Temporal and Spatio-Temporal Data Models and Their Expressive Power

Currently, there are strong efforts to integrate spatial and temporal database technology into spatio-temporal database systems. This paper views the topic from a more fundamental perspective and makes several contributions. First, it reviews existing temporal and spatial data models and presents a completely new approach to temporal data modeling based on the very general notion of temporal objects. The definition of temporal objects is centered around the observation that anything that changes over time can be expressed as a function over time. For the modeling of spatial objects the well known concept of spatial data types is employed. As specific subclasses, linear temporal and spatial objects are identified. Second, the paper proposes the database embedding of temporal objects by means of the abstract data type (ADT) approach to the integration of complex objects into databases. In spatial database technology, spatial data types have already been successfully integrated as ADTs for attributes in relational schemas for a while now. Furthermore, we make statements about the expressive power of different temporal and spatial database embeddings. Third, we consider the combination of temporal and spatial objects into spatio-temporal objects in (relational) databases. We explain various alternatives for spatio-temporal data models and databases and compare their expressive power. Spatio-temporal objects turn out to be specific instances of temporal objects.