Qualitative representation of positional information

A framework for the qualitative representation of positional information in a two-dimensional space is presented. Qualitative representations use discrete quantity spaces, where a particular distinction is introduced only if it is relevant to the context being modeled. This allows us to build a flexible framework that accommodates various levels of granularity and scales of reasoning. Knowledge about position in large-scale space is commonly represented by a combination of orientation and distance relations, which we express in a particular frame of reference between a primary object and a reference object. While the representation of orientation comes out to be more straightforward, the model for distances requires that qualitative distance symbols be mapped to geometric intervals in order to be compared; this is done by defining structure relations that are able to handle, among others, order of magnitude relations; the frame of reference with its three components (distance system, scale, and type) captures the inherent context dependency of qualitative distances. The principal aim of the qualitative representation is to perform spatial reasoning: as a basic inference technique, algorithms for the composition of positional relations are developed with respect to same and different frames of reference. The model presented in this paper has potential applications in areas as diverse as Geographical Information Systems (GIS), Computer Aided Design (CAD), and Document Recognition.