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Big Data Integration Theory: Theory and Methods of Database Mappings, Programming Languages, and Semantics [Kõva köide]

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  • Formaat: Hardback, 516 pages, kõrgus x laius: 235x155 mm, kaal: 9221 g, 170 Illustrations, black and white; XX, 516 p. 170 illus., 1 Hardback
  • Sari: Texts in Computer Science
  • Ilmumisaeg: 05-Feb-2014
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 331904155X
  • ISBN-13: 9783319041551
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Big Data Integration Theory: Theory and Methods of Database Mappings, Programming Languages, and SemanticsSuurem pilt
  • Formaat: Hardback, 516 pages, kõrgus x laius: 235x155 mm, kaal: 9221 g, 170 Illustrations, black and white; XX, 516 p. 170 illus., 1 Hardback
  • Sari: Texts in Computer Science
  • Ilmumisaeg: 05-Feb-2014
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 331904155X
  • ISBN-13: 9783319041551
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319041551.html
Märksõnad:
This book presents a novel approach to database concepts, describing a categorical logic for database schema mapping based on views, within a framework for database integration and exchange and peer-to-peer computing. Includes practical examples.

This book presents a novel approach to database concepts, describing a categorical logic for database schema mapping based on views, within a framework for database integration/exchange and peer-to-peer. Database mappings, database programming languages, 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. Features: provides an introduction to logics, co-algebras, databases, schema mappings and category theory; describes the core concepts of big data integration theory, with examples; examines the properties of the DB category; defines the categorial RDB machine; presents full operational semantics for database mappings; discusses matching and merging operators for databases, universal algebra considerations and algebraic lattices of the databases; explores the relationship of the database weak monoidal topos w.r.t. intuitionistic logic.

Arvustused

All topics are studied in detail consistently in terms of category theory. Each chapter of the book ends with a couple of review questions. Textbooks often provide teachers with supplementary material indicating the correct answer surely this will also be the case here. Also by researchers interested in methods of computer science used in databases and logics, and the original contributions a category theory applied to databases will this book be well accepted. (Antonin Riha, zbMATH, Vol. 1325. 68004, 2016)

The author has written a number of papers on data integration theory and this book is a compendium of these papers . It would be an ideal companion for a research student working with theoretical database concepts. (M. S. Krishnamoorthy, Computing Reviews, September, 2014)

