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Guarded Ontology-Mediated Queries

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Hajnal Andréka and István Németi on Unity of Science

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 19))

Abstract

We concentrate on ontology-mediated queries (OMQs) expressed using guarded Datalog\(^\exists \) and conjunctive queries. Guarded Datalog\(^\exists \) is a rule-based knowledge representation formalism inspired by the guarded fragment of first-order logic, while conjunctive queries represent a prominent database query language that lies at the core of relational calculus (i.e., first-order queries). For such guarded OMQs we discuss three main algorithmic tasks: query evaluation, query containment, and first-order rewritability. The first one is the task of computing the answer to an OMQ over an input database. The second one is the task of checking whether the answer to an OMQ is contained in the answer of some other OMQ on every input database. The third one asks whether an OMQ can be equivalently rewritten as a first-order query. For query evaluation, we explain how classical results on the satisfiability problem for the guarded fragment of first-order logic can be applied. For query containment, we discuss how tree automata techniques can be used. Finally, for first-order rewritability, we explain how techniques based on a more sophisticated automata model, known as cost automata, can be exploited.

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Notes

  1. 1.

    For technical clarity, we assume that CQs do not mention constants from \(\mathbf {C}\). However, all the results that we discuss can be extended to CQs with constants.

  2. 2.

    For brevity, in the rest of the chapter we adopt the acronym TGD instead of the term Datalog\(^\exists \).

  3. 3.

    Here, we see models as sets of atoms, i.e., as instances.

  4. 4.

    Recall that \(\mathsf {F}\) denotes the class of full TGDs, i.e., TGDs without existentially quantified variables.

  5. 5.

    This result from [11] initially relied on an unpublished result. Such a result has been now published in [21].

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Author information

Authors and Affiliations

  1. Institute for Mathematical and Computational Engineering, Pontificia Universidad Católica de Chile & IMFD Chile, Santiago, Chile

    Pablo Barceló

  2. Institute of Logic and Computation, TU Wien, Vienna, Austria

    Gerald Berger & Georg Gottlob

  3. Department of Computer Science, University of Oxford, Oxford, UK

    Georg Gottlob

  4. School of Informatics, University of Edinburgh, Edinburgh, UK

    Andreas Pieris

Authors
  1. Pablo Barceló
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  2. Gerald Berger
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  3. Georg Gottlob
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  4. Andreas Pieris
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Correspondence to Andreas Pieris .

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Editors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Judit Madarász

  2. Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Gergely Székely

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Barceló, P., Berger, G., Gottlob, G., Pieris, A. (2021). Guarded Ontology-Mediated Queries. In: Madarász, J., Székely, G. (eds) Hajnal Andréka and István Németi on Unity of Science. Outstanding Contributions to Logic, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-030-64187-0_2

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