Exploiting persistent mappings in cross-domain analogical learning of physical domains

Abstract

Cross-domain analogies are a powerful method for learning new domains. This paper extends the Domain Transfer via Analogy (DTA) method with persistent mappings, correspondences between domains that are incrementally built up as a cognitive system gains experience with a new domain. DTA uses analogies between pairs of textbook example problems, or worked solutions, to create a domain mapping between a familiar and a new domain. This mapping enables the initialization of a new domain theory. Another analogy is then made between the domain theories themselves, providing additional conjectures about the new domain. After these conjectures are verified, the successful mappings are stored as persistent mappings to constrain future analogies between the domains. We show that DTA plus persistent mappings enables a Companion, the first structure mapping cognitive architecture, to learn the equation schemas and control knowledge necessary to solve problems in three domains (rotational mechanics, electricity, and heat) by analogy with linear mechanics. We provide a detailed analysis categorizing transfer failures. As with people, the most difficult step in cross-domain analogy is identifying an appropriate example. Once an analogous example has been found, DTA successfully transfers the domain knowledge necessary to solve the problem in the new domain 78% of the time. Furthermore, we illustrate how persistent mappings assist in retrieval of analogous examples and overcoming two types of mapping failures.