On the design of formal theories of geographic space

This paper discusses the design of formal theories of geographic space for the application in Geographic Information Systems. GIS software is an implementation of formal theories of geographic space. The notions of formal theories are introduced and discussed in the context of examples from the GIS field. Our approach is an application of the general framework of formal theories to the special class of theories of geographic space, in particular to the geometry of geographic space. A framework is introduced for characterizing and evaluating formal theories of geographic space and the process of their design. This is used to provide (1) a classification of formal theories of geographic space, (2) criteria of their adequacy, and (3) an evaluation of design decisions in the process of formalization. The paper demonstrates the choices in the design of GIS and the dependencies between these choices. Considering the design space for theories underlying a GIS, we can see that current GIS are based on one choice: analytical geometry. Other designs are possible and a systematic exploration of alternative types of GIS, for example, based on constraints or based on stored spatial relations, becomes necessary.