The Object Role Modelling language (ORM2) is a conceptual modelling language similar to UML and ER, adopted by Visual Studio, the integrated development environment from Microsoft. This paper introduces a new linear syntax and complete set-theoretic semantics for a generalisation of ORM2, which can be shown correctly embedding the original proposal. A provably correct encoding of the core fragment of ORM2 (similarly expressive to UML class diagrams) in the ALCQI description logic is presented. On the basis of these results, a systematic critique of alternative approaches to the formalisation of ORM2 in (description) logics published so far is provided. A prototype has been implemented providing a backend for the automated support of consistency and entailment checks for ORM2 conceptual schemas along with its translation into ALCQI knowledge bases.