Chair for Automata Theory LTCS – Report 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 lcsor msc-concepts are known. This report provides necessary and suffcient 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 roledepth of the lcsand msc-concepts. The latter allows to compute the lcs and the msc, respectively.