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Matching in Description Logics with Existential Restrictions

F. Baader and R. Küsters

Matching of concepts against patterns is a new inference task in Description Logics, which was originally motivated by applications of the CLASSIC system. Consequently, the work on this problem was until now mostly concerned with sublanguages of the CLASSIC language, which does not allow for existential restrictions. This paper extends the existing work on matching in two directions. On the one hand, the question of what are the most ``interesting" solutions of matching problems is explored in more detail. On the other hand, for languages with existential restrictions both, the complexity of deciding the solvability of matching problems and the complexity of actually computing sets of ``interesting" matchers are determined. The results show that existential restrictions make these computational tasks more complex. Whereas for sublanguages of CLASSIC both problems could be solved in polynomial time, this is no longer possible for languages with existential restrictions.