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Deciding termination of query evaluation in transitiveclosure logics for constraint databases
, 2003
"... We study extensions of firstorder logic over the reals with different types of transitiveclosure operators as query languages for constraint databases that can be described by Boolean combinations of polynomial inequalities. We are in particular interested in deciding the termination of the evalu ..."
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We study extensions of firstorder logic over the reals with different types of transitiveclosure operators as query languages for constraint databases that can be described by Boolean combinations of polynomial inequalities. We are in particular interested in deciding the termination of the evaluation of queries expressible in these transitiveclosure logics. It turns out that termination is undecidable in general. However, we show that the termination of the transitive closure of a continuous function graph in the twodimensional plane is decidable, and even expressible in firstorder logic over the reals. Based on this result, we identify a particular transitiveclosure logic for which termination of query evaluation is decidable and which is more expressive than firstorder logic. Furthermore, we can define a guarded fragment in which exactly the terminating queries of this language are expressible.
Expressing the box cone radius in the relational calculus with real polynomial constraints
 Discrete and Computational Geometry
"... Abstract. We show that there is a query expressible in firstorder logic over the reals that returns, on any given semialgebraic set A, for every point, a radius around which A is conical in every small enough box. We obtain this result by combining results from differential topology and real algeb ..."
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Abstract. We show that there is a query expressible in firstorder logic over the reals that returns, on any given semialgebraic set A, for every point, a radius around which A is conical in every small enough box. We obtain this result by combining results from differential topology and real algebraic geometry, with recent algorithmic results by Rannou. 1.
LINEARIZATION AND COMPLETENESS RESULTS FOR TERMINATING TRANSITIVE CLOSURE QUERIES ON SPATIAL DATABASES
, 2006
"... We study queries to spatial databases, where spatial data are modeled as semialgebraic sets, using the relational calculus with polynomial inequalities as a basic query language. We work with the extension of the relational calculus with terminating transitive closures. The main result is that this ..."
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We study queries to spatial databases, where spatial data are modeled as semialgebraic sets, using the relational calculus with polynomial inequalities as a basic query language. We work with the extension of the relational calculus with terminating transitive closures. The main result is that this language can express the linearization of semialgebraic databases. We also show that the sublanguage with linear inequalities only can express all computable queries on semilinear databases. As a consequence of these results, we obtain a completeness result for topological queries on semialgebraic databases.