The objective of this thesis is the design of a spatial theory for GIS (consisting of representation, meta data, and transformations) that allows complete integration of data sets that differ in resolution and format. The scope is limited to a discrete view of geographic reality similar to "area-class maps", "categorical coverages", and "nominal fields". The spatial theory consists of representations of resolution-limited spatial knowledge, meta data that describe the knowledge content of representations, and transformations between representations of different type, resolution, format (raster or vector).

The spatial theory addresses the following problems: (1) What limitations does limited resolution impose on spatial knowledge that is represented in GIS? (2) How can such resolution-limited knowledge be represented in a way that keeps precise track of the contained spatial knowledge and its limitations? (3) How can the same spatial knowledge be represented in different formats such as raster and vector? (4) How can spatial knowledge be transformed to other representation types, levels of resolution, and formats? The viability of the proposed spatial theory is shown by demonstrating the implementability of representations and transformations. The practical applicability of the proposed resolution concept is shown by relating it to the resolution of sensors and by showing that resolution-limited representations can always be visualized within the limitations of display media.