Qualitative distance and direction reasoning in geographic space

This thesis is inspired by the need to build a reasoning mechanism that deals with qualitative distances and directions, such as the approximate distances and the cardinal directions (e.g., near, North). Spatial reasoning has been recognized as an important capability for the knowledge-based Geographic Information Systems (GISs). While humans do it constantly in our lives, the formalization of such reasoning behavior in computers is still incomplete. Although a number of researchers have built computational models that deal with the reasoning about spatial relations in geographic space, only few have investigated the combination of distances and directions. The major obstacle for the qualitative distance and direction reasoning is that qualitative distances are context-dependent, therefore, the composition operator of such locational relations may depend on the geometric definitions of qualitative distances. This thesis builds models for qualitative distances and directions with two criteria: complete coverage and mutual exclusiveness. These models serve as the basis for the design of reasoning model, whose basic methods are (1) the transformation between qualitative and quantitative locational relations and (2) the well-developed quantitative reasoning methods. Qualitative composition can then be defined via the simulation of quantitative locational relations. Three reasoning models--the all-answer model, the likely-answer model, and the single-answer model--are introduced to assess the qualitative compositions. To evaluate the reasoning models, data based on (1) the number of qualitative distances, (2) the number of qualitative directions, and (3) the geometric patterns of distance intervals are simulated and tested. The results indicate that the compositions of qualitative distances and directions are primarily robust and only few compositions are affected by the interval patterns of qualitative distances. It is hence possible to build a reasoning mechanism based on inference rules instead of analytical calculations. The assessments of compositions show that careful selections of answers for each composition can increase the efficiency of reasoning while maintaining a satisfactory approximation. It is also found that the proposed reasoning models can provide reasonable guesses for the requested relations.