On Horn Knowledge Bases in Regular Description Logic with Inverse

Abstract

We study a Horn fragment called Horn-\(\mathcal{R}eg^I\) of the regular description logic with inverse \(\mathcal{R}eg^I\), which extends the description logic \(\mathcal{ALC}\) with inverse roles and regular role inclusion axioms characterized by finite automata. In contrast to the well-known Horn fragments \(\mathcal{EL}\), DL-Lite, DLP, Horn-\(\mathcal{SHIQ}\) and Horn-\(\mathcal{SROIQ}\) of description logics, Horn-\(\mathcal{R}eg^I\) 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-\(\mathcal{R}eg^I\) knowledge bases.KeywordsKnowledge BaseDescription LogicEdge BaseConcept ConstructorUniversal RestrictionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.