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Relational queries over interpreted structures

Authors:

Michael Benedikt,

Leonid LibkinAuthors Info & Claims

Journal of the ACM (JACM), Volume 47, Issue 4

Pages 644 - 680

https://doi.org/10.1145/347476.347477

Published: 01 July 2000 Publication History

Abstract

We rework parts of the classical relational theory when the underlying domain is a structure with some interpreted operations that can be used in queries. We identify parts of the classical theory that go through 'as before' when interpreted structure is present, parts that go through only for classes of nicely behaved structures, and parts that only arise in the interpreted case. The first category include a number of results on language equivalence and expressive power characterizations for the active-domain semantics for a variety of logics. Under this semantics, quantifiers range over elements of a relational database. The main kind of results we prove here are generic collapse results: for generic queries, adding operations beyond order, does not give us extra power.

The second category includes results on the natural semantics, under which quantifiers range over the entire interpreted structure. We prove, for a variety of structures, natural-active collapse results, showing that using unrestricted quantification does not give us any extra power. Moreover, for a variety of structures, including the real field, we give a set of algorithms for eliminating unbounded quantifications in favor of bounded ones. Furthermore, we extend these collapse results to a new class of higher-order logics that mix unbounded and bounded quantification. We give a set of normal forms for these logics, under special conditions on the interpreted structures. As a by-product, we obtain an elementary proof of the fact that parity test is not definable in the relational calculus with polynomial inequality constraints. We also give examples of structures with nice model-theoretic properties over which the natural-active collapse fails.

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Benedikt MHrushovski E(2023)Embedded Finite Models beyond Restricted Quantifier Collapse2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175804(1-13)Online publication date: 26-Jun-2023
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Figueira DJez ALin ALibkin LBarceló P(2022)Data Path Queries over Embedded Graph DatabasesProceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3517804.3524159(189-201)Online publication date: 12-Jun-2022
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Index Terms

Relational queries over interpreted structures
1. Information systems
  1. Data management systems
    1. Query languages
2. Theory of computation
  1. Logic
    1. Constraint and logic programming
    2. Finite Model Theory

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cover image Journal of the ACM

Journal of the ACM Volume 47, Issue 4

July 2000

238 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/347476

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Copyright © 2000 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 2000

Published in JACM Volume 47, Issue 4

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Cited By

Benedikt MHrushovski E(2023)Embedded Finite Models beyond Restricted Quantifier Collapse2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175804(1-13)Online publication date: 26-Jun-2023
https://doi.org/10.1109/LICS56636.2023.10175804
Figueira DJez ALin ALibkin LBarceló P(2022)Data Path Queries over Embedded Graph DatabasesProceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3517804.3524159(189-201)Online publication date: 12-Jun-2022
https://dl.acm.org/doi/10.1145/3517804.3524159
Benedikt M(2022)The Past and Future of Embedded Finite Model TheoryReachability Problems10.1007/978-3-031-19135-0_3(37-46)Online publication date: 17-Oct-2022
https://dl.acm.org/doi/10.1007/978-3-031-19135-0_3
Liu HLiu J(2019)On the Expressive Power of Logics on Constraint Databases with Complex ObjectsJournal of Computer Science and Technology10.1007/s11390-019-1943-734:4(795-817)Online publication date: 19-Jul-2019
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Geerts F(2018)Constraint Query LanguagesEncyclopedia of Database Systems10.1007/978-1-4614-8265-9_1240(586-591)Online publication date: 7-Dec-2018
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Wu LChen ZWu XXie Z(2015)Distributed Geographic Structure Query Language-DGSQLJournal of Software Engineering10.3923/jse.2015.328.3369:2(328-336)Online publication date: 1-Feb-2015
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Krebs ASreejith A(2012)Non-definability of Languages by Generalized First-order Formulas over (N,+)Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science10.1109/LICS.2012.55(451-460)Online publication date: 25-Jun-2012
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