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Constraint Query Languages
, 1992
"... We investigate the relationship between programming with constraints and database query languages. We show that efficient, declarative database programming can be combined with efficient constraint solving. The key intuition is that the generalization of a ground fact, or tuple, is a conjunction ..."
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Cited by 380 (44 self)
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We investigate the relationship between programming with constraints and database query languages. We show that efficient, declarative database programming can be combined with efficient constraint solving. The key intuition is that the generalization of a ground fact, or tuple, is a conjunction of constraints over a small number of variables. We describe the basic Constraint Query Language design principles and illustrate them with four classes of constraints: real polynomial inequalities, dense linear order inequalities, equalities over an infinite domain, and boolean equalities. For the analysis, we use quantifier elimination techniques from logic and the concept of data complexity from database theory. This framework is applicable to managing spatial data and can be combined with existing multidimensional searching algorithms and data structures.
Constraint Programming and Database Query Languages
 In Proc. 2nd Conference on Theoretical Aspects of Computer Software (TACS
, 1994
"... . The declarative programming paradigms used in constraint languages can lead to powerful extensions of Codd's relational data model. The development of constraint database query languages from logical database query languages has many similarities with the development of constraint logic progr ..."
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Cited by 62 (3 self)
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. The declarative programming paradigms used in constraint languages can lead to powerful extensions of Codd's relational data model. The development of constraint database query languages from logical database query languages has many similarities with the development of constraint logic programming from logic programming, but with the additional requirements of data efficient, setatatime, and bottomup evaluation. In this overview of constraint query languages (CQLs) we first present the framework of [41]. The principal idea is that: "the ktuple (or record) data type can be generalized by a conjunction of quantifierfree constraints over k variables". The generalization must preserve various language properties of the relational data model, e.g., the calculus/algebra equivalence, and have time complexity polynomial in the size of the data. We next present an algebra for dense order constraints that is simpler to evaluate than the calculus described in [41], and we sharpen some of...
On the expressive power of database queries with intermediate types
 Journal of Computer and System Sciences
, 1991
"... The setheight of a complex object type is defined to be its level of nesting of the set construct. In a query of the complex object calculus which maps a database D to an output type T,anintermediate type is a type which is used by some variable of the query, but which is not present in D or T.Fore ..."
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Cited by 47 (2 self)
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The setheight of a complex object type is defined to be its level of nesting of the set construct. In a query of the complex object calculus which maps a database D to an output type T,anintermediate type is a type which is used by some variable of the query, but which is not present in D or T.Foreachk, i ≥ 0 we define CALCk,i to be the family of calculus queries mapping from and to types with setheight ≤ k and using intermediate types with setheight ≤ i. In particular, CALC0,0 is the classical relational calculus, and CALC0,1 is equivalent to the family of secondorder (relational) queries. Several results concerning these families of languages are obtained. A primary focus is on the families CALC0,i, which map relations to relations. Upper and lower bounds in terms of hyperexponential time and space on the complexity of these families are provided. The CALC0,i hierarchy does not collapse with respect to expressive power. The union ∪0≤iCALC0,i is exactly the family of elementary queries, i.e., queries with hyperexponential complexity. The expressive power of queries from the complex object calculus interpreted using semantics based on the use of arbitrarily large finite or infinite set of invented values is studied. Under these semantics, the expressive power of the relational calculus is not increased, and the CALC0,i hierarchy collapses at CALC0,1. In general, queries with these semantics may not be computable. We also consider an alternative semantics which yields a family of queries equivalent to the computable queries. 1
Firstorder queries on finite structures over the reals
"... We investigate properties of finite relational structures over the reals expressed by firstorder 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, ..."
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Cited by 33 (2 self)
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We investigate properties of finite relational structures over the reals expressed by firstorder 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 firstorder theory of the reals can be evaluated by letting each quantifier range over only a finite set of real numbers without changing its truth value. Inspired by this observation, we then show that when all polynomials used are linear, each query can be expressed uniformly on all finite structures by a sentence of which the quantifiers range only over the finite domain of the structure. In other words, linear constraint programming on finite structures can be reduced to ordinary query evaluation as usual in finite model theory and databases. Moreover, if only "generic" queries are taken into consideration, we show that this can be reduced even further by proving that such
A Closed Form Evaluation For Datalog Queries With Integer (GAP)Order Constraints
 Theoretical Computer Science
, 1993
"... : We provide a generalization of Datalog based on generalizing databases by adding integer order constraints to relational tuples. For Datalog queries with integer (gap)order constraints (denoted Datalog !Z ) we show that there is a closed form evaluation. We also show that the tuple recognition ..."
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Cited by 30 (8 self)
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: We provide a generalization of Datalog based on generalizing databases by adding integer order constraints to relational tuples. For Datalog queries with integer (gap)order constraints (denoted Datalog !Z ) we show that there is a closed form evaluation. We also show that the tuple recognition problem can be done in PTIME in the size of the generalized database, assuming that the size of the constants in the query is logarithmic in the size of the database. Note that the absence of negation is critical, Datalog : queries with integer order constraints can express any Turing computable function. 1 Introduction In this paper we consider a generalization of Datalog based on the notion of a constraint tuple. The important idea of a constraint tuple comes from constraint logic programming systems, e.g. CLP [14], Prolog III [4], and CHIP [8], and it generalizes the notion of a ground fact. This allows the declarative programming of new applications, including various combinatorial se...
