Foundations of Databases: The Logical Level by Serge Abiteboul, Richard Hull, Victor Vianu

By Serge Abiteboul, Richard Hull, Victor Vianu

Written by means of 3 prime researchers within the box, this publication presents in-depth assurance of the idea in regards to the logical point of database administration platforms, together with either classical and complicated issues. good points *Emphasizes question languages for the relational version together with insurance of alternative language paradigms, expressive strength, and complexity. *Presents a unified concept of dependencies, together with these often coming up in perform, and their use in optimization and schema layout. *Provides theoretical underpinnings of numerous rising themes, together with deductive and object-oriented databases. *Includes distinct proofs and various examples and workouts. 0201537710B04062001

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Given a term t in U , the function F(S) maps t to the term S(t). Given terms t1 and t2, the function F(+) maps the pair (t1, t2) to the term +(t1, t2), and the function F(×) is defined analogously. , the set of atoms that do not contain variables) is sometimes called the Herbrand base of LN . There is a natural one-one correspondence 24 Theoretical Background between interpretations of LN that extend the Herbrand preinterpretation and subsets of the Herbrand base of LN . One Herbrand interpretation of particular interest is the one that mimics the usual interpretation.

One Herbrand interpretation of particular interest is the one that mimics the usual interpretation. In particular, this interpretation maps ≤ to the set I I {(t1, t2) | (t1 N , t2 N ) ∈ ≤IN }. We now turn to the notion of satisfaction of a formula by an interpretation. The definition is recursive on the structure of formulas; as a result we need the notion of variable assignment to accommodate variables occurring free in formulas. Let L be a language and I an interpretation of L with universe U .

3 Basics from Logic The field of mathematical logic is a main foundation for database theory. It serves as the basis for languages for queries, deductive databases, and constraints. We briefly review the basic notions and notations of mathematical logic and then mention some key differences between this logic in general and the specializations usually considered in database theory. The reader is referred to [EFT84, End72] for comprehensive introductions to mathematical logic, and to the chapter [Apt91] in [Lee91] and [Llo87] for treatments of Herbrand models and logic programming.

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