Abstract
We analyze the complexity of finite model reasoning in the description logic \(\mathcal{ALC QI}\), i.e. \(\mathcal{ALC}\) augmented with qualifying number restrictions, inverse roles, and general TBoxes. It turns out that all relevant reasoning tasks such as concept satisfiability and ABox consistency are ExpTime-complete, regardless of whether the numbers in number restrictions are coded unarily or binarily. Thus, finite model reasoning with \(\mathcal{ALC QI}\) is not harder than standard reasoning with \(\mathcal{ALC QI}\).
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Lutz, C., Sattler, U., Tendera, L. (2003). The Complexity of Finite Model Reasoning in Description Logics. In: Baader, F. (eds) Automated Deduction – CADE-19. CADE 2003. Lecture Notes in Computer Science(), vol 2741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45085-6_6
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DOI: https://doi.org/10.1007/978-3-540-45085-6_6
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