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Data Complexity of Query Answering in Expressive Description Logics via Tableaux

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Abstract

The logical foundations of the standard web ontology languages are provided by expressive Description Logics (DLs), such as \(\mathcal{SHIQ}\) and \(\mathcal{SHOIQ}\). In the Semantic Web and other domains, ontologies are increasingly seen also as a mechanism to access and query data repositories. This novel context poses an original combination of challenges that has not been addressed before: (i) sufficient expressive power of the DL to capture common data modelling constructs; (ii) well established and flexible query mechanisms such as those inspired by database technology; (iii) optimisation of inference techniques with respect to data size, which typically dominates the size of ontologies. This calls for investigating data complexity of query answering in expressive DLs. While the complexity of DLs has been studied extensively, few tight characterisations of data complexity were available, and the problem was still open for most DLs of the \(\mathcal{SH}\) family and for standard query languages like conjunctive queries and their extensions. We tackle this issue and prove a tight coNP upper bound for positive existential queries without transitive roles in \(\mathcal{SHOQ{\text{,}}\, SHIQ}\), and \(\mathcal{SHOI}\). We thus establish that, for a whole range of sublogics of \(\mathcal{SHOIQ}\) that contain \(\mathcal{AL}\), answering such queries has coNP-complete data complexity. We obtain our result by a novel tableaux-based algorithm for checking query entailment, which uses a modified blocking condition in the style of Carin. The algorithm is sound for \(\mathcal{SHOIQ}\), and shown to be complete for all considered proper sublogics in the \(\mathcal{SH}\) family.

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Authors and Affiliations

  1. Institute of Information Systems, Vienna University of Technology, Favoritenstraße 9-11, Vienna, Austria

    Magdalena Ortiz & Thomas Eiter

  2. Faculty of Computer Science, Free University of Bozen-Bolzano, Piazza Domenicani 3, Bolzano, Italy

    Diego Calvanese

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  1. Magdalena Ortiz
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  2. Diego Calvanese
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  3. Thomas Eiter
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Correspondence to Magdalena Ortiz.

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This work has been partially supported by FET project TONES (Thinking ONtologiES), funded within the EU 6th Framework Programme under contract FP6-7603, by the PRIN 2006 project NGS (New Generation Search), funded by MIUR, and by the Mexican National Council for Science and Technology (CONACYT).

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Ortiz, M., Calvanese, D. & Eiter, T. Data Complexity of Query Answering in Expressive Description Logics via Tableaux. J Autom Reasoning 41, 61–98 (2008). https://doi.org/10.1007/s10817-008-9102-9

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