A Decidable Very Expressive Description Logic for Databases (Extended Version)
This work addresses the need for more expressive and decidable description logics in database modeling, particularly for conceptual data models like EER, UML, and ORM, but it is incremental as it builds on existing $\mathcal{DLR}$ logic.
The authors tackled the problem of extending description logics to better model databases by introducing $\mathcal{DLR}^+$, which adds features like attribute-labelled tuples and projections to express dependencies, and they showed that a restricted version $\mathcal{DLR}^\pm$ maintains decidability with the same computational complexity as the base logic.
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.