A New n-Ary Existential Quantifier in Description Logics

Abstract

Motivated by a chemical process engineering application, we introduce a new concept constructor in Description Logics (DLs), an n-ary variant of the existential restriction constructor, which generalizes both the usual existential restrictions and so-called qualified number restrictions. We show that the new constructor can be expressed in $\mathcal{ALCQ}$, the extension of the basic DL $\mathcal{ALC}$ by qualified number restrictions. However, this representation results in an exponential blow-up. By giving direct algorithms for $\mathcal{ALC}$ extended with the new constructor, we can show that the complexity of reasoning in this new DL is actually not harder than the one of reasoning in $\mathcal{ALCQ}$. Moreover, in our chemical process engineering application, a restricted DL that provides only the new constructor together with conjunction, and satisfies an additional restriction on the occurrence of roles names, is sufficient. For this DL, the subsumption problem is polynomial.