A Decidable Very Expressive Description Logic for Databases (Extended Version)

TL;DR

This paper introduces $ ext{DLR}^+$, a highly expressive description logic extension that can model complex database constraints and conceptual data models while maintaining decidable reasoning.

Contribution

It extends $ ext{DLR}$ with features for attribute-labelled tuples, projections, and objectification, ensuring decidability with a simple syntactic restriction.

Findings

Decidability is preserved under certain restrictions.

The logic can encode EER, UML, ORM models.

Reasoning complexity remains the same as $ ext{DLR}$.

Abstract

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.