On the Problem of Computing Small Representations of Least Common Subsumers

Authors:
Franz Baader;Anni-Yasmin Turhan
Affiliations:
-;-
Venue:
KI '02 Proceedings of the 25th Annual German Conference on AI: Advances in Artificial Intelligence
Year:
2002

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Abstract

For Description Logics with existential restrictions, the size ofthe least common subsumer (lcs) of concept descriptions may grow exponentially in the size of the input descriptions. The first (negative) result presented in this paper is that it is in general not possible to express the exponentially large concept description representing the lcs in a more compact way by using an appropriate (acyclic) terminology. In practice, a second and often more severe cause of complexity was the fact that concept descriptions containing concepts defined in a terminology must first be unfolded (by replacing defined names by their definition) before the known lcs algorithms could be applied. To overcome this problem, we present a modified lcs algorithm that performs lazy unfolding, and show that this algorithm works well in practice.