Completeness of Relational Algebra via Cylindric Algebra

TL;DR

This paper provides an algebraic proