Theorem about Amplification of Relational Algebra by Recursive Objects

Abstract

This paper discusses relational algebra extended by recursive relations (tables). The interpretation of the recursive table is proposed, the closure of the extended relational algebra is proved, and a new approach to modeling a physical database structure is offered that is suitable for representing complicated hierarchical data sets. It combines methods of set theory for the recursive relations within the framework of a single modeling paradigm, which allows users to define self-similar, partially self-similar, or hierarchical sets. The use of recursive relations in the definitions of self-similar objects yields representations that can be rendered at varying levels of detail or precision at run time.