be applied to many reasoning settings while being computationally tractable enough for the analysis within the framework to be useful.

In this work, we broaden the investigation of admissibility notions in the context of assumption-based argumentation (ABA). More specifically, we study two prominent alternatives to the standard notion of admissibility from abstract argumentation, namely strong and weak admissibility, and introduce the respective preferred, complete and grounded semantics for general (sometimes called non-flat) ABA. To do so, we use abstract bipolar set-based argumentation frameworks (BSAFs) as formal playground since they concisely capture the relations between assumptions and are expressive enough to represent general non-flat ABA frameworks, as recently shown. While weak admissibility has been recently investigated for a restricted fragment of ABA in which assumptions cannot be derived (flat ABA), strong admissibility has not been investigated for ABA so far. We introduce strong admissibility for ABA and investigate desirable properties. We furthermore extend the recent investigations of weak admissibility in the flat ABA fragment to the non-flat case. We show that the central modularization property is maintained under classical, strong, and weak admissibility. We also show that strong and weakly admissible semantics in non-flat ABA share some of the shortcomings of standard admissible semantics and discuss ways to address these.

In computational argumentation, gradual semantics are fine-grained alternatives to extension-based and labelling-based semantics . They ascribe a dialectical strength to (components of) arguments sanctioning their degree of acceptability. Several gradual semantics have been studied for abstract, bipolar and quantitative bipolar argumentation frameworks (QBAFs), as well as, to a lesser extent, for some forms of structured argumentation. However, this has not been the case for assumption-based argumentation (ABA), despite it being a popular form of structured argumentation with several applications where gradual semantics could be useful. In this paper, we fill this gap and propose a family of novel gradual semantics for equipping assumptions, which are the core components in ABA frameworks, with dialectical strengths. To do so, we use bipolar set-based argumentation frameworks as an abstraction of (potentially non-flat) ABA frameworks and generalise state-of-the-art modular gradual semantics for QBAFs. We show that our gradual ABA semantics satisfy suitable adaptations of desirable properties of gradual QBAF semantics, such as balance and monotonicity. We also explore an argument-based approach that leverages established QBAF modular semantics directly, and use it as baseline. Finally, we conduct experiments with synthetic ABA frameworks to compare our gradual ABA semantics with its argument-based counterpart and assess convergence.

Ensuring transparency and trust in AI-driven public health and biomedical sciences systems requires more than accurate predictions-it demands explanations that are clear, contextual, and socially accountable. While explainable AI (XAI) has advanced in areas like feature attribution and model interpretability, most methods still lack the structure and adaptability needed for diverse health stakeholders, including clinicians, policymakers, and the general public. We introduce PHAX-a Public Health Argumentation and eXplainability framework-that leverages structured argumentation to generate human-centered explanations for AI outputs. PHAX is a multi-layer architecture combining defeasible reasoning, adaptive natural language techniques, and user modeling to produce context-aware, audience-specific justifications. More specifically, we show how argumentation enhances explainability by supporting AI-driven decision-making, justifying recommendations, and enabling interactive dialogues across user types. We demonstrate the applicability of PHAX through use cases such as medical term simplification, patient-clinician communication, and policy justification. In particular, we show how simplification decisions can be modeled as argument chains and personalized based on user expertise-enhancing both interpretability and trust. By aligning formal reasoning methods with communicative demands, PHAX contributes to a broader vision of transparent, human-centered AI in public health.

Argumentation frameworks (AFs) provide formal approaches for legal reasoning, but identifying sources of ambiguity and explaining argument acceptance remains challenging for non-experts. We present AF-XRAY, an open-source toolkit for exploring, analyzing, and visualizing abstract AFs in legal reasoning. AF-XRAY introduces: (i) layered visualizations based on game-theoretic argument length revealing well-founded derivation structures; (ii) classification of attack edges by semantic roles (primary, secondary, blunders); (iii) overlay visualizations of alternative 2-valued solutions on ambiguous 3-valued grounded semantics; and (iv) identification of critical attack sets whose suspension resolves undecided arguments. Through systematic generation of critical attack sets, AF-XRAY transforms ambiguous scenarios into grounded solutions, enabling users to pinpoint specific causes of ambiguity and explore alternative resolutions. We use real-world legal cases (e.g., Wild Animals as modeled by Bench-Capon) to show that our tool supports teleological legal reasoning by revealing how different assumptions lead to different justified conclusions.