The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics

@article{Tobies2000TheCO,
  title={The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics},
  author={Stephan Tobies},
  journal={J. Artif. Intell. Res.},
  year={2000},
  volume={12},
  pages={199-217}
}
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, the two variable fragment of predicate logic with counting quanti ers, 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 (NExpTime-complete). In contrast, we… CONTINUE READING
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