Terminological reasoning is inherently intractable (research note)
Artificial Intelligence
Attributive concept descriptions with complements
Artificial Intelligence
The complexity of existential quantification in concept languages
Artificial Intelligence
Computing Least Common Subsumers in Description Logics with Existential Restrictions
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
On the Problem of Computing Small Representations of Least Common Subsumers
KI '02 Proceedings of the 25th Annual German Conference on AI: Advances in Artificial Intelligence
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Computing least common subsumers in ALEN
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
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This paper introduces a compact representation which helps to avoid the exponential blow-up in space of the Least Common Subsumer (lcs) of two ALE-concept descriptions. Based on the compact representation we define a space of specific graphs which represents all ALE-concept descriptions including the lcs. Next, we propose an algorithm exponential in time and polynomial in space for deciding subsumption between concept descriptions represented by graphs in this space. These results provide better understanding of the double exponential blow-up of the approximation of ALC-concept descriptions by ALE-concept descriptions: double exponential size of the approximation in the ordinary representation is unavoidable in the worst case.