The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics (2000)
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| Venue: | Journal of Artificial Intelligence Research |
| Citations: | 45 - 0 self |
BibTeX
@ARTICLE{Tobies00thecomplexity,
author = {Stephan Tobies Tobies},
title = {The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics},
journal = {Journal of Artificial Intelligence Research},
year = {2000},
volume = {12},
pages = {2000}
}
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Abstract
We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts. These combinations can naturally be embedded into C 2 , the two variable fragment of predicate logic with counting quantiers, which yields decidability in NExpTime. We show that this approach leads to an optimal solution for ALCQI , as ALCQI with cardinality restrictions has the same complexity as C 2 (NExpTime-complete). In contrast, we show that for ALCQ, the problem can be solved in ExpTime. This result is obtained by a reduction of reasoning with cardinality restrictions to reasoning with the (in general weaker) terminological formalism of general axioms for ALCQ extended with nominals . Using the same reduction, we show that, for the extension of ALCQI with nominals, reasoning with general axioms is a NExpTime-complete problem. Finally, we sharpen this result and show that pure concept satisability for A...
