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Safety and translation of relational calculus

Authors:

Allen Van Gelder and

Rodney W. ToporAuthors Info & Claims

ACM Transactions on Database Systems (TODS), Volume 16, Issue 2

Pages 235 - 278

https://doi.org/10.1145/114325.103712

Published: 01 May 1991 Publication History

Abstract

Not all queries in relational calculus can be answered sensibly when disjunction, negation, and universal quantification are allowed. The class of relation calculus queries or formulas that have sensible answers is called the domain independent class which is known to be undecidable. Subsequent research has focused on identifying large decidable subclasses of domain independent formulas. In this paper we investigate the properties of two such classes: the evaluable formulas and the allowed formulas. Although both classes have been defined before, we give simplified definitions, present short proofs of their main properties, and describe a method to incorporate equality.

Although evaluable queries have sensible answers, it is not straightforward to compute them efficiently or correctly. We introduce relational algebra normal form for formulas from which form the correct translation into relational algebra is trivial. We give algorithms to transform an evaluable formula into an equivalent allowed formula and from there into relational algebra normal form. Our algorithms avoid use of the so-called Dom relation, consisting of all constants appearing in the database or the query.

Finally, we describe a restriction under which every domain independent formula is evaluable and argue that the class of evaluable formulas is the largest decidable subclass of the domain independent formulas that can be efficiently recognized.

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Cited By

Bonacina MWinkler S(2023)Semantically-Guided Goal-Sensitive Reasoning: Decision Procedures and the Koala ProverJournal of Automated Reasoning10.1007/s10817-022-09656-w67:1Online publication date: 11-Jan-2023
https://dl.acm.org/doi/10.1007/s10817-022-09656-w
Basin DKrstić SSchneider JTraytel D(2023)Correct and Efficient Policy Monitoring, a RetrospectiveAutomated Technology for Verification and Analysis10.1007/978-3-031-45329-8_1(3-30)Online publication date: 24-Oct-2023
https://dl.acm.org/doi/10.1007/978-3-031-45329-8_1
Wernhard C(2023)Range-Restricted and Horn Interpolation through Clausal TableauxAutomated Reasoning with Analytic Tableaux and Related Methods10.1007/978-3-031-43513-3_1(3-23)Online publication date: 18-Sep-2023
https://dl.acm.org/doi/10.1007/978-3-031-43513-3_1
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Index Terms

Safety and translation of relational calculus
1. Information systems
  1. Data management systems
    1. Database management system engines
      1. Database query processing
    2. Query languages
2. Theory of computation
  1. Logic
    1. Finite Model Theory
  2. Theory and algorithms for application domains
    1. Database theory
      1. Database query processing and optimization (theory)

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Reviews

Reviewer: Charles William Bash

“Not all queries in relational calculus can be answered sensibly when disjunction, negation and universal quantification are allowed.” Given the growing number of intermediate query generators on the market, more and more problems will not be stated in simple terms, and methods are needed to simplify those statements so that they can be correctly solved. Even apparently simple queries such as “SELECT P.name FROM P,Q,R WHERE P.name = Q.name OR P.name = R.name ” may yield counterintuitive results using current methods. The authors state that if R is empty, both SQL and QUEL return nothing, even if matches exist between P and Q . The importance of this can be seen if we translate the request into English: “Give me a list of the parts that I have in inventory, or that are currently on order.” This paper is for those deeply involved in the process of relational calculus, not for the lay reader. The calculus is long and involved, and will not be obvious without careful study. The work is important to the evolution of database system, however, and I strongly urge those involved in this area to read the document.

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Published In

cover image ACM Transactions on Database Systems

ACM Transactions on Database Systems Volume 16, Issue 2

June 1991

160 pages

ISSN:0362-5915

EISSN:1557-4644

DOI:10.1145/114325

Issue’s Table of Contents

Copyright © 1991 ACM.

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 May 1991

Published in TODS Volume 16, Issue 2

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Cited By

Bonacina MWinkler S(2023)Semantically-Guided Goal-Sensitive Reasoning: Decision Procedures and the Koala ProverJournal of Automated Reasoning10.1007/s10817-022-09656-w67:1Online publication date: 11-Jan-2023
https://dl.acm.org/doi/10.1007/s10817-022-09656-w
Basin DKrstić SSchneider JTraytel D(2023)Correct and Efficient Policy Monitoring, a RetrospectiveAutomated Technology for Verification and Analysis10.1007/978-3-031-45329-8_1(3-30)Online publication date: 24-Oct-2023
https://dl.acm.org/doi/10.1007/978-3-031-45329-8_1
Wernhard C(2023)Range-Restricted and Horn Interpolation through Clausal TableauxAutomated Reasoning with Analytic Tableaux and Related Methods10.1007/978-3-031-43513-3_1(3-23)Online publication date: 18-Sep-2023
https://dl.acm.org/doi/10.1007/978-3-031-43513-3_1
Huerta y Munive J(2022)Relaxing Safety for Metric First-Order Temporal Logic via Dynamic Free VariablesRuntime Verification10.1007/978-3-031-17196-3_3(45-66)Online publication date: 28-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-17196-3_3
Wernhard C(2021)Craig Interpolation with Clausal First-Order TableauxJournal of Automated Reasoning10.1007/s10817-021-09590-365:5(647-690)Online publication date: 1-Jun-2021
https://dl.acm.org/doi/10.1007/s10817-021-09590-3
Cao YFan WYuan T(2020)Bounded Evaluation: Querying Big Data with Bounded ResourcesInternational Journal of Automation and Computing10.1007/s11633-020-1236-117:4(502-526)Online publication date: 1-Aug-2020
https://dl.acm.org/doi/10.1007/s11633-020-1236-1
Cao YFan WGeerts FLu P(2018)Bounded Query Rewriting Using ViewsACM Transactions on Database Systems10.1145/318367343:1(1-46)Online publication date: 23-Mar-2018
https://dl.acm.org/doi/10.1145/3183673
Topor R(2018)Safety and Domain IndependenceEncyclopedia of Database Systems10.1007/978-1-4614-8265-9_1255(3269-3273)Online publication date: 7-Dec-2018
https://doi.org/10.1007/978-1-4614-8265-9_1255
Cao YFan WGeerts FLu PMilo TTan W(2016)Bounded Query Rewriting Using ViewsProceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/2902251.2902294(107-119)Online publication date: 15-Jun-2016
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Cao YFan WÖzcan FKoutrika GMadden S(2016)An Effective Syntax for Bounded Relational QueriesProceedings of the 2016 International Conference on Management of Data10.1145/2882903.2882942(599-614)Online publication date: 26-Jun-2016
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