Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive DLs whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to re-use concepts defined in such terminologies and still support the definition of new concepts by computing the lcs, we extend the notion of the lcs of concept descriptions to the notion of the lcs w.r.t. a background terminology.

No abstract

a b s t r a c tWe investigate whether the pseudo-intents of a given formal context can efficiently be enumerated. We show that they cannot be enumerated in a specified lexicographic order with polynomial delay unless P = NP. Furthermore we show that if the restriction on the order of enumeration is removed, then the problem becomes at least as hard as enumerating minimal transversals of a given hypergraph. We introduce the notion of minimal pseudo-intents and show that recognizing minimal pseudo-intents is polynomial. Despite their less complicated nature, surprisingly it turns out that minimal pseudo-intents cannot be enumerated in output-polynomial time unless P = NP.

Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive Description Logics (DLs) whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to re-use concepts defined in such terminologies and still support the definition of new concepts by computing the lcs, we extend the notion of the lcs of concept descriptions to the notion of the lcs w.r.t. a background terminology. We will show both theoretical results on the existence of the least common subsumer in this setting, and describe a practical approach-based on a method from formal concept analysis-for computing good common subsumers, which may, however, not be the least ones. We will also describe results obtained in a first evaluation of this practical approach.