Representation and processing of knowledge about distances in environmental spaces - a computational model of inferred route distances investigating their qualitative and quantitative determinants

To solve tasks concerning distances along a route, between locations which cannot be perceived from a single vantage point, people and other cognitive agents must generate inferred route distances. Inferred route distances, and inferred distances in general, are a special kind of subjective distances: Inferred distances cannot be retrieved from memory, but have to be inferred from several pieces of knowledge about distances which each have been perceived from a single vantage point. What is the information content of inferred route distances, and how are they inferred? In this context, an important question is in what sense they, like other central concepts of spatial cognition, are qualitative, and in what sense they are quantitative. To answer these questions, the present study relates di erent theories of subjective distances to one another, and it develops a computational model of inferred route distances. It thereby aims to integrate research from arti cial intelligence, in particular Qualitative Spatial Reasoning, and cognitive psychology. Theories of distance cognition in these scienti c elds seem to deal with incomparable subject matters. It is shown in this study, however, that psychophysical descriptions of subjective distances as power functions of objective distances and the modelling of Qualitative Distances in arti cial intelligence can be related to one another from a representationtheoretic perspective. Both theories claim that subjective distances represent an aspect of objective distances|the di erence is which aspect, ratio or order relations. However, aspects of objective distances alone can neither incorporate the in uence of environmental features, hierarchies, and order of estimation on subjective distances, nor can they explain memory structures or processes involved in distance cognition. A computational model of knowledge about distances, and of the subjective distances generated from this knowledge, is described, which integrates these considerations. The model explains existing empirical data, and it generates further predictions. It describes distance estimates as produced by two representations, in which subjective distances and other subjective spatial relations represent objective distances and other objective spatial relations. Which aspects of objective distances are represented depends on whether the corresponding subjective distances are retrieved or inferred. Subjective distances have quantitative and qualitative determinants. Quantitativeness is characterised by stored distances, the pieces of knowledge inferred distances are computed from, described as power functions of objective distances. Retrieved distances are also described in this way. Qualitativeness is characterised by inferred route distances being constructed from a representation determined by qualitative relations of succession and containment. Another form of qualitativeness is also explored: Subjective distances based on stored distances which are metrical prototypes of the qualitative relation `immediate-succession'.