The goal of this work is to examine the nature and role of visual representations and inferences in analogical reasoning, and especially in analogical transfer. Analogy involves learning about some target analog by transferring knowledge from a source analog. The process consists of several steps: retrieval is identifying a candidate source analog in memory; mapping is finding the best set of correspondences between components of the analogs; transfer is the application of knowledge from the source analog to the target analog; evaluation is determining if the target problem has been solved appropriately; storage is storing the target analog in memory for potential reuse.
Traditional conceptual and computational theories of analogy have focused primarily on causal knowledge and inferences (see [Holyoak and Thagard1997] [Bhatta and Goel1997] [Falkenhainer et al.1990] for examples). Psychological research, however, shows that visual reasoning often occurs in analogy [Holyoak and Thagard1997], [Pedone et al.1999] Some recent theories [Bhatta and Goel1997] [Griffith et al.2000] represent structural knowledge in addition to causal knowledge. Structural knowledge describes a system's physical composition but typically includes only the information directly relevant for analyzing the causal behaviors of the system. Structural knowledge might be thought of as a schematic that shows the components of the system and the connections among them but leaves out other visual information such as what a wire looks like, which side of a pump is up, etc.
We define visual representations as those that consist only of information relevant to how an image appears. Note that this definition of ``visual'' includes both high-level symbolic representations and low-level bitmap representations (which only represent the locations of points of light). We view visual and causal knowledge as lying on a spectrum, where one extreme has raw sensory data, (such as a bitmap image), and the other has highly interpreted and abstracted knowledge (e.g., teleological knowledge). Visual knowledge is closer to the perceptual, or modal, end of the spectrum, and causal knowledge is nearer to the amodal end. Causality can only be represented implicitly in a visual representation. In contrast to a bitmap image, the visual knowledge we use contains abstractions of objects and relations, and is thus represented symbolically.
Our hypothesis is that symbolically represented visual knowledge provides a level of abstraction at which two otherwise dissimilar domains may look more alike. For example, the concepts of an army on the march and a ray of radiation are quite different, but if both are represented as lines, it may facilitate analogical retrieval, mapping and transfer. We hypothesize that evaluation, on the other hand, requires explicit causal knowledge: simply because the path of the army and the ray look alike does not imply that the two behave similarly. Since other's work has begun to explore the use of visual knowledge for mapping, our work focuses on analogical transfer.
In this paper, we sketch an outline of our computational theory of visual analogical transfer for a class of problems in which the source analog contains a sequence of images (or can be analyzed in terms of an image sequence). This theory has been implemented in an operational computer program called Galatea. We illustrate the theory using the classical fortress/tumor problem [Duncker1926] as an example. This example was chosen because psychological data indicates that experimental participants used visual inferences in solving it [Holyoak and Thagard1997]. In this task, experimental participants first read a story about a problem-solving situation: A general with a large army wants to overthrow a dictator who lives in a fortress. All roads to the fortress are armed with mines that will go off if many people are on them at the same time. To solve this problem he breaks up his army into small groups and has them take different roads. The groups arrive at the same time and take the fortress. Then, the subjects are given a new problem: A patient needs radiation treatment on a tumor inside the body, but the radiation will harm the healthy tissue it reaches on the way in. Finally, the participants are asked to solve the tumor problem. The analogous solution is to target the tumor with low-level rays coming from different directions, and have them converge on the tumor.