Effects of Logical Form and Geometrical Content on Spatial Deductive Reasoning

摘要

In air navigation, pilots must mentally represent the relative position ofaircraft in a three dimensions. They must also deduce from their mental representation the relative position of other aircraft which has not been explicitly specified in any of the information that they have received. Spatial deductive reasoning is critical for both the pilot's safety and the accomplishment of his mission. It is a difficult aspect of formal logic which is particular prone to errors especially under intense mental workload. Despite the importance of spatial deductive reasoning, the processes that underlie this logical activity are still unclear as scientists have proposed opponent theorie of formal logic to account for these processes. The overall goal of this study is to investigate the effects of logical form and geometrical content on spatial deductive reasoning by comparing two opponent theories of deductive reasoning: Hagert's Formal Rules theory and Johnson-Laird's Mental Models theory. Our second goal is to specify, through the effects of geometrical content, how humans structure their mental representation of geometrical relations, and if they do so relative to spatial reference frames. We will address this issue in view of the Content-Specific Rules theory and the Spatial Reference Frame theory. Twenty-six subjects solved 144 spatial deductive problems which differed by their logical form and geometrical content. We addressed the effects of logical form by varying the continuity and the determinacy of the entities' order in the arguments. The logical form of the arguments allowed comparison of pairs of problems having either: (a) formal derivations of equal length but different numbers of mental models, and (b) formal derivations of different lengths but equal numbers of mental models.