We extend the formal framework of classifier models used in the legal domain. While the existing classifier framework characterises cases solely through the facts involved, legal reasoning fundamentally relies on both facts and rules, particularly the ratio decidendi. This paper presents an initial approach to incorporating sets of rules within a classifier. Our work is built on the work of Canavotto et al. (2023), which has developed the rule-based reason model of precedential constraint within a hierarchy of factors. We demonstrate how decisions for new cases can be inferred using this enriched rule-based classifier framework. Additionally, we provide an example of how the time element and the hierarchy of courts can be used in the new classifier framework

The use of machine and deep learning techniques to predict outcomes in legal proceedings is a highly debated topic among legal scholars and policymakers. These technologies have the potential for supporting judicial decision-making, assist litigants, and analyze biases within the legal process. However, challenges remain, notably in the reluctance of judges to adopt such tools due to concerns over judicial independence, the normative correctness, accuracy, and robustness of algorithmic decisions, and the transparency of AI systems. It is claimed that methods are needed to validate AI-based judicial predication mechanisms. This paper contributes to addressing these challenges by developing a rich computational normative framework for judicial case-based reasoning grounded in Defeasible Deontic Logic. We explore legal CBR, focusing on inconsistencies and incomplete knowledge within case bases, and emphasize the importance of normative explanations to ensure transparency and justification in legal decision-making. By reconstructing CBR and deontic explanations, we provide a formal mechanism for validating AI-based judicial predictions where cases are represented using a fine-grained deontic language.

Consistency of case bases is a way to avoid the problem of retrieving conflicting constraining precedents for new cases to be decided. However, in legal practice the consistency requirements for cases bases may not be satisfied. As pointedout in [6], a model of precedential constraint should take into account the hierarchical structure of the specific legal system under consideration and the temporaldimension of cases. This article continues the research initiated in [18,9], whichestablished a connection between Boolean classifiers and legal case-based reasoning. On this basis, we enrich the classifier models with an organisational structurethat takes into account both the hierarchy of courts and which courts issue decisions that are binding/constraining on subsequent cases. We focus on common lawsystems. We also introduce a temporal relation between cases. Within this enrichedframework, we can formalise the notions of overruled cases and cases decided perincuriam: such cases are not to be considered binding on later cases. Finally, weshow under which condition principles based on the hierarchical structure and onthe temporal dimension can provide an unambiguous decision-making process fornew cases in the presence of conflicting binding precedents.

This article continues the research initiated in [1,2], which established a connection between Boolean classifiers and legal case-based reasoning. We relax the assumption that case bases are such that all situations have been decided in favour of the defendant or the plaintiff and we introduce an inductive strategy for assigning plausible outcomes to undecided cases. Using counterfactual reasoning, we propose a method to determine whether, at each step of the induction, a feature is a factor, i.e., it consistently favours a single outcome, or is irrelevant, i.e., it is does not favour any outcome, or is ambiguous, i.e., it favours opposite outcomes.

We introduce a general theory of quantitative and metric rewriting systems, namely systems with a rewriting relation enriched over quantales modelling abstract quantities. We develop theories of abstract and term-based systems, refining cornerstone results of rewriting theory (such as Newman’s Lemma, Church-Rosser Theorem, and critical pair-like lemmas) to a metric and quantitative setting. To avoid distance trivialisation and lack of confluence issues, we introduce non-expansive, linear term rewriting systems, and then generalise the latter to the novel class of graded term rewriting systems. These systems make quantitative rewriting modal and context-sensitive, this way endowing rewriting with coeffectful behaviours.