1 Introduction and Technical Preliminaries
1(36)
1.1 Historical Background
1(4)
1.2 Introduction to Lattices, Algebras and Intuitionistic Logics
5(7)
1.3 Introduction to First-Order Logic (FOL)
12(4)
1.3.1 Extensions of the FOL for Database Theory
14(2)
1.4 Basic Database Concepts
16(6)
1.4.1 Basic Theory about Database Observations: Idempotent Power-View Operator
18(1)
1.4.2 Introduction to Schema Mappings
19(3)
1.5 Basic Category Theory
22(15)
1.5.1 Categorial Symmetry
30(3)
References
33(4)
2 Composition of Schema Mappings: Syntax and Semantics
37(58)
2.1 Schema Mappings: Second-Order tgds (SOtgds)
37(6)
2.2 Transformation of Schema Integrity Constraints into SOtgds
43(5)
2.2.1 Transformation of Tuple-Generating Constraints into SOtgds
44(2)
2.2.2 Transformation of Equality-Generating Constraints into SOtgds
46(2)
2.3 New Algorithm for General Composition of SOtgds
48(8)
2.3.1 Categorial Properties for the Schema Mappings
54(2)
2.4 Logic versus Algebra: Categorification by Operads
56(27)
2.4.1 R-Algebras, Tarski's Interpretations and Instance-Database Mappings
65(10)
2.4.2 Query-Answering Abstract Data-Object Types and Operads
75(2)
2.4.3 Strict Semantics of Schema Mappings: Information Fluxes
77(6)
2.5 Algorithm for Decomposition of SOtgds
83(6)
2.6 Database Schema Mapping Graphs
89(2)
2.7 Review Questions
91(4)
References
93(2)
3 Definition of DB Category
95(74)
3.1 Why Do We Need a New Base Database Category?
95(9)
3.1.1 Introduction to Sketch Data Models
100(2)
3.1.2 Atomic Sketch's Database Mappings
102(2)
3.2 DB (Database) Category
104(51)
3.2.1 Power-View Endofunctor and Monad T
133(5)
3.2.2 Duality
138(3)
3.2.3 Symmetry
141(6)
3.2.4 (Co)products
147(4)
3.2.5 Partial Ordering for Databases: Top and Bottom Objects
151(4)
3.3 Basic Operations for Objects in DB
155(4)
3.3.1 Data Federation Operator in DB
155(1)
3.3.2 Data Separation Operator in DB
156(3)
3.4 Equivalence Relations in DB Category
159(6)
3.4.1 The (Strong) Behavioral Equivalence for Databases
160(1)
3.4.2 Weak Observational Equivalence for Databases
161(4)
3.5 Review Questions
165(4)
References
167(2)
4 Functorial Semantics for Database Schema Mappings
169(34)
4.1 Theory: Categorial Semantics of Database Schema Mappings
169(8)
4.1.1 Categorial Semantics of Database Schemas
170(3)
4.1.2 Categorial Semantics of a Database Mapping System
173(1)
4.1.3 Models of a Database Mapping System
174(3)
4.2 Application: Categorial Semantics for Data Integration/Exchange
177(22)
4.2.1 Data Integration/Exchange Framework
178(1)
4.2.2 GLAV Categorial Semantics
179(4)
4.2.3 Query Rewriting in GAV with (Foreign) Key Constraints
183(10)
4.2.4 Fixpoint Operator for Finite Canonical Solution
193(6)
4.3 Review Questions
199(4)
References
200(3)
5 Extensions of Relational Codd's Algebra and DB Category
203(48)
5.1 Introduction to Codd's Relational Algebra and Its Extensions
203(12)
5.1.1 Initial Algebras and Syntax Monads: Power-View Operator
209(6)
5.2 Action-Relational-Algebra RA Category
215(21)
5.2.1 Normalization of Terms: Completeness of RA
220(6)
5.2.2 RA versus DB Category
226(10)
5.3 Relational Algebra and Database Schema Mappings
236(2)
5.4 DB Category and Relational Algebras
238(9)
5.5 Review Questions
247(4)
Reference
249(2)
6 Categorial RDB Machines
251(46)
6.1 Relational Algebra Programs and Computation Systems
251(11)
6.1.1 Major DBMS Components
257(5)
6.2 The Categorial RBD Machine
262(22)
6.2.1 The Categorial Approach to SQL Embedding
271(6)
6.2.2 The Categorial Approach to the Transaction Recovery
277(7)
6.3 The Concurrent-Categorial RBD Machine
284(10)
6.3.1 Time-Shared DBMS Components
289(2)
6.3.2 The Concurrent Categorial Transaction Recovery
291(3)
6.4 Review Questions
294(3)
Reference
296(1)
7 Operational Semantics for Database Mappings
297(76)
7.1 Introduction to Semantics of Process-Programming Languages
297(3)
7.2 Updates Through Views
300(9)
7.2.1 Deletion by Minimal Side-Effects
302(3)
7.2.2 Insertion by Minimal Side-Effects
305(4)
7.3 Denotational Model (Database-Mapping Process) Algebra
309(24)
7.3.1 Initial Algebra Semantics for Database-Mapping Programs
314(3)
7.3.2 Database-Mapping Processes and DB-Denotational Semantics
317(16)
7.4 Operational Semantics for Database-Mapping Programs
333(8)
7.4.1 Observational Comonad
338(2)
7.4.2 Duality and Database-Mapping Programs: Specification Versus Solution
340(1)
7.5 Semantic Adequateness for the Operational Behavior
341(25)
7.5.1 DB-Mappings Denotational Semantics and Structural Operational Semantics
348(11)
7.5.2 Generalized Coinduction
359(7)
7.6 Review Questions
366(7)
References
369(4)
8 The Properties of DB Category
373(82)
8.1 Expressive Power of the DB Category
373(39)
8.1.1 Matching Tensor Product
377(4)
8.1.2 Merging Operator
381(2)
8.1.3 (Co)Limits and Exponentiation
383(9)
8.1.4 Universal Algebra Considerations
392(6)
8.1.5 Algebraic Database Lattice
398(14)
8.2 Enrichment
412(10)
8.2.1 DB Is a V-Category Enriched over Itself
414(6)
8.2.2 Internalized Yoneda Embedding
420(2)
8.3 Database Mappings and (Co)monads: (Co)induction
422(23)
8.3.1 DB Inductive Principle and DB Objects
426(10)
8.3.2 DB Coinductive Principle and DB Morphisms
436(9)
8.4 Kleisli Semantics for Database Mappings
445(5)
8.5 Review Questions
450(5)
References
453(2)
9 Weak Monoidal DB Topos
455(60)
9.1 Topological Properties
455(14)
9.1.1 Database Metric Space
456(3)
9.1.2 Subobject Classifier
459(4)
9.1.3 Weak Monoidal Topos
463(6)
9.2 Intuitionistic Logic and DB Weak Monoidal Topos
469(40)
9.2.1 Birkhoff Polarity over Complete Lattices
472(7)
9.2.2 DB-Truth-Value Algebra and Birkhoff Polarity
479(11)
9.2.3 Embedding of WMTL (Weak Monoidal Topos Logic) into Intuitionistic Bimodal Logics
490(8)
9.2.4 Weak Monoidal Topos and Intuitionism
498(11)
9.3 Review Questions
509(6)
References
512(3)
Index 515
Dr. Zoran Majki is Chief Technology Advisor at Jumper Consulting Investment Ltd., Dublin, Ireland. He is also affiliated with the International Society for Research in Science and Technology, Tallahassee, FL, USA.