By Gabriel Kuper, Leonid Libkin, Jan Paredaens
This publication is the 1st complete survey of the sector of constraint databases. Constraint databases are a pretty new and lively quarter of database study. the foremost inspiration is that constraints, comparable to linear or polynomial equations, are used to symbolize huge, or perhaps countless, units in a compact method. the facility to house limitless units makes constraint databases fairly promising as a expertise for integrating spatial and temporal facts with normal re lational databases. Constraint databases carry innovations from various fields, resembling good judgment and version idea, algebraic and computational geometry, in addition to symbolic computation, to the layout and research of information versions and question languages. The publication is a collaborative attempt regarding many authors who've con tributed chapters on their fields of workmanship. regardless of this, the e-book is designed to be learn as an entire, in preference to a set 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 overdue Paris Kanellakis.
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Note that in this definition we are being very formal, using square brackets cp[a] to denote interpretations for free variables; however, in the sequel, we shall also use a more intuitive notation with round brackets cp(a). 2. ) . ). 1 Quantifier Elimination We now introduce a very important concept in the context of constraint databases. 3. Structure M is said to admit quantifier elimination if for every first-order formula
While linear constraint systems are easier to implement, they may appear to be too restrictive in the type of data they can represent; however, linear constraints turn out to be sufficient in many real-life applications, including, in particular, GIS (Geographical Information Systems) . To illustrate how linear constraints can be used to describe a specific spatial database, consider the following example, representing an approximate map of Belgium (a real map will have many more constraints, but the basic ideas are the same) .
The formula corresponding to a constraint relation r is the disjunction '1/JI V · · · V 'ljJ M. We denote this formula by 'Pr; note that it is quantifier-free. 4- A constraint database is a finite collection of constraint relations. In database theory, a k-ary relation r is assumed to be a finite set of ktuples (or points in a k-dimensional space). We shall use the term unrestricted relation for arbitrary finite or infinite sets of points in a k-dimensional space. One can develop query languages using such unrestricted relations; however, in order to be able to do something useful with them, we need a finite representation that can be manipulated.