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

Non-Rigid Designators in Epistemic and Temporal Free Description Logics (Extended Version)