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.

We introduce Supported Abstract Argumentation for Case-Based Reasoning (sAA-CBR), a binary classification model in which past cases engage in debates by arguing in favour of their labelling and attacking or supporting those with opposing or agreeing labels. With supports, sAA-CBR overcomes the limitation of its precursor AA-CBR, which can contain extraneous cases (or spikes) that are not included in the debates. We prove that sAA-CBR contains no spikes, without trading off key model properties

Argumentation is a central subarea of Artificial Intelligence (AI) for modeling and reasoning about arguments. The semantics of abstract argumentation frameworks (AFs) is given by sets of arguments (extensions) and conditions on the relationship between them, such as stable or admissible. Today's solvers implement tasks such as finding extensions, deciding credulous or skeptical acceptance, counting, or enumerating extensions. While these tasks are well charted, the area between decision, counting/enumeration and fine-grained reasoning requires expensive reasoning so far. We introduce a novel concept (facets) for reasoning between decision and enumeration. Facets are arguments that belong to some extensions (credulous) but not to all extensions (skeptical). They are most natural when a user aims to navigate, filter, or comprehend the significance of specific arguments, according to their needs. We study the complexity and show that tasks involving facets are much easier than counting extensions. Finally, we provide an implementation, and conduct experiments to demonstrate feasibility.

In this paper, we introduce a new family of argument-ranking semantics which can be seen as a refinement of the classification of arguments into skeptically accepted, credulously accepted and rejected. To this end we use so-called social ranking functions which have been developed recently to rank individuals based on their performance in groups. We provide necessary and sufficient conditions for a social ranking function to give rise to an argument-ranking semantics satisfying the desired refinement property.

Abstract argumentation is a popular toolkit for modeling, evaluating, and comparing arguments. Relationships between arguments are specified in argumentation frameworks (AFs), and conditions are placed on sets (extensions) of arguments that allow AFs to be evaluated. For more expressiveness, AFs are augmented with \emph{acceptance conditions} on directly interacting arguments or a constraint on the admissible sets of arguments, resulting in dialectic frameworks or constrained argumentation frameworks. In this paper, we consider flexible conditions for \emph{rejecting} an argument from an extension, which we call rejection conditions (RCs). On the technical level, we associate each argument with a specific logic program. We analyze the resulting complexity, including the structural parameter treewidth. Rejection AFs are highly expressive, giving rise to natural problems on higher levels of the polynomial hierarchy.

In the pursuit of enhancing the efficacy and flexibility of interpretable, data-driven classification models, this work introduces a novel incorporation of user-defined preferences with Abstract Argumentation and Case-Based Reasoning (CBR). Specifically, we introduce Preference-Based Abstract Argumentation for Case-Based Reasoning (which we call AA-CBR-P), allowing users to define multiple approaches to compare cases with an ordering that specifies their preference over these comparison approaches. We prove that the model inherently follows these preferences when making predictions and show that previous abstract argumentation for case-based reasoning approaches are insufficient at expressing preferences over constituents of an argument. We then demonstrate how this can be applied to a real-world medical dataset sourced from a clinical trial evaluating differing assessment methods of patients with a primary brain tumour. We show empirically that our approach outperforms other interpretable machine learning models on this dataset.

An Argumentation Framework (AF) is a directed graph F = A,R where A is a set of abstract entities called arguments and R A A is the attack relation. Although Dung does not put additional constraints regarding the set of arguments, in this work we assume that A is a non-empty finite set of arguments. When(a,b) R, we say that a attacks b, and similarly if a S s.t. a attacks b, then the set of arguments S attacks b. Classical AF semantics rely on a notion of collective acceptability: the semantics allow to determine sets of extensions, which are sets of jointly acceptable arguments. Most extension-based semantics satisfy two basic properties: Definition 2 (Conflict-freeness and defense). Given an AF F = A,R and the set of arguments S A, we say that S is conflict-free if a,b S, (a,b) R. Then, given an argument a A, we say that S defends a if b A s.t.

This volume contains revised versions of the papers selected for the fourth volume of the Online Handbook of Argumentation for AI (OHAAI). Previously, formal theories of argument and argument interaction have been proposed and studied, and this has led to the more recent study of computational models of argument. Argumentation, as a field within artificial intelligence (AI), is highly relevant for researchers interested in symbolic representations of knowledge and defeasible reasoning. The purpose of this handbook is to provide an open access and curated anthology for the argumentation research community. OHAAI is designed to serve as a research hub to keep track of the latest and upcoming PhD-driven research on the theory and application of argumentation in all areas related to AI.

Case-based reasoning is known to play an important role in several legal settings. In this paper we focus on a recent approach to case-based reasoning, supported by an instantiation of abstract argumentation whereby arguments represent cases and attack between arguments results from outcome disagreement between cases and a notion of relevance. In this context, relevance is connected to a form of specificity among cases. We explore how relevance can be learnt automatically in practice with the help of decision trees, and explore the combination of case-based reasoning with abstract argumentation (AA-CBR) and learning of case relevance for prediction in legal settings. Specifically, we show that, for two legal datasets, AA-CBR and decision-tree-based learning of case relevance perform competitively in comparison with decision trees. We also show that AA-CBR with decision-tree-based learning of case relevance results in a more compact representation than their decision tree counterparts, which could be beneficial for obtaining cognitively tractable explanations.

Argument graphs provide an abstract representation of an argumentative situation. A bipolar argument graph is a directed graph where each node denotes an argument, and each arc denotes the influence of one argument on another. Here we assume that the influence is supporting, attacking, or ambiguous. In a bipolar argument graph, each argument is atomic and so it has no internal structure. Yet to better understand the nature of the individual arguments, and how they interact, it is important to consider their internal structure. To address this need, this paper presents a framework based on the use of logical arguments to instantiate bipolar argument graphs, and a set of possible constraints on instantiating arguments that take into account the internal structure of the arguments, and the types of relationship between arguments.