How to ground a language for legal discourse in a prototypical perceptual semantics

In a pair of papers from 1995 and 1997, I developed a computational theory of legal argument, but left open a question about the key concept of a "prototype." Contemporary trends in machine learning have now shed new light on the subject. In this paper, I will describe my recent work on "manifold learning," as well as some work in progress on "deep learning." Taken together, this work leads to a logical language grounded in a prototypical perceptual semantics, with implications for legal theory. The main technical contribution of the paper is a categorical logic based on the category of differential manifolds (Man), which is weaker than a logic based on the category of sets (Set) or the category of topological spaces (Top). The paper also shows how this logic can be extended to a full Language for Legal Discourse (LLD), and suggests a solution to the elusive problem of "coherence" in legal argument.