# First-order queries on finite structures over the reals

@article{Paredaens1995FirstorderQO,
title={First-order queries on finite structures over the reals},
author={Jan Paredaens and Jan Van den Bussche and Dirk Van Gucht},
journal={Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science},
year={1995},
pages={79-87}
}
• Published 26 June 1995
• Computer Science
• Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science
We investigate properties of finite relational structures over the reals expressed by first-order sentences whose predicates are the relations of the structure plus arbitrary polynomial inequalities, and whose quantifiers can range over the whole set of reals. In constraint programming terminology, this corresponds to Boolean real polynomial constraint queries on finite structures. The fact that quantifiers range over all reals seems crucial; however, we observe that each sentence in the first…
• Computer Science
Proceedings 11th Annual IEEE Symposium on Logic in Computer Science
• 1996
It is shown that for a large class of signatures, including real arithmetic constraints, unbounded quantification can be eliminated and one can transform a sentence containing unrestricted quantification over the infinite universe to get an equivalent sentence in which quantifiers range over the finite relational structure.
• Computer Science, Mathematics
Theor. Comput. Sci.
• 1997
• Computer Science
CP
• 1995
This paper proves that parity and connectivity are first-order expressible in presence of (enough) arithmetic, and develops reductions techniques for queries over constraint databases, that allow for conclusions with respect to their undefinability in various constraint query languages.
• Computer Science
PODS
• 1996
The value of these results is not limited to the specific set of problems considered in this paper, as a matter of fact, they show that order-constraint and finite databases are equally powerful— although the constraint representation does provide a more *This work has been partially supported by NSF Grant CCR 9403809.
• Computer Science
JACM
• 2000
It is proved, for a variety of structures, natural-active collapse results, showing that using unrestricted quantification does not give us any extra power, and a set of algorithms for eliminating unbounded quantifications in favor of bounded ones are given.
• Computer Science
PODS '97
• 1997
A set of algorithms for eliminating unbounded quantifications in favor of bounded ones is given, and an elementary proof of the fact that parity test is not definable in the relational calculus with polynomial inequality constraints is obtained.
• Computer Science, Mathematics
PODS '98
• 1998
This work shows how to give an effective syntax to safe queries and prove that for conjunctive queries the preservation properties are decidable, and gets syntactic characterizations of the queries on constraint databases that preserve geometric conditions in the constraint data model.
• Computer Science, Mathematics
• 1997
The theory of finitely representable models is investigated and it is proved that it differs from both classical model theory and finite model theory, and most of the well known theorems of logic are shown to be failures.
• Computer Science, Mathematics
J. Comput. Syst. Sci.
• 1997
The theory of finitely representable models is investigated and it is proved that it differs from both classical model theory and finite model theory, and most of the well-known theorems of logic are shown to be failures.
• Mathematics, Computer Science
PODS '97
• 1997
The counter machine technique is used to show that for “connected” first-order queries with linear constraints over Z and lV, the containment and equivalence problems are decidable over “bounded-degree databases”.

## References

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• Computer Science
Proceedings 11th Annual IEEE Symposium on Logic in Computer Science
• 1996
It is shown that for a large class of signatures, including real arithmetic constraints, unbounded quantification can be eliminated and one can transform a sentence containing unrestricted quantification over the infinite universe to get an equivalent sentence in which quantifiers range over the finite relational structure.
• Computer Science, Mathematics
J. Comput. Syst. Sci.
• 1997
The theory of finitely representable models is investigated and it is proved that it differs from both classical model theory and finite model theory, and most of the well-known theorems of logic are shown to be failures.
• Mathematics, Computer Science
• 1996
A general lifting technique is developed that allows us to extend any result of the kind the authors are interested in, from finite to finitely-representable states, and thus all the results in this paper are proved for the general case of {\em constraint databases.
This survey considers some of the remarkable and totally unforeseen ways in which Tarski's theorem functions nowadays in mathematics, logic and computer science.
Tarski made a fundamental contribution to our understanding of R, perhaps mathematics’ most basic structure. His theorem is the following. To any formula ϕ(X1, …, Xm) in the vocabulary {0, 1, +, ·,
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LCC
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An AC0 upper bound on the complexity of first-oder queries over (infinite) databases defined by restricted linear constraints is given and the non-expressibility of various usual queries is deduced.
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POPL
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Although relational algebra and relational calculus satisfy these principles, there are certain queries involving least fixed points that cannot be expressed by these languages, yet that also satisfy the principles.
• Computer Science
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This book discusses Languages, Computability, and Complexity, and the Relational Model, which aims to clarify the role of Semantic Data Models in the development of Query Language Design.