A Modal Logic for Temporal and Jurisdictional Classifier Models
Cecilia Di Florio, Huimin Dong, Antonino Rotolo
TL;DR
This paper addresses verifying ML classifiers used in legal decision-making by extending classifier models with a modal logic that captures temporal and jurisdictional constraints on precedents. It introduces the Temporal Jurisdictional Classifier Models (TJCM) and a corresponding modal language $\mathcal{L}(\mathrm{Atm})$ (including $\mathtt{H}, \mathtt{B}, [\leq_T], \mathtt{R^\forall}$) to formalize how binding and potentially binding precedents are determined, including notions of per incuriam and overruling. The framework defines binding without exception, a recursive notion of overruling, and a Temporal Hierarchical Principle via BestBinding to resolve conflicts, yielding a concrete decision rule $f^*$ and conditions like $Cl_n(o)$. The contribution combines semantics and axiomatization (TJCL, TJCL$^+$) with running examples to illustrate how temporal and hierarchical information guides legally compliant decisions, offering a foundation for future verification algorithms. The work situates itself relative to prior legal-CBR models, extending them to handle conflicts and practical aspects of real-world precedent management.
Abstract
Logic-based models can be used to build verification tools for machine learning classifiers employed in the legal field. ML classifiers predict the outcomes of new cases based on previous ones, thereby performing a form of case-based reasoning (CBR). In this paper, we introduce a modal logic of classifiers designed to formally capture legal CBR. We incorporate principles for resolving conflicts between precedents, by introducing into the logic the temporal dimension of cases and the hierarchy of courts within the legal system.