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

We introduce a Horn description logic called Horn-DL, which is strictly and essentially richer than Horn‐RegHorn‐RegI, Horn‐SHIQHorn‐SHIQ and Horn‐SROIQHorn‐SROIQ, while still has PTime data complexity. In comparison with Horn‐SROIQHorn‐SROIQ, Horn-DL additionally allows the universal role and assertions of the form irreflexive(s)irreflexives, ¬s(a, b  ), a≠˙b. More importantly, in contrast to all the well-known Horn fragments ELEL, DL-Lite, DLP, Horn‐SHIQHorn‐SHIQ, and Horn‐SROIQHorn‐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.