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Safe constraint queries
 In PODS'98
"... We extend some of the classical characterization theorems of relational database theory  particularly those related to query safety  to the context where database elements come with xed interpreted structure, and where formulae over elements of that structure can be used in queries. We show that ..."
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Cited by 25 (7 self)
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We extend some of the classical characterization theorems of relational database theory  particularly those related to query safety  to the context where database elements come with xed interpreted structure, and where formulae over elements of that structure can be used in queries. We show that the addition of common interpreted functions such as real addition and multiplication to the relational calculus preserves important characterization theorems of the relational calculus, and also preserves certain combinatorial properties of queries. Our main result of the rst kind is that there is a syntactic characterization of the collection of safe queries over the relational calculus supplemented by a wide class of interpreted functions  a class that includes addition, multiplication, and exponentiation  and that this characterization gives us an interpreted analog of the concept of rangerestricted query from the uninterpreted setting. Furthermore, our rangerestricted queries are particularly intuitive for the relational calculus with real arithmetic, and give a natural syntax for safe queries in the presence of polynomial functions. We use these characterizations to show that safety is decidable for Boolean combinations of conjunctive queries for a large class of interpreted structures. We show a dichotomy theorem that sets a polynomial bound on the growth of the output of a query that might refer to addition, multiplication and exponentiation. We apply the above results for nite databases to get results on constraint databases, representing potentially innite objects. We start by getting syntactic characterizations of the queries on constraint databases that preserve geometric conditions in the constraint data model. We consider classes of convex polytopes, polyhedra, and compact semilinear sets, the latter corresponding to many spatial applications. We show how to give an eective syntax to safe queries, and prove that for conjunctive queries the preservation properties are decidable. 1
Exact and Approximate Aggregation in Constraint Query Languages
, 1999
"... Weinvestigatetheproblemofhowtoextendconstraint querylanguageswithaggregateoperators.Wedeal withstandardrelationalaggregation,andalsowithaggregatesspecictospatialdata,suchasvolume.We studyseveralapproaches,includingtheadditionofa newclassofapproximateaggregateoperatorswhichallowanerrortoleranceinthec ..."
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Cited by 11 (2 self)
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Weinvestigatetheproblemofhowtoextendconstraint querylanguageswithaggregateoperators.Wedeal withstandardrelationalaggregation,andalsowithaggregatesspecictospatialdata,suchasvolume.We studyseveralapproaches,includingtheadditionofa newclassofapproximateaggregateoperatorswhichallowanerrortoleranceinthecomputation.Weshow howtechniquesbasedonVCdimensioncanbeusedto givelanguageswithapproximationoperators,butalso showthattheselanguageshaveanumberofshortcomings.Wethengiveasetofresultsshowingthatitis impossibletogetconstraintbasedlanguagesthatadmit denableaggregationoperators,bothforexactoperatorsandforapproximateones.Theseresultsarequite robust,inthattheyshowthatclosureunderaggregation isproblematicevenwhentheclassoffunctionspermittedinconstraintsisexpanded. Thismotivatesadierentapproachtotheaggregation problem.WeintroducealanguageFO+Poly+Sum, whichpermitsstandarddiscreteaggregationoperators tobeappliedtotheoutputsofrangerestrictedconstraintqueries.Weshowthatthislanguagehasanumberofattractiveclosureandexpressivityproperties, andthatitcancomputevolumesoflinearconstraint databases.Wealsoshow,usingtechniquesfrommachinelearning,thatasmallextensionofFO+Poly+ Sumcanprobabilisticallyndapproximationsofvolumesforpolynomialconstraintdatabases.
Aggregate Operators in Constraint Query Languages
 J. Comput. System Sci
, 2002
"... We investigate the problem of how to extend constraint query languages with aggregate operators. We deal with standard relational aggregation, and also with aggregates specific to spatial data, such as volume. We study several approaches, including the addition of a new class of approximate aggregat ..."
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Cited by 6 (0 self)
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We investigate the problem of how to extend constraint query languages with aggregate operators. We deal with standard relational aggregation, and also with aggregates specific to spatial data, such as volume. We study several approaches, including the addition of a new class of approximate aggregate operators which allow an error tolerance in the computation. We show how techniques of [23, 25] based on VCdimension can be used to give languages with approximation operators, but also show that these languages have a number of shortcomings. We then give a set of results showing that it is impossible to get constraintbased languages that admit de nable aggregation operators, both for exact operators and for approximate ones. These results are quite robust, in that they show that closure under aggregation is problematic even when the class of functions permitted in constraints is expanded. This motivates a different approach to the aggregation problem. We introduce a language FO + Poly+Sum, which permits standard discrete aggregation operators to be applied to the outputs of rangerestricted constraint queries. We show that this language has a number of attractive closure and expressivity properties, and that it can compute volumes of linearconstraint databases.
