  Definite descriptions, such as 'the smallest planet in the Solar System',
have been recently recognised as semantically transparent devices for object
identification in knowledge representation formalisms. Along with individual
names, they have been introduced also in the context of description logic
languages, enriching the expressivity of standard nominal constructors.
Moreover, in the first-order modal logic literature, definite descriptions have
been widely investigated for their non-rigid behaviour, which allows them to
denote different objects at different states. In this direction, we introduce
epistemic and temporal extensions of standard description logics, with nominals
and the universal role, additionally equipped with definite descriptions
constructors. Regarding names and descriptions, in these languages we allow
for: possible lack of denotation, ensured by partial models, coming from free
logic semantics as a generalisation of the classical ones; and non-rigid
designation features, obtained by assigning to terms distinct values across
states, as opposed to the standard rigidity condition on individual
expressions. In the absence of the rigid designator assumption, we show that
the satisfiability problem for epistemic free description logics is
NExpTime-complete, while satisfiability for temporal free description logics
over linear time structures is undecidable.
