Counterfactual explanations (CXs) are widely recognised as an essential technique for providing recourse recommendations for AI models. However, it is not obvious how to determine CXs in model multiplicity scenarios, where equally performing but different models can be obtained for the same task. In this paper, we propose novel qualitative and quantitative definitions of CXs based on explicit, nested quantification over (groups) of model decisions. We also study properties of these notions and identify decision problems of interest therefor. While our CXs are broadly applicable, in this paper we instantiate them within computational argumentation where model multiplicity naturally emerges, e.g. with incomplete and case-based argumentation frameworks. We then illustrate the suitability of our CXs for model multiplicity in legal and healthcare contexts, before analysing the complexity of the associated decision problems.

We introduce Gradual Abstract Argumentation for Case-Based Reasoning (Gradual AA-CBR), a data-driven, neurosymbolic classification model in which the outcome is determined by an argumentation debate structure that is learned simultaneously with neural-based feature extractors. Each argument in the debate is an observed case from the training data, favouring their labelling. Cases attack or support those with opposing or agreeing labellings, with the strength of each argument and relationship learned through gradient-based methods. This argumentation debate structure provides human-aligned reasoning, improving model interpretability compared to traditional neural networks (NNs). Unlike the existing purely symbolic variant, Abstract Argumentation for Case-Based Reasoning (AA-CBR), Gradual AA-CBR is capable of multi-class classification, automatic learning of feature and data point importance, assigning uncertainty values to outcomes, using all available data points, and does not require binary features. We show that Gradual AA-CBR performs comparably to NNs whilst significantly outperforming existing AA-CBR formulations.

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.