| Spatial problem-solving tasks are often used to evaluate people's cognitive abilities. For example, Raven's Progressive Matrices is a popular intelligence test. In it, an individual is shown an array of two-dimensional images, with one image missing. The individual must compare the images and identify a pattern of differences between them, in order to solve for the missing image. Performance on tasks such as Raven's and geometric analogy ("A is to B as C is to..?") correlates strongly with performance on many other ability tasks, in the spatial, verbal, and mathematical domains. Thus, these tasks appear to depend on core, general-purpose representations and processes. However, it is as yet unclear what those representations and processes are.;To better understand these tasks, we developed Spatial Routines for Sketches (SRS), a general framework for modeling spatial problem-solving. SRS is based on a set of psychological claims about how people perform spatial problem-solving: 1) When possible, people use qualitative representations describing features such as relative position or orientation, rather than exact numerical values. 2) Spatial representations are hierarchical. A given image might be represented as object groups, individual objects, or the parts within each object. 3) Qualitative spatial representations can be compared via structure-mapping. Structure-mapping involves aligning the relational structure in two representations to find the corresponding elements.;Three task models were built within the SRS framework: geometric analogy, Raven's Progressive Matrices, and the oddity task, in which one sees a set of images and picks the one that is different. The three task models use identical representations and similar processes. Thus, they allow us to test the generality of the psychological claims, as well as the representations and processes that implement these claims.;Each task model was compared against human performance. All three models perform at least as well as human adults, and problems that are difficult for the models are also difficult for people. This supports the claims on which the models are based. Furthermore, by ablating a model's ability to perform certain operations and examining the error pattern this produces, we are able to produce new hypotheses about human reasoning. |
