Abstract. Although maps and partitions are ubiquitous in geographical information systems and spatial databases, there is only little work investigating their foundations. We give a rigorous definition for spatial partitions and propose partitions as a generic spatial data type that can be used to model arbitrary maps and to support spatial analysis. We identify a set of three powerful operations on partitions and show that the type of partitions is closed under them. These basic operators are sufficient to express all known application-specific operations. Moreover, many map operations will be considerably generalized in our framework. We also indicate that partitions can be effectively used as a meta-model to describe other spatial data types. 1

Maps are a fundamental metaphor in GIS. We introduce several new operations on maps that go far beyond well-known operations like overlay or reclassification. In particular, we identify and generalize operations that are of practical interest for spatial analysis and that can be useful in many GIS applications. We give a precise definition of these operations based on a formal model of spatial partitions. This provides a theoretical foundation for maps which also serves as a specification for implementations.