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Computing Most Specific Concepts in Description Logics with Existential Restrictions

R. Küsters and R. Molitor

Computing the most specific concept (msc) is an inference task that can be used to support the "bottom-up" construction of knowledge bases for KR systems based on description logics. For description logics that allow for number restrictions or existential restrictions, the msc need not exist, though. Previous work on this problem has concentrated on description logics that allow for universal value restrictions and number restrictions, but not for existential restrictions. The main new contribution of this paper is the treatment of description logics with existential restrictions. More precisely, we show that, for the description logic ALE (which allows for conjunction, universal value restrictions, existential restrictions, negation of atomic concepts, as well as the top and the bottom concept), and its sublanguages EL (which allows for conjunction, existential restrictions and the top-concept) and EL- (which extends EL by negation of atomic concepts) the msc of an ABox-individual only exists in case of acyclic ABoxes. For cyclic ABoxes, we show how to compute an approximation of the msc. Our approach for computing the msc and its approximation, respectively, is based on representing concept descriptions by certain trees and ABoxes by certain graphs, and then characterizing instance relationships by homomorphisms from trees into graphs. The msc/approximation operation then mainly corresponds to unraveling the graphs into trees and translating them back into concept descriptions.