A theory of spatio-temporal database queries

We address a fundamental question concerning spatio-temporal database systems: "What are exactly spatio-temporal queries?" We define spatio-temporal queries to be computable mappings that are also generic, meaning that the result of a query may only depend to a limited extent on the actual internal representation of the spatio-temporal data. Genericity is defined as invariance under transformations that preserve certain characteristics of spatio-temporal data (e.g., collinearity, distance, velocity, acceleration,...) that are relevant to a database user. These transformations also respect the monotone nature of time. We investigate different genericity classes relative to the constraint database model for spatio-temporal databases and we identify sound and complete languages for the first-order, respectively the computable, queries in these genericity classes.