Expansion of Codd algebra operations with recursive objects

In this paper, we discuss the relational algebra and recursive relationships between binary and ternary relationships in entity-relationship modeling. We define the interpretation of the recursive tables that can be applied to the complicated relationships having the same participating entities. We propose a new approach to modeling that is suitable for representing self-similar objects and for creating hierarchical structures. It combines methods of the set theory for the recursive relations within a single modeling paradigm, allowing users to define self-similar, partially self-similar, or hierarchical systems in a consistent and flexible manner. The use of recursive relationships in the definitions of self-similar objects yields representations that can be rendered at varying levels of detail or precision at run time.