By Gabriel Kuper, Leonid Libkin, Jan Paredaens

This e-book is the 1st complete survey of the sphere of constraint databases. Constraint databases are a reasonably new and energetic sector of database study. the major notion is that constraints, reminiscent of linear or polynomial equations, are used to symbolize huge, or maybe countless, units in a compact method. the facility to house limitless units makes constraint databases relatively promising as a know-how for integrating spatial and temporal information with regular re lational databases. Constraint databases carry innovations from a number of fields, akin to common sense and version concept, algebraic and computational geometry, in addition to symbolic computation, to the layout and research of knowledge versions and question languages. The ebook is a collaborative attempt concerning many authors who've con tributed chapters on their fields of craftsmanship. regardless of this, the ebook is designed to be learn as a complete, instead of a suite of person surveys. In par ticular, the terminology and the fashion of presentation were standardized, and there are a number of cross-references among the chapters. the assumption of constraint databases is going again to the past due Paris Kanellakis.

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For instance, the classical compactness theorem from first-order model theory implies that any first-order sentence having arbitrary large finite models also has an infinite model, so finiteness of arbitrary unrestricted relations is certainly not expressible in first-order logic. Still, as we shall see shortly, if one focuses (as we do in constraint databases) only on relations that are definable using constraints, finiteness can become expressible in the relational calculus over certain constraint structures M.

The existence of equivalent calculus and algebraic query languages enables the user to write queries in a declarative language (relational calculus, SQL) , while the system can use a procedural language (for example, relational algebra) for evaluating them. query program database input database output

Suppose the formula corresponding to Q~, (D'), 2. Constraint Databases, Queries, and Query Languages after renaming the variables x 1 , ... 'ljJ(y1, . , Yk)· Consider the formula , Xk to y 1 , ... , 35 Yk, respectively, is f\j = Fxj = Yij . Compute a quantifier-free formula"(, equivalent to x, in DNF 'Yl V · · · V "/£· x(x1, ... ,xp) := 3yl ... 3yn'l/J 1\ Then Q~(D') := {"11, .. , 'Yd· - Finally, if e is ao(e'), then Qe(D) := {a I a E Qe' (D) and M f= B(a)}. Suppose the formula corresponding to Q~, (D') is '1/J.