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We describe a method for constructing a structural model of an unlabeled target two-dimensional line drawing by analogy to a known source model of a drawing with similar structure. The source case is represented as a schema that contains its line drawing and its structural model represented at multiple levels of abstraction: the lines and intersections in the drawing, the shapes, the structural components, and connections of the device are depicted in the drawing. Given a target drawing and a relevant source case, our method of compositional analogy first constructs a representation of the lines and the intersections in the target drawing, then uses the mappings at the level of line intersections to transfer the shape representations from the source case to the target; next, it uses the mappings at the level of shapes to transfer the full structural model of the depicted system from the source to the target.

The core issue of analogical reasoning is the transfer of relational knowledge from a source case to a target problem. Visual analogical reasoning pertains to problems containing only visual knowledge. Holyoak and Thagard proposed that the retrieval and mapping tasks of analogy in general can be productively viewed as constraint satisfaction problems, and provided connectionist implementations of their proposal. In this paper, we reexamine the retrieval and mapping tasks of analogy in the context of diagrammatic cases, representing the spatial structure of source and target diagrams as semantic networks in which the nodes represent spatial elements and the links represent spatial relations. We use a method of constraint satisfaction with backtracking for the retrieval and mapping tasks, with subgraph isomorphism over a particular domain language as the similarity measure. Results in the domain of 2D line drawings suggest that at least for this domain the above method is quite promising.

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