This paper presents the authors’ particular view of analogy and relates it to machine learning. It begins by describing the classical paradigm, dating back to Aristotle, of analogy as proportions: A is to B as C is to D is an analogy between the A/B domain and the C/D domain. (This is the intelligence-test style of analogy that was investigated early in the history of artificial intelligence [1].) The structure within each domain is based solely on causal reasoning, written as a causality relation c(A,B) that enables B to be inferred from A. The relations between domains are based on similarity and dissimilarity, written sd(A,C). Given this situation, we can deduce similarities between B and D and partially infer D. The paper discusses this structure with several examples and highlights the role of dissimilarities in the interdomain matching. It gives an application to the incremental learning of concepts, with A and B playing the role of example and generalization, C and D of new example and new generalization, and the problem being to infer D. Apparently this forms the basis of a concept learning system that has been developed by the authors.

The paper is quite clear and specific; it is easy to understand exactly what is going on. In particular, the role of dissimilarities is spelled out in detail--while other authors acknowledge in general terms the need to take account of dissimilarity, this paper shows how it can actually be done. On the other hand, the paper lacks any real discussion of the underlying assumptions about analogy that the authors make. The introduction states that this is their point of view--and it is; take it or leave it. For example, it is stated flatly that “analogy theory relies on causal reasoning” without any discussion or support (it seems questionable, at the very least, to us). The paper claims “we can define the following causality relations between A and B” and goes on to list them without explaining where they come from or who it is that does the defining.

But perhaps the main criticism is that the paper adopts the strict, classical paradigm of analogy as proportion. Most modern authors view analogy in more general terms [2]. By insisting on the classical analogy paradigm, the authors have locked themselves into example-to-example comparisons rather than example-to-generalization ones. While their case-based approach may well be the most practical one, leading to an analysis of similarities and differences between individual cases and to the interesting question of selecting examples that give the most useful analogues, the choice of analogy as proportion over the more prevalent and general notion of analogy certainly deserves to be spotlighted and discussed.