  We design temporal description logics suitable for reasoning about temporal
conceptual data models and investigate their computational complexity. Our
formalisms are based on DL-Lite logics with three types of concept inclusions
(ranging from atomic concept inclusions and disjointness to the full Booleans),
as well as cardinality constraints and role inclusions. In the temporal
dimension, they capture future and past temporal operators on concepts,
flexible and rigid roles, the operators `always' and `some time' on roles, data
assertions for particular moments of time and global concept inclusions. The
logics are interpreted over the Cartesian products of object domains and the
flow of time (Z,<), satisfying the constant domain assumption. We prove that
the most expressive of our temporal description logics (which can capture
lifespan cardinalities and either qualitative or quantitative evolution
constraints) turn out to be undecidable. However, by omitting some of the
temporal operators on concepts/roles or by restricting the form of concept
inclusions we obtain logics whose complexity ranges between PSpace and
NLogSpace. These positive results were obtained by reduction to various clausal
fragments of propositional temporal logic, which opens a way to employ
propositional or first-order temporal provers for reasoning about temporal data
models.
