A Computer Model of Diagrammatic Reasoning

Reasoning with Diagrammatic Representations

Volume

Reasoning with Diagrammatic Representations

Contents

Hum,ms are capable of giving plausible answers to questions about spatial interactions among objects when provided with a diagrammatic depiction of their spatial configurations and motions. Consider the problem posed in figure 1; try to imagine how you will proceed to solve it. Given this particular type of diagrammatic reasoning, it is instructive to reflect upon what kinds of questions such a reasoning process is capable of answering. It is clearly impossible, by merely looking at figure 1 without additional metric information or paper-and-pencil calculations, to calculate the velocity at which the block will move after a predicted collision. On the other hand, we are indeed adept at making qualitative predictions typified by the following verbal report fragment: "Well, the rod is going to hit the block, that will make it (the block) slide to the right, and, oh, it will hit that wall; then everything will stop." All predictions stated above involve the explicit indication of particular object configurations (e.g., rod hitting block) at which the evolution of the configuration is about to undergo a change. Each prediction also includes directional specification of this predicted change (e.g., the commencement of rightward motion of block). Thus it seems that questions about configurations of objects that induce qualitative changes in their spatial behaviors, and questions about directional aspects of such changes can in principle be answered by using a diagrammatic representation. Here we describe the first version of a computational methodology that is being developed for automating such qualitative diagrammatic reasoning about spatial behaviors of objects. This methodology is inspired by human performance in diagrammatic reasoning tasks. The goal is to emulate the functional characteristics of this particular human capability.