Towards richer rule languages with polynomial data complexity for the Semantic Web

Abstract

We introduce a Horn description logic called Horn-DL, which is strictly and essentially richer than Horn‐RegI, Horn‐SHIQ and Horn‐SROIQ, while still has PTime data complexity. In comparison with Horn‐SROIQ, Horn-DL additionally allows the universal role and assertions of the form irreflexives, ¬s(a, b), a≠˙b. More importantly, in contrast to all the well-known Horn fragments EL, DL-Lite, DLP, Horn‐SHIQ, and Horn‐SROIQ of description logics, Horn-DL 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. We develop the first algorithm with PTime data complexity for checking satisfiability of Horn-DL knowledge bases.