Hierarchical precedential constraint

In recent work, theories of case-based legal reasoning have been applied to the development of explainable artificial intelligence methods, through the analogy of training examples as previously decided cases. One such theory is that of precedential constraint. A downside of this theory with respect to this application is that it performs single-step reasoning, moving directly from the case base to an outcome. For this reason we propose a generalization of the theory of precedential constraint which allows multi-step reasoning, moving from the case base through a series of intermediate legal concepts before arriving at an outcome. Our generalization revolves around the notion of factor hierarchy, so we call this hierarchical precedential constraint. We present the theory, demonstrate its applicability to case-based legal reasoning, and perform a preliminary analysis of its theoretical properties.