article

The Semijoin Algebra and the Guarded Fragment

Authors:

Dirk Leinders,

Maarten Marx,

Jerzy Tyszkiewicz,

Jan BusscheAuthors Info & Claims

Journal of Logic, Language and Information, Volume 14, Issue 3

Pages 331 - 343

https://doi.org/10.1007/s10849-005-5789-8

Published: 01 June 2005 Publication History

Abstract

In the 1970s Codd introduced the relational algebra, with operators selection, projection, union, difference and product, and showed that it is equivalent to first-order logic. In this paper, we show that if we replace in Codd's relational algebra the product operator by the "semijoin" operator, then the resulting "semijoin algebra" is equivalent to the guarded fragment of first-order logic. We also define a fixed point extension of the semijoin algebra that corresponds to GF.

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Cited By

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Zhang XVan den Bussche JWang KWang ZMcIlraith SWeinberger K(2018)On the satisfiability problem of patterns in SPARQL 1.1Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence and Thirtieth Innovative Applications of Artificial Intelligence Conference and Eighth AAAI Symposium on Educational Advances in Artificial Intelligence10.5555/3504035.3504285(2054-2061)Online publication date: 2-Feb-2018
https://dl.acm.org/doi/10.5555/3504035.3504285
Hellings JPilachowski CVan Gucht DGyssens MWu YRompf TAlexandrov A(2017)From relation algebra to semi-join algebraProceedings of The 16th International Symposium on Database Programming Languages10.1145/3122831.3122833(1-10)Online publication date: 1-Sep-2017
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Daenen JNeven FTan TVansummeren S(2016)Parallel evaluation of multi-semi-joinsProceedings of the VLDB Endowment10.14778/2977797.29778009:10(732-743)Online publication date: 1-Jun-2016
https://dl.acm.org/doi/10.14778/2977797.2977800
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Reviews

Reviewer: Jonathan Samuel Golan

Among the tools used extensively in database theory are relational algebras, developed by Codd in the 1970s. The operators appearing in these algebras are selection, projection, union, difference, and join. The importance of relational algebras lies in the fact that they are equivalent, in their expressive power, to first-order logic. In this paper, the authors replace the join operator by the semijoin operator, which has been in use in database theory since the 1980s and has several advantages over the join operator. As a consequence, they create a notion of a semijoin algebra, and show that such algebras are equivalent to the guarded fragment of first-order logic. The paper is technical and theoretical, and does not do more than mention the potential applications. Online Computing Reviews Service

Reviewer: Kamal Lodaya

The guarded fragment of first-order logic has several desirable properties, for example, an exponential time upper bound (and lower bound) for satisfiability checking. Codd's theorem showed that first-order logic has the same expressive power as relational algebra. The authors of this paper show that the guarded fragment has the same expressive power as semijoin algebra, that is, allowing semijoins rather than joins in the relational algebra. This is an interesting theoretical characterization, but it remains to be seen how much the requirement of guardedness coincides with the demands of actual use. Online Computing Reviews Service

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Published In

Journal of Logic, Language and Information Volume 14, Issue 3

June 2005

132 pages

ISSN:0925-8531

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Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 June 2005

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Cited By

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Zhang XVan den Bussche JWang KWang ZMcIlraith SWeinberger K(2018)On the satisfiability problem of patterns in SPARQL 1.1Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence and Thirtieth Innovative Applications of Artificial Intelligence Conference and Eighth AAAI Symposium on Educational Advances in Artificial Intelligence10.5555/3504035.3504285(2054-2061)Online publication date: 2-Feb-2018
https://dl.acm.org/doi/10.5555/3504035.3504285
Hellings JPilachowski CVan Gucht DGyssens MWu YRompf TAlexandrov A(2017)From relation algebra to semi-join algebraProceedings of The 16th International Symposium on Database Programming Languages10.1145/3122831.3122833(1-10)Online publication date: 1-Sep-2017
https://dl.acm.org/doi/10.1145/3122831.3122833
Daenen JNeven FTan TVansummeren S(2016)Parallel evaluation of multi-semi-joinsProceedings of the VLDB Endowment10.14778/2977797.29778009:10(732-743)Online publication date: 1-Jun-2016
https://dl.acm.org/doi/10.14778/2977797.2977800
Libkin LReutter JVrgoč DHull RFan W(2013)Trial for RDFProceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI symposium on Principles of database systems10.1145/2463664.2465226(201-212)Online publication date: 22-Jun-2013
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Bárány Vten Cate BOtto M(2012)Queries with guarded negationProceedings of the VLDB Endowment10.14778/2350229.23502505:11(1328-1339)Online publication date: 1-Jul-2012
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Schweikardt NSchwentick TSegoufin L(2010)Database theoryAlgorithms and theory of computation handbook10.5555/1882723.1882742(19-19)Online publication date: 1-Jan-2010
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Fletcher GVan Den Bussche JVan Gucht DVansummeren S(2010)Towards a theory of search queriesACM Transactions on Database Systems10.1145/1862919.186292535:4(1-33)Online publication date: 12-Oct-2010
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Nash ASegoufin LVianu V(2010)Views and queriesACM Transactions on Database Systems10.1145/1806907.180691335:3(1-41)Online publication date: 30-Jul-2010
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Fletcher GVan den Bussche JVan Gucht DVansummeren S(2009)Towards a theory of search queriesProceedings of the 12th International Conference on Database Theory10.1145/1514894.1514919(201-211)Online publication date: 23-Mar-2009
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Bry FEisinger NEiter TFurche TGottlob GLey CLinse BPichler RWei F(2007)Foundations of rule-based query answeringProceedings of the Third international summer school conference on Reasoning Web10.5555/2391482.2391484(1-153)Online publication date: 3-Sep-2007
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