We consider the notion of reification as adopted in standard conceptual modelling languages and provide a logical formalisation using description logics. To this purpose, we use the description logic DLR⁺, an extension of the n-ary propositionally closed description logic DLR to deal with attribute-labelled tuples (generalising the positional notation), projections of relations, and objectification/reification of relations. This paper conducts a general investigation on the expressive power required on description logics to capture the different constructs used in conceptual models with a particular emphasis on relation reification.