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Ontology-Mediated Query Answering with Data-Tractable Description Logics

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Book cover Reasoning Web. Web Logic Rules (Reasoning Web 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9203))

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Abstract

Recent years have seen an increasing interest in ontology-mediated query answering, in which the semantic knowledge provided by an ontology is exploited when querying data. Adding an ontology has several advantages (e.g. simplifying query formulation, integrating data from different sources, providing more complete answers to queries), but it also makes the query answering task more difficult. In this chapter, we give a brief introduction to ontology-mediated query answering using description logic (DL) ontologies. Our focus will be on DLs for which query answering scales polynomially in the size of the data, as these are best suited for applications requiring large amounts of data. We will describe the challenges that arise when evaluating different natural types of queries in the presence of such ontologies, and we will present algorithmic solutions based upon two key concepts, namely, query rewriting and saturation. We conclude the chapter with an overview of recent results and active areas of ongoing research.

This work has been supported by ANR project PAGODA (ANR-12-JS02-007-01) and the Austrian Science Fund (FWF) project T515.

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Notes

  1. 1.

    The order of the letters is irrelevant, although some orderings are more frequent in the literature than others, e.g., \(\mathcal {SHIQ}\), vs. \(\mathcal {SHQI}\). We also point out that some DLs impose additional restrictions, for example, restricting the interaction of number restrictions and transitive roles in \(\mathcal {SHIQ}\) and \(\mathcal {SHOIQ}\).

  2. 2.

    http://www.ihtsdo.org/snomed-ct.

  3. 3.

    \(\mathcal {SHIQ}\) does not support negative role inclusions. These could be added at no computational cost, and they are expressible in extensions of \(\mathcal {SHIQ}\) for which reasoning has the same complexity, like \(\mathcal {ZIQ}\) [57] and the simple fragment of \(\mathcal {SRIQ}\) [109].

  4. 4.

    Note that for simplicity, and to facilitate the comparison with \(\mathcal {I} _D\), the interpretation \(\mathcal {J} \) interprets individuals as themselves. However, we could instead have chosen domain elements distinct from the individual names.

  5. 5.

    More precisely, Datalog rules correspond to function-free Horn clauses.

  6. 6.

    The certain answer semantics is also used in other contexts, such as incomplete databases [112], data integration [142], and data exchange [6].

  7. 7.

    We recall that a decision problem (alternatively known as a recognition problem) is a problem with a yes-or-no answer.

  8. 8.

    We typically omit \(|{{\varvec{a}}}|\) since we have \(|{{\varvec{a}}}| \le |q| \cdot |\mathcal {A} |\) (or \(|{{\varvec{a}}}| \le |q| \cdot |\mathcal {D} |\)).

  9. 9.

    In this section, it will prove convenient to allow ABox assertions using the atomic concepts \(\top \) and \(\bot \), in addition to concept names. Refer to Sect. 2 for discussion.

  10. 10.

    Recall that we treat conjunctions of concepts as sets. Abusing notation, we use \(A \in M\) to mean that A is a conjunct of M.

  11. 11.

    If desired, we could use standard equivalence-preserving transformations to turn \(q_{ rew }\) into an equivalent UCQ.

  12. 12.

    A predicate is called recursive if it occurs in a cycle in the dependency graph of the Datalog program, whose nodes are the program’s predicates and which contains an edge between two predicates whenever there is a rule that contains one of the predicates in the body and the other in the head.

  13. 13.

    As earlier, we treat conjunctions of concepts as sets, ignoring order and repetitions.

  14. 14.

    We note that for \({\mathcal {ELH}} \) and DL-Lite\(_{\mathcal {R}}\), the construction is simpler as we only need to store concept names, rather than conjunctions of concept names.

  15. 15.

    The query languages considered in [132, 203] also allow unary tests to be combined using conjunctive and disjunction. A similar construct was considered in [31].

  16. 16.

    http://optique-project.eu/.

  17. 17.

    http://www.roman-ep.net.

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Authors and Affiliations

  1. LRI - CNRS and Université Paris Sud, Orsay, France

    Meghyn Bienvenu

  2. Institute of Information Systems, Vienna University of Technology, Vienna, Austria

    Magdalena Ortiz

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  1. Meghyn Bienvenu
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  2. Magdalena Ortiz
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Correspondence to Meghyn Bienvenu or Magdalena Ortiz .

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  1. University of Huddersfield, Huddersfield, United Kingdom

    Wolfgang Faber

  2. FU Berlin Institut für Informatik, Berlin, Germany

    Adrian Paschke

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Bienvenu, M., Ortiz, M. (2015). Ontology-Mediated Query Answering with Data-Tractable Description Logics. In: Faber, W., Paschke, A. (eds) Reasoning Web. Web Logic Rules. Reasoning Web 2015. Lecture Notes in Computer Science(), vol 9203. Springer, Cham. https://doi.org/10.1007/978-3-319-21768-0_9

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