# 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} }

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…

## 70 Citations

### On the structure of queries in constraint query languages

- Computer ScienceProceedings 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.

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- 1995

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### Linear vs. order constraint queries over rational databases (extended abstract)

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- 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.

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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.

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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.

### Finitely Representable Databases

- Computer Science, MathematicsJ. 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.

### On the containment and equivalence of database queries with linear constraints (extended abstract)

- Mathematics, Computer SciencePODS '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”.

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