  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 groups of geometric transformations that preserve
certain characteristics of spatio-temporal data (e.g., collinearity, distance,
velocity, acceleration, ...). These groups depend on the notions that are
relevant in particular spatio-temporal database applications.
  These transformations also have the distinctive property that they respect
the monotone and unidirectional nature of time.
  We investigate different genericity classes with respect to the constraint
database model for spatio-temporal databases and we identify sound and complete
languages for the first-order and the computable queries in these genericity
classes. We distinguish between genericity determined by time-invariant
transformations, genericity notions concerning physical quantities and
genericity determined by time-dependent transformations.
