A horn fragment with ptime data complexity of regular description logic with inverse

We study a Horn fragment called Horn-RegI of the regular description logic with inverse RegI , which extends the description logic ALC with inverse roles and regular role inclusion axioms characterized by finite automata. In contrast to the well-known Horn fragments EL, DL-Lite, DLP, Horn-SHIQ and Horn-SROIQ of description logics, Horn-RegI allows a form of the concept constructor “universal restriction” to appear at the left hand side of terminological inclusion axioms, while still has PTime data complexity.