Structure-Mapping: A Computational Model of Analogy and Similarity

The basic idea of Gentner's structure-mapping theory is that an analogy is a mapping of knowledge from one domain (the base) into another (the target) which conveys that a system of relations which holds among the base objects also holds among the target objects. Thus an analogy is a way of noticing relational commonalties independently of the objects in which those relations are embedded. Central to the mapping process is the principle of systematicity: people prefer to map systems of predicates that contain higher-order relations, rather than to map isolated predicates. The systematicity principle is a structural expression of our tacit preference for coherence and deductive power in interpreting analogy. Besides analogy, other kinds of similarity matches can be distinguished in this framework. Whereas analogies disregard object descriptions and map relational structure, appearance matches do the opposite -- they map aspects of object descriptions and disregard relational structure. Literal similarity matches map both relational structure and object-descriptions. As discussed below, these different kinds of similarity play different roles in psychological processes of learning and reasoning.

We view structure-mapping as the mechanism by which much of experiential learning takes place. We conjecture that much of experiential learning is driven by implicit comparisons among a person's knowledge structures at a given time. Analogy is also crucial in learning from instruction and in aligning experiential knowledge with knowledge gained via instruction.

We have built a set of computational tools to facilitate detailed modeling of human analogical learning and reasoning. Our tools are accountable cognitive simulations. What we mean by this is that we use a theoretically-driven decomposition of the processes being simulated. Any choices that are not determined by the theory (i.e., are empirically open) are made explicitly testable by tightly constrained programming options. This allows us to tie particular aspects of the results to particular explicit theoretical assumptions. For instance, this enables us to perform sensitivity analyses over assumptions at the levels of numerical parameters, processing assumptions, and representation of stimuli, to gain deeper insights.

SME: The Structure-Mapping Engine

The Structure-mapping Engine (SME) is a computer simulation of the analogy and similarity comparisons sanctioned by structure-mapping theory. SME takes as input two descriptions, one as the base and the other as the target. It produces as output a mappings which are interpretations of the comparison. (SME can produce up to two additional mappings, if they are sufficiently close to the best.) Each mapping contains three parts: the correspondences between the constituents of the base and target descriptions, a set of candidate inferences, which are surmises about the target sanctioned by the mapping (and vice-versa), and a structural evaluation score, which provides an indication of the quality of the match, based on structural properties.

SME can operates incrementally, i.e. new information can be added about the base and/or target, and the existing mappings will be extended with this new information. Incremental match processes allow us to more accurately model the use of analogy in a variety of cognitive processing, including problem solving and extended metaphors in discourse processing.

SME has several unique features. First, SME is very robust, having been applied to many thousands of examples at this writing, and has been used by a variety of research groups worldwide. Second, its performance has been compared with human performance in several studies, with encouraging results. Third, it is designed to be used as a module in larger systems, so it functions as a component for building more complex simulations and machine learning systems, as well as being a useful simulation tool in its own right.

Here are some examples of how SME has been used in larger-scale models and performance-oriented AI systems:

We note that in these systems the input representations were/are generated automatically or provided by external organizations. The fact that the same matching algorithm works well in visual reasoning, problem solving, and moral reasoning is, we believe, further evidence for the generality of structure-mapping's notion of comparison in cognition.

Selected Relevant Papers

Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7, pp 155-170.

Forbus, K. D., Ferguson, R. W., Lovett, A., and Gentner, D. (2016). Extending SME to handle large-scale cognitive modeling.  Cognitive Science, DOI: 10.1111/cogs.12377, pp 1-50.

Relevant Projects

Articulate Software for Teaching Science and Engineering

Articulate Virtual Laboratories for Science and Engineering Education

Analogy, Mental Models, and Conceptual Change

Building and Using Large Common Sense Knowledge Bases

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