Formal Properties of Cognitive Distance in Geographical Space

In geographic space, spatial behaviors of humans are driven directly by their spatial cognition, and indirectly by the physical or geometrical reality. The recognition of cognitive distance is fundamental in human intelligent computation, particularly in commonsense knowledge engineering. The cognitive distance is dialectically used for measuring the similarities between cognized geographic objects. Traditionally, physical or Euclidean distances are used very often. However, many inconsistencies between cognitive distance and physical distance are practically found. As a matter of a fact, the physical distance is mostly overestimated or underestimated in the process of human spatial cognition and spatial behaviors. This paper is intended to illustrate the cognitive distance and its distortions in a conceptual and computational way. Some innovative arguments are made. That is, the cognitive distance could be two-dimensional, exist in heterogeneous space, and hold the property of quasi-metric. Alternatively, the cognitive distance could be multi-dimensional, exist in homogeneous space, and hold the property of metric. Distance distortions arise from the transformations of homogeneous into heterogeneous spaces and two-dimensional into multi-dimensional distances