HornDL: An Expressive Horn Description Logic with PTime Data Complexity

Abstract

We introduce a Horn description logic called Horn-DL, which is strictly and essentially richer than Horn-$\mathcal{SROIQ}$, while still has PTime data complexity. In comparison with Horn-$\mathcal{SROIQ}$, HornDL additionally allows the universal role and assertions of the form irreflexive (s), $\lnot s(a,b)$, $a \not\doteq b$. More importantly, in contrast to all the well-known Horn fragments $\mathcal{EL}$, DL-Lite, DLP, Horn-$\mathcal{SHIQ}$, Horn-$\mathcal{SROIQ}$ of description logics, HornDL allows a form of the concept constructor “universal restriction” to appear at the left hand side of terminological inclusion axioms. Namely, a universal restriction can be used in such places in conjunction with the corresponding existential restriction. In the long version of this paper, we present the first algorithm with PTime data complexity for checking satisfiability of HornDL knowledge bases.