Constraints on Analogical Mapping: A Comparison of Three Models

Three theories of analogy have been proposed that are supported by computational models and data from experiments on human analogical abilities. In this article we show how these theories can be unified within a common metatheoretical framework that distinguishes among levels of informational, behavioral, and hardware constraints. This framework clarifies the distinctions among three computational models in the literature: the Analogical Constraint Mapping Engine (ACME), the Structure-Mapping Engine (SME), and the Incremental Analogy Machine (1AM). We then go on to develop a methodology for the comparative testing of these models. In two different manipulations of an analogical mapping task we compare the results of computational experiments with these models against the results of psychological experiments. In the first experiment we show that increasing the number of similar elements in two analogical domains decreases the response time taken to reach the correct mapping for an analogy problem. In the second psychological experiment we find that the order in which the elements of the two domains are presented has significant facilitative effects on the ease of analogical mapping. Of the three models, only 1AM embodies behavioral constraints and predicts both of these results. Finally, the immediate implications of these results for analogy research are discussed, along with the wider implications the research has for cognitive science methodology.