Hierarchical models of precedential constraint

In recent years, models of a fortiori argumentation from the field of artificial intelligence and law, developed to describe legal case-based reasoning based on precedent, have been successfully applied to improve interpretability of data-driven decision systems. To aid with these applications, we further develop the theory of a fortiori case-based reasoning by extending the knowledge representations on which these models operate. More specifically, we modify the representations to accommodate incomplete information, as well as to incorporate both dimensional (as opposed to binary) and hierarchical (as opposed to unstructured) information. This results in four models-one for each combination of accommodating dimensional or hierarchical information. We investigate their formal properties, and find they are monotonic with respect to the addition of new precedents and of new facts, and that some are conservative extensions of other models. In addition, we exemplify each through a running example from the penitentiary law domain.