A Horn Fragment with PTime Data Complexity of Regular Description Logic with Inverse

Abstract

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. Namely, a universal restriction can be used in such places in conjunction with the corresponding existential restriction. We provide an algorithm with PTIME data complexity for checking satisfiability of Horn-RegI knowledge bases.