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 26 (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
Constraint Databases: A Survey
 Semantics in Databases, number 1358 in LNCS
, 1998
"... . Constraint databases generalize relational databases by finitely representable infinite relations. This paper surveys the state of the art in constraint databases: known results, remaining open problems and current research directions. The paper also describes a new algebra for databases with inte ..."
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Cited by 25 (3 self)
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. Constraint databases generalize relational databases by finitely representable infinite relations. This paper surveys the state of the art in constraint databases: known results, remaining open problems and current research directions. The paper also describes a new algebra for databases with integer order constraints and a complexity analysis of evaluating queries in this algebra. In memory of Paris C. Kanellakis 1 Introduction There is a growing interest in recent years among database researchers in constraint databases, which are a generalization of relational databases by finitely representable infinite relations. Constraint databases are parametrized by the type of constraint domains and constraint used. The good news is that for many parameters constraint databases leave intact most of the fundamental assumptions of the relational database framework proposed by Codd. In particular, 1. Constraint databases can be queried by constraint query languages that (a) have a semantics ba...
Relational queries over interpreted structures
 Journal of the ACM
, 2000
"... 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 ..."
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Cited by 24 (13 self)
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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 nicelybehaved structures, and parts that only arise in the interpreted case. The rst category includes a number of results on language equivalence and expressive power characterizations for the activedomain semantics for a variety of logics. Under this semantics, quanti ers 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 quantiers range over the entire interpreted structure. We prove, for a variety of structures, naturalactive collapse results, showing that using unrestricted quantication does not give us any extra power. Moreover, for a variety of structures, including the real eld, we give a set of algorithms for eliminating unbounded quantications in favor of bounded ones. Furthermore, we extend these collapse results to a new class of higherorder logics that mix unbounded and bounded quantication. We give a set of normal forms for these logics, under special conditions on the interpreted structures. As a byproduct, we obtain an elementary proof of the fact that parity test is not denable in the relational calculus with polynomial inequality constraints. We also give examples of structures with nice modeltheoretic properties over which the naturalactive collapse fails. 1
Stability theory, Permutations of Indiscernibles, and Embedded Finite Models
 Trans. Amer. Math. Soc
, 2000
"... Abstract. We show that the expressive power of firstorder logic over finite models embedded in a model M is determined by stabilitytheoretic properties of M. In particular, we show that if M is stable, then every class of finite structures that can be defined by embedding the structures in M, can ..."
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Cited by 23 (1 self)
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Abstract. We show that the expressive power of firstorder logic over finite models embedded in a model M is determined by stabilitytheoretic properties of M. In particular, we show that if M is stable, then every class of finite structures that can be defined by embedding the structures in M, can be defined in pure firstorder logic. We also show that if M does not have the independence property, then any class of finite structures that can be defined by embedding the structures in M, can be defined in firstorder logic over a dense linear order. This extends known results on the definability of classes of finite structures and ordered finite structures in the setting of embedded finite models. These results depend on several results in infinite model theory. Let I be a set of indiscernibles in a model M and suppose (M,I) is elementarily equivalent to (M1,I1) whereM1 is I1  +saturated. If M is stable and (M,I) is saturated, then every permutation of I extends to an automorphism of M and the theory of (M,I) isstable. LetI be a sequence of <indiscernibles in a model M, which does not have the independence property, and suppose (M,I) is elementarily equivalent to (M1,I1) where(I1,<) is a complete dense linear order and M1 is I1  +saturated. Then (M, I)types over I are orderdefinable and if (M, I) isℵ1saturated, every order preserving permutation of I can be extended to a backandforth system. 1.
Domain Independence and the Relational Calculus
 Acta Informatica
, 1993
"... Several alternative semantics (or interpretations) of the relational (domain) calculus are studied here. It is shown that they all have the same expressive power, i.e., the selection of any of the semantics neither gains nor loses expressive power. Since the domain is potentially infinite, the answe ..."
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Cited by 22 (7 self)
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Several alternative semantics (or interpretations) of the relational (domain) calculus are studied here. It is shown that they all have the same expressive power, i.e., the selection of any of the semantics neither gains nor loses expressive power. Since the domain is potentially infinite, the answer to a relational calculus query is sometimes infinite (and hence not a relation). The following approaches which guarantee the finiteness of answers to queries are studied here: outputrestricted unlimited interpretation, domain independent queries, outputrestricted finite and countable invention, and limited interpretation. Of particular interest is the outputrestricted unlimited interpretation  although the output is restricted to the active domain of the input and query, the quantified variables range over the infinite underlying domain. While this is close to the intuitive interpretation given to calculus formulas, the naive approach to evaluating queries under this semantics calls ...