Efficient TBox Reasoning with Value Restrictions—Introducing the $\mathcal {F\!L}_{o}{} \textit{wer}$ Reasoner

Abstract

The Description Logic (DL) ${\mathcal {F\!L}_0}$ uses universal quantification, whereas its well-known counter-part $\mathcal {E\!L}$ uses the existential one. While for $\mathcal {E\!L}$ deciding subsumption in the presence of general TBoxes is tractable, this is no the case for ${\mathcal {F\!L}_0}$. We present a novel algorithm for solving the ExpTime-hard subsumption problem in ${\mathcal {F\!L}_0}$ w.r.t. general TBoxes, which is based on the computation of so-called least functional models. To build a such a model our algorithm treats TBox axioms as rules that are applied to objects of the interpretation domain. This algorithm is implemented in the $\mathcal {F\!L}_{o}{} \textit{wer}$ reasoner, which uses a variant of the Rete pattern matching algorithm to find applicable rules. We present an evaluation of $\mathcal {F\!L}_{o}{} \textit{wer}$ on a large set of TBoxes generated from real world ontologies. The experimental results indicate that our prototype implementation of the specialised technique for ${\mathcal {F\!L}_0}$ leads in most cases to a huge performance gain in comparison to the highly-optimised tableau reasoners.