  This thesis studies the model theoretic properties of the Description Logics
(DLs) ALC, ALCI, ALCQ, as well as ALCO, ALCQO, ALCQIO and EL.
  TBoxes of ALC, ALCI and ALCQ are characterised as fragments of FO which are
invariant under global bisimulation and disjoint unions. The logics ALCO, ALCQO
and ALCQIO, which incorporate individuals, are characterised w.r.t. to the
class K of all interpretations which interpret individuals as singleton sets.
The characterisations for TBoxes of ALCO and ALCQO both require additionally
that an FO-sentence is, under certain circumstances, preserved under forward
generated subinterpretations. FO-sentences equivalent to ALCQIO-TBoxes, are -
due to ALCQIO's inverse roles - characterised similarly but are required to be
preserved under generated subinterpretations.
  EL as sub-boolean DL is characterised on concept level as the FO-fragment
which is preserved under simulation and preserved under direct products.
Equally valid is the characterisation by being preserved under simulation and
having minimal models. For EL-TBoxes, a global version of simulation was not
sufficient but FO-sentences of EL-TBoxes are invariant under global
equi-simulation, disjoint unions and direct products.
  For each of these description logics, the characteristic concepts are
explicated and the characterisation is accompanied by an investigation under
which notion of saturation the logic in hand enjoys the
Hennessy-and-Milner-Property.
  As application of the results we determine the minimal globally bisimilar
companion w.r.t. ALCQO-bisimulation and introduce the L1-to-L2-rewritability
problem for TBoxes, where L1 and L2 are (description) logics. The latter is the
problem to decide whether or not an L1-TBox can be equivalently expressed as
L2-TBox. We give algorithms which decide ALCI-to-ALC-rewritability and
ALC-to-EL-rewritability. (See also abstract in the thesis.)
