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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 338 (35 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.
Relational Queries Computable in Polynomial Time
 Information and Control
, 1986
"... We characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe. We also show that even without the ordering one application of fixed point suffices to express any query expressible with several ..."
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Cited by 269 (17 self)
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We characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe. We also show that even without the ordering one application of fixed point suffices to express any query expressible with several alternations of fixed point and negation. This proves that the fixed point query hierarchy suggested by Chandra and Harel collapses at the first fixed point level. It is also a general result showing that in finite model theory one application of fixed point suffices. Introduction and Summary Query languages for relational databases have received considerable attention. In 1972 Codd showed that two natural languages for queries  one algebraic and the other a version of first order predicate calculus  have identical powers of expressibility, [Cod72]. Query languages which are as expressive as Codd's Relational Calculus are sometimes called complete. This term is misleading however becau...
The Lazy Lambda Calculus
 Research Topics in Functional Programming
, 1990
"... Introduction The commonly accepted basis for functional programming is the calculus; and it is folklore that the calculus is the prototypical functional language in puri ed form. But what is the calculus? The syntax is simple and classical; variables, abstraction and application in the pure cal ..."
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Cited by 239 (3 self)
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Introduction The commonly accepted basis for functional programming is the calculus; and it is folklore that the calculus is the prototypical functional language in puri ed form. But what is the calculus? The syntax is simple and classical; variables, abstraction and application in the pure calculus, with applied calculi obtained by adding constants. The further elaboration of the theory, covering conversion, reduction, theories and models, is laid out in Barendregt's already classical treatise [Bar84]. It is instructive to recall the following crux, which occurs rather early in that work (p. 39): Meaning of terms: rst attempt The meaning of a term is its normal form (if it exists). All terms without normal forms are identi ed. This proposal incorporates such a simple and natural interpretation of the calculus as
The Alternating Fixpoint of Logic Programs with Negation
, 1995
"... The alternating fixpoint of a logic program with negation is defined constructively. The underlying idea is monotonically to build up a set of negative conclusions until the least fixpoint is reached, using a transformation related to the one that defines stable models. From a fixed set of negative ..."
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Cited by 208 (2 self)
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The alternating fixpoint of a logic program with negation is defined constructively. The underlying idea is monotonically to build up a set of negative conclusions until the least fixpoint is reached, using a transformation related to the one that defines stable models. From a fixed set of negative conclusions, the positive conclusions follow (without deriving any further negative ones), by traditional Horn clause semantics. The union of positive and negative conclusions is called the alternating xpoint partial model. The name "alternating" was chosen because the transformation runs in two passes; the first pass transforms an underestimate of the set of negative conclusions into an (intermediate) overestimate; the second pass transforms the overestimate into a new underestimate; the composition of the two passes is monotonic. The principal contributions of this work are (1) that the alternating fixpoint partial model is identical to the wellfounded partial model, and (2) that alternating xpoint logic is at least as expressive as xpoint logic on all structures. Also, on finite structures, fixpoint logic is as expressive as alternating fixpoint logic.
ConjunctiveQuery Containment and Constraint Satisfaction
 Journal of Computer and System Sciences
, 1998
"... Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have in c ..."
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Cited by 132 (13 self)
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Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have in common? Our main conceptual contribution in this paper is to point out that, despite their very different formulation, conjunctivequery containment and constraint satisfaction are essentially the same problem. The reason is that they can be recast as the following fundamental algebraic problem: given two finite relational structures A and B, is there a homomorphism h : A ! B? As formulated above, the homomorphism problem is uniform in the sense that both relational structures A and B are part of the input. By fixing the structure B, one obtains the following nonuniform problem: given a finite relational structure A, is there a homomorphism h : A ! B? In general, nonuniform tractability results do not uniformize. Thus, it is natural to ask: which tractable cases of nonuniform tractability results for constraint satisfaction and conjunctivequery containment do uniformize? Our main technical contribution in this paper is to show that several cases of tractable nonuniform constraint satisfaction problems do indeed uniformize. We exhibit three nonuniform tractability results that uniformize and, thus, give rise to polynomialtime solvable cases of constraint satisfaction and conjunctivequery containment.
The expressive powers of logic programming semantics
 Abstract in Proc. PODS 90
, 1995
"... We study the expressive powers of two semantics for deductive databases and logic programming: the wellfounded semantics and the stable semantics. We compare them especially to two older semantics, the twovalued and threevalued program completion semantics. We identify the expressive power of the ..."
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Cited by 86 (5 self)
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We study the expressive powers of two semantics for deductive databases and logic programming: the wellfounded semantics and the stable semantics. We compare them especially to two older semantics, the twovalued and threevalued program completion semantics. We identify the expressive power of the stable semantics, and in fairly general circumstances that of the wellfounded semantics. In particular, over infinite Herbrand universes, the four semantics all have the same expressive power. We discuss a feature of certain logic programming semantics, which we call the Principle of Stratification, a feature allowing a program to be built easily in modules. The threevalued program completion and wellfounded semantics satisfy this principle. Over infinite Herbrand models, we consider a notion of translatability between the threevalued program completion and wellfounded semantics which is in a sense uniform in the strata. In this sense of uniform translatability we show the wellfounded semantics to be more expressive than the threevalued program completion. The proof is a corollary of our result that over nonHerbrand infinite models, the wellfounded semantics is more expressive than the threevalued program completion semantics. 1
Extending Classical Logic with Inductive Definitions
, 2000
"... The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of nonmonotonic reasoning, logic programming and deductiv ..."
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Cited by 58 (38 self)
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The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of nonmonotonic reasoning, logic programming and deductive databases, and to show its application for knowledge representation by giving a typology of definitional knowledge.
Describing Graphs: a FirstOrder Approach to Graph Canonization
, 1990
"... In this paper we ask the question, "What must be added to firstorder logic plus leastfixed point to obtain exactly the polynomialtime properties of unordered graphs?" We consider the languages Lk consisting of firstorder logic restricted to k variables and Ck consisting of Lk plus "counting ..."
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Cited by 57 (7 self)
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In this paper we ask the question, "What must be added to firstorder logic plus leastfixed point to obtain exactly the polynomialtime properties of unordered graphs?" We consider the languages Lk consisting of firstorder logic restricted to k variables and Ck consisting of Lk plus "counting quantifiers". We give efficient canonization algorithms for graphs characterized by Ck or Lk . It follows from known results that all trees and almost all graphs are characterized by C2 .
A Procedural Semantics for Well Founded Negation in Logic Programs
 Journal of Logic programming
, 1989
"... We introduce global SLSresolution, a procedural semantics for wellfounded negation as defined by Van Gelder, Ross and Schlipf. Global SLSresolution extends Przymusinski 's SLSresolution, and may be applied to all programs, whether locally stratified or not. 1 Global SLSresolution is defined in ..."
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Cited by 54 (2 self)
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We introduce global SLSresolution, a procedural semantics for wellfounded negation as defined by Van Gelder, Ross and Schlipf. Global SLSresolution extends Przymusinski 's SLSresolution, and may be applied to all programs, whether locally stratified or not. 1 Global SLSresolution is defined in terms of global trees, a new data structure representing the dependence of goals on derived negative subgoals. We prove that global SLSresolution is sound with respect to the wellfounded semantics, and complete for nonfloundering queries. While not effective in general, global SLSresolution is effective for classes of "acyclic" programs, and can be augmented with a memoing device to be effective for all functionfree programs. This research was supported by the National Science Foundation under grant IRI8722886, by a grant from IBM Corporation, and by the United States Air Force Office of Scientific Research under contract AFOSR880266. A preliminary version of this paper was presen...