  We introduce $\mathcal{DLR}^+$, an extension of the n-ary propositionally
closed description logic $\mathcal{DLR}$ to deal with attribute-labelled tuples
(generalising the positional notation), projections of relations, and global
and local objectification of relations, able to express inclusion, functional,
key, and external uniqueness dependencies. The logic is equipped with both TBox
and ABox axioms. We show how a simple syntactic restriction on the appearance
of projections sharing common attributes in a $\mathcal{DLR}^+$ knowledge base
makes reasoning in the language decidable with the same computational
complexity as $\mathcal{DLR}$. The obtained $\mathcal{DLR}^\pm$ n-ary
description logic is able to encode more thoroughly conceptual data models such
as EER, UML, and ORM.
