Most Specific Generalizations w.r.t. General EL-TBoxes

In the area of Description Logics the least common subsumer (lcs) and the most specific concept (msc) are inferences that generalize a set of concepts or an individual, respectively, into a single concept. If computed w.r.t. a general EL-TBox neither the lcs nor the msc need to exist. So far in this setting no exact conditions for the existence of lcs-or msc-concepts are known. This paper provides necessary and sufficient conditions for the existence of these two kinds of concepts. For the lcs of a fixed number of concepts and the msc we show decidability of the existence in PTime and polynomial bounds on the maximal role-depth of the lcs-and msc-concepts. This bound allows to compute the lcs and the msc, respectively.

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