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A Framework for Comparing Query Languages in Their Ability to Express Boolean Queries

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Foundations of Information and Knowledge Systems (FoIKS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10833))

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Abstract

We identify three basic modalities for expressing boolean queries using the expressions of a query language: nonemptiness, emptiness, and containment. For the class of first-order queries, these three modalities have exactly the same expressive power. For other classes of queries, e.g., expressed in weaker query languages, the modalities may differ in expressiveness. We propose a framework for studying the expressive power of boolean query modalities. Along one dimension, one may work within a fixed query language and compare the three modalities, e.g., we can compare a fixed query language \(\mathcal {F}\) under emptiness to \(\mathcal {F}\) under nonemptiness. Here, we identify crucial query features that enable us to go from one modality to another. Furthermore, we identify semantical properties that reflect the lack of these query features to establish separations. Along a second dimension, one may fix a modality and compare different query languages. This second dimension is the one that has already received quite some attention in the literature, whereas in this paper we emphasize the first dimension. Combining both dimensions, it is interesting to compare the expressive power of a weak query language using a strong modality, against that of a seemingly stronger query language but perhaps using a weaker modality. We present some initial results within this theme. As an important auxiliary result, we establish a preservation theorem for monotone containments of conjunctive queries.

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Notes

  1. 1.

    In this paper, \(e_1 \subseteq e_2\) stands for a boolean query which, in general, may return true on some databases and return false on the other databases. Thus \(e_1 \subseteq e_2\) as considered in this paper should not be misconstrued as an instance of the famous query containment problem [1, 5], where the task would be to verify statically if \(e_1(D)\) is a subset of \(e_2(D)\) on every database D. Indeed, if \(e_1\) is contained in \(e_2\) in this latter sense, then the boolean query \(e_1 \subseteq e_2\) is trivial as it returns true on every database.

  2. 2.

    Some of our results can be refined to fragments containing just one of the two projections or coprojections, but for others this remains a technical open problem [21].

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Authors and Affiliations

  1. Hasselt University, Hasselt, Belgium

    Dimitri Surinx & Jan Van den Bussche

  2. Indiana University, Bloomington, IN, USA

    Dirk Van Gucht

Authors
  1. Dimitri Surinx
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  2. Jan Van den Bussche
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  3. Dirk Van Gucht
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Correspondence to Dimitri Surinx .

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Editors and Affiliations

  1. Software Competence Center Hagenberg, Hagenberg im Mühlkreis, Austria

    Flavio Ferrarotti

  2. Vienna University of Technology, Vienna, Austria

    Stefan Woltran

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Surinx, D., Van den Bussche, J., Van Gucht, D. (2018). A Framework for Comparing Query Languages in Their Ability to Express Boolean Queries. In: Ferrarotti, F., Woltran, S. (eds) Foundations of Information and Knowledge Systems. FoIKS 2018. Lecture Notes in Computer Science(), vol 10833. Springer, Cham. https://doi.org/10.1007/978-3-319-90050-6_20

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  • DOI: https://doi.org/10.1007/978-3-319-90050-6_20

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