The challenges of big data demand a clear theoretical and algebraicframework, extending the standard relational database (RDB) with more powerful features in order to manage the complex schema mappings.
This unique textbook/reference presents a novel approach to database concepts, describing a categorical logic for database schema mapping based on views, within a very general framework for database integration/exchange and peer-to-peer. Issues of database mappings, database programming languages (algebras), and denotational and operational semantics are discussed in depth. An analysis method is also developed that combines techniques from second order logic, data modeling, co-algebras, and functorial categorial semantics.
Topics and features:
Provides a concise, formal introduction to logics, (co-)algebras, databases, schema mappings and category theoryDescribes the core concepts of big data integration theory, supported by a number of practical examplesExamines the computational properties of the DB category, compared to the extensions of Codd’s SPRJU relational algebra and structured query language (SQL)Defines the abstract computational machine, the categorial RDB machine, able to support all DB computations by SQL embeddingPresents full operational semantics for database mappings (programs)Discusses matching and merging operators (tensors) for databases, universal algebra considerations, and algebraic lattices of the databasesExplores the relationship of the database weak monoidal topos with respect to intuitionistic logic
This self-contained textbook is ideal for graduate courses on database engineering methods, and can also be used as a supplementary text for courses on co-algebras and category theory. Researchers and software engineers interested in databases and logics will also find the book to be a useful reference.
Big Data Integration Theory Theory and Methods of Database Mappings, Programming Languages, and Semantics.pdf
Table of contents :
Content:
Front Matter....Pages I-XX
Introduction and Technical Preliminaries....Pages 1-36
Composition of Schema Mappings: Syntax and Semantics....Pages 37-93
Definition of DB Category....Pages 95-167
Functorial Semantics for Database Schema Mappings....Pages 169-201
Extensions of Relational Codd’s Algebra and DB Category....Pages 203-249
Categorial RDB Machines....Pages 251-296
Operational Semantics for Database Mappings....Pages 297-371
The Properties of DB Category....Pages 373-453
Weak Monoidal DB Topos....Pages 455-513
Back Matter....Pages 515-516
Big Data Integration Theory Theory and Methods of Database Mappings, Programming.rar
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