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Author Benedikt, Michael ♦ Libkin, Leonid
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2000
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword 0-minimality ♦ Collapse results ♦ Constraints ♦ Quantifier elimination ♦ Relational calculus
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.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2000-07-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 47
Issue Number 4
Page Count 37
Starting Page 644
Ending Page 680


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Source: ACM Digital Library