Using Gestalt Principles to Compute Analogies of Geometric Figures

Analogy making is a highly sophisticated cognitive process in which two stimuli are compared and analyzed for common patterns. Analogical reasoning is the adaptation of knowledge about one stimulus such that it can be applied to the second stimulus and new analogous inferences can be drawn. Analogy making requires intelligence, since such analogous patterns and transfers often are not obvious and require a certain conceptualization of the stimuli. Intelligence tests often use proportional analogies, where subjects have to find a follow-up for a series of geometric figures. Heuristic-Driven-Theory-Projection (HDTP) is a formal system for analogy making and analogical reasoning. This paper shows how HDTP can be used to analyze proportional analogies between geometric figures. It uses VREG, a language of perception developed by Dastani (1998), to compute different Gestalts from 2-dimensional geometric figures. Depending on the Gestalt perception, HDTP proposes analogical inferences at different levels of cognitive plausibility. Since HDTP describes stimuli formally in first-order logic, it is possible to separate the description of a concrete stimulus from the specification of general Gestalt principles of perception. Therefore it is possible to generate conceptualizations of geometric figures on the fly (called re-representation). The ability of automatic re-representation is one of the central advantages of HDTP compared to other analogy models.