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A framework for comparing query languages in their ability to express boolean queries

A framework for comparing query languages in their ability to express boolean queries For any query language F $\mathcal {F}$ , we consider three natural families of boolean queries. Nonemptiness queries are expressed as e ≠ ∅ with e an F $\mathcal {F}$ expression. Emptiness queries are expressed as e = ∅. Containment queries are expressed as e 1 ⊆ e 2. We refer to syntactic constructions of boolean queries as modalities. In first order logic, the emptiness, nonemptiness and containment 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. 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. The two main query languages to which we apply our framework are the algebra of binary relations, and the language of conjunctive queries. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

A framework for comparing query languages in their ability to express boolean queries

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References (44)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer Nature Switzerland AG
Subject
Computer Science; Artificial Intelligence; Mathematics, general; Computer Science, general; Complex Systems
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/s10472-019-09639-5
Publisher site
See Article on Publisher Site

Abstract

For any query language F $\mathcal {F}$ , we consider three natural families of boolean queries. Nonemptiness queries are expressed as e ≠ ∅ with e an F $\mathcal {F}$ expression. Emptiness queries are expressed as e = ∅. Containment queries are expressed as e 1 ⊆ e 2. We refer to syntactic constructions of boolean queries as modalities. In first order logic, the emptiness, nonemptiness and containment 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. 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. The two main query languages to which we apply our framework are the algebra of binary relations, and the language of conjunctive queries.

Journal

Annals of Mathematics and Artificial IntelligenceSpringer Journals

Published: Jun 8, 2019

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