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Reasoning in the Description Logic EL Extended with an n-ary Existential Quantifier

Motivated by a chemical process engineering application, we introduce a new concept constructor, namely an n-ary variant of the existential restriction, into the Description Logic (DL) EL. We refer to the resulting logic as EL (n) and to its fragment that matches the needs of the real world application as restricted EL (n). Although the new constructor can be expressed in the DL ALCQ, its translation is exponential and introduces many expensive constructors, thus making the translation-based reasoning impractical. In the present work, we design direct algorithms for deciding the main inference problem, namely subsumption, in restricted EL (n). We show that reasoning in restricted EL (n) is polynomial when we allow for acyclic TBoxes. Additionally, we examine the complexity of reasoning in (unrestricted) EL (n) with general TBoxes. In particular, we show that subsumption in EL (n) with GCIs is ExpTime-complete. In order to test the practical efficiency of our approach, we implement the polynomial algorithm for restricted EL (n) with acyclic TBoxes in a system called Eln. Comparison between Eln and the state-of-the-art DL reasoner Racer demonstrates a considerable advantage of the direct algorithm over the translation-based approach.