MAGI: Analogy-based Encoding Using Regularity and Symmetry

Analogy has always been considered a mechanism for interrelating distinct parts of the world, but it is perhaps just as important to consider how analogy might be used to break the world into comprehensible parts. The MAGI program uses the Structure-Mapping Engine (SME) to flexibly and reliably match a description against itself. The resulting mapping pulls out the two maximally consistent parts of the given description . MAGI then divides out the parts of the mapping and categorizes the mapping as symmetrical or regular . These parts may then be used as the basis for new comparisons . We theorize that MAGI models how people use symmetry and regularity to facilitate the encoding task . We demonstrate this with three sets of examples . First, we show how MAGI can augment traditional axis detection and reference frame adjustment in geometric figures . Next, we demonstrate how MAGI detects visual and functional symmetry in logic circuits, where symmetry of form aids encoding symmetry of function . Finally, to emphasize that regularity and symmetry detection is not simply visual, we show how MAGI models some aspects of expectation generation in story understanding . In general, MAGI shows symmetry and regularity to be not only pretty, but also cognitively valuable . Introduction : Why regularity and symmetry aren't (just) pretty Regularity and symmetry are phenomena strangely divided between disciplines . Researchers in computer vision (Witkin & Tenenbaum, 1983) and perceptual psychology (Palmer, 1985 ; Rock, 1983) have long recognized regularity and especially symmetry as important, but have understood it strictly as a perceptual effect . Although researchers in analogy might easily agree that symmetry and regularity must involve some form of self-similarity, this community has produced little work in the area, perhaps due to an emphasis on problem solving and learning, rather than encoding . This paper is an attempt to bridge this gap by recasting symmetry and regularity as analogical processes that operate on structured but undivided representations in the world. There are two central theoretical claims in the MAGI model . The first is that regularity and symmetry are like analogy--they work by mapping a maximal common set of structurally interconnected relations, but within a Ronald W. Ferguson Qualitative Reasoning Group Institute for the Learning Sciences Northwestern University Evanston, Illinois 60202 fergusongils .nwu .edu single description instead of between separate base and target descriptions . The second is illustrated by Figure 1 . Regularity and symmetry are not strictly perceptual, but may be found in any task involving the encoding of relational knowledge structures . For example, regularity and symmetry may be found imperfect figures (a), in diagrams (b), or in story narratives (c). To support these two claims, we have constructed MAGI, a system that uses SME to detect regularity and symmetry, and can handle all