Query Languages for Constraint Databases: FirstOrder Logic, FixedPoints, and Convex Hulls
 In Proceedings of the 8th International Conference on Database Theory (ICDT), number 1973 in Lecture Notes in Computer Science
, 2001
"... . We dene various extensions of rstorder logic on linear as well as polynomial constraint databases. First, we extend rstorder logic by a convex closure operator and show this logic, FO(conv), to be closed and to have Ptime datacomplexity. We also show that a weak form of multiplication is de ..."
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Cited by 4 (1 self)
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. We dene various extensions of rstorder logic on linear as well as polynomial constraint databases. First, we extend rstorder logic by a convex closure operator and show this logic, FO(conv), to be closed and to have Ptime datacomplexity. We also show that a weak form of multiplication is denable in this language and prove the equivalence between this language and the multiplication part of PFOL. We then extend FO(conv) by xedpoint operators to get a query languages expressive enough to capture Ptime. In the last part of the paper we lift the results to polynomial constraint databases. 1 Introduction In recent years new application areas have reached the limits of the standard relational database model. Especially, geographical information systems, which are of growing importance, exceed the power of the relational model with their need to store geometrical gures, naturally viewed as innite sets of points. Therefore, new database models have been proposed to handl...
Introducing External Functions in Constraint Query Languages
, 1998
"... . Constraint databases use constraints to model and query data. In particular, constraints allow a finite representation of infinite sets of relational tuples (also called generalized tuples). The choice of different logical theories to express constraints inside relational languages leads to the de ..."
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Cited by 3 (2 self)
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. Constraint databases use constraints to model and query data. In particular, constraints allow a finite representation of infinite sets of relational tuples (also called generalized tuples). The choice of different logical theories to express constraints inside relational languages leads to the definition of constraint languages with different expressive power. Practical constraint database languages typically use linear constraints. This choice allows the use of efficient algorithms but, at the same time, some useful queries, needed by the considered application, may not be represented inside the resulting languages (for example, the convex hull cannot be computed [19]). These additional queries can only be modeled by changing the theory (thus, loosing the advantages of the linear theory), or extending the language, or using external functions. In this paper we consider the last approach and we propose an algebra and a calculus for constraint relational databases extended with exter...
Linear approximation of semialgebraic spatial databases using transitive closure logic, in arbitrary dimension
 IN PROCEEDINGS OF THE 8TH INTERNATIONAL WORKSHOP ON DATABASES AND PROGRAMMING LANGUAGES, LECTURE NOTES IN COMPUT. SCI
, 2002
"... ..."
Uniform Generation in Spatial Constraint Databases and Applications (Extended Abstract)
, 2000
"... We study the efficient approximation of queries in linear constraint databases using sampling techniques. We define the notion of an almost uniform generator for a generalized relation and extend the classical generator of Dyer, Frieze and Kannan for convex sets to the union and the projection of re ..."
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We study the efficient approximation of queries in linear constraint databases using sampling techniques. We define the notion of an almost uniform generator for a generalized relation and extend the classical generator of Dyer, Frieze and Kannan for convex sets to the union and the projection of relations. For the intersection and the difference, we give sufficient conditions for the existence of such generators. We show how such generators give relative estimations of the volume and approximations of generalized relations as the composition of convex hulls obtained from the samples.
Finite Model Theory and its Applications This document contains Leonid Libkin’s chapter Embedded Finite Models and Constraint Databases
, 2006
"... 1.2 Relational Databases and Embedded Finite Models.......... 2 ..."
A Representation Independent Language for Planar Spatial Databases with Euclidean Distance
"... Abstract. Linear constraint databases and query languages are appropriate for spatial database applications. Not only the data model is natural to represent a large portion of spatial data suchas in GIS systems, but also there exist efficient algorithms for the core operations in the query languages ..."
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Abstract. Linear constraint databases and query languages are appropriate for spatial database applications. Not only the data model is natural to represent a large portion of spatial data suchas in GIS systems, but also there exist efficient algorithms for the core operations in the query languages. However, an important limitation of the linear constraint data model is that it cannot model constructs such as “Euclidean distance. ” A previous attempt to expend linear constraint languages withthe ability to express Euclidean distance, by Kuijpers, Kuper, Paredaens, and Vandeurzen is to adapt two fundamental Euclidean constructions withruler and compass in a first order logic over points. The language, however, requires the input database to be encoded in an ad hoc LPC representation so that the logic operations can apply. This causes a problem that sometimes queries in their language may depend on the encoding and thus do not have any natural meaning. In this paper, we propose an alternative approach and develop an algebraic language in which the traditional operators and Euclidean constructions work directly on the data represented by “semicircular ” constraints. By avoiding the encoding step, our language do not suffer from this problem. We show that the language is closed under these operations. 1