Database and database systems have become an essential part of everyday life, such as in banking activities, online shopping, or reservations of airline tickets and hotels. These trends place more demands on the capabilities of future database systems, which need to evolve into decision making systems based on data from multiple sources with varying reliability. In this book a model for the next generation of database systems is presented. It is demonstrated how to quantize favorable and unfavorable qualitative facts so that they can be stored and processed efficiently, as well as how to use the reliability of the contributing sources in our decision makings. The concept of a confidence index set (ciset), is introduced in order to mathematically model the above issues. A simple introduction to relational database systems is given allowing anyone with no background in database theory to appreciate the further contents of this work, especially the extended relational operations and semantics of the ciset relational database model.

A Mathematical Model for the New Generation of Databases Includes a simple introduction to relational databases systems New concept of a confidence index set (ciset) Includes supplementary material: sn.pub/extras

Inhalt
1 Ciset.- 1.1 Confidence Index.- 1.2 Confidence Index Set.- 1.3 Basic Operations.- 1.4 Relations.- 2 The Relational Model.- 2.1 Formalization of Relation.- 2.2 Integrity Constraints.- 2.3 The Relational Operators.- 3 The Ciset Relational Model.- 3.1 Formalization of Ciset Relation.- 3.2 Integrity Constraints.- 4 The Ciset Relational Algebra.- 4.1 Union, Intersection and Difference.- 4.2 Select and Project.- 4.3 Product and Join.- 4.4 Equi-join and Theta-join.- 4.5 Divide.- 5 Alternate Worlds.- 5.1 Introduction.- 5.2 Precision of Ciset Relational Operations.- 6 Additional Ciset Operations.- 6.1 Confidence Index Operations.- 6.2 Ciset Operations.- 6.3 C-relations.- 7 Information Source Tracking.- 7.1 The IST Model.- 7.2 Alternate Worlds.- 7.3 Extended Relational Algebra Operations.- 7.4 Probabilistic Approach.- References.- List of Figures.- List of Tables.