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Universal Algebra, Algebraic Logic, and Databases : Mathematics and Its Applications - B. I. Plotkin

Universal Algebra, Algebraic Logic, and Databases

Mathematics and Its Applications


Published: 31st January 1994
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This volume is devoted to the development of an algebraic model of databases. The first chapter presents a general introduction. The following sixteen chapters are divided into three main parts. Part I deals with various aspects of universal algebra. The chapters of Part I discuss topics such as sets, algebras and models, fundamental structures, categories, the category of sets, topoi, fuzzy sets, varieties of algebras, axiomatic classes, category algebra and algebraic theories.
Part II deals with different approaches to the algebraization of predicate calculus. This material is intended to be applied chiefly to databases, although some discussion of pure algebraic applications is also given. Discussed here are topics such as Boolean algebras and propositional calculus, Halmos algebras and predicate calculus, connections with model theory, and the categorial approach to algebraic logic.
Part III is concerned specifically with the algebraic model of databases, which considers the database as an algebraic structure. Topics dealt with in this part are the algebraic aspects of databases, their equivalence and restructuring, symmetries and the Galois theory of databases, and constructions in database theory. The volume closes with a discussion and conclusions, and an extensive bibliography.
For mathematicians, computer scientists and database engineers, with an interest in applications of algebra and logic.

Introductionp. 1
General View on Objectives and Contents of the Bookp. 3
Universal Algebrap. 27
Sets, Algebras, Modelsp. 29
Fundamental Structuresp. 47
Categoriesp. 65
The Category of Sets. Topoi. Fuzzy Setsp. 85
Varieties of Algebras. Axiomatizable Classesp. 115
Category Algebra and Algebraic Theoriesp. 129
Algebraic Logicp. 153
Boolean Algebras and Propositional Calculusp. 155
Halmos Algebras and Predicate Calculusp. 173
Specialized Halmos Algebrasp. 201
Connections with Model Theoryp. 229
The Categorial Approach to Algebraic Logicp. 247
Databases - Algebraic Aspectsp. 275
Algebraic Model of a Databasep. 277
Equivalence and Reorganization of Databasesp. 305
Symmetries of Relations and Galois Theory of Databasesp. 329
Constructions in Database Theoryp. 365
Discussion and Conclusionp. 389
Bibliographyp. 423
Indexp. 434
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792326656
ISBN-10: 0792326652
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 438
Published: 31st January 1994
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 3.18
Weight (kg): 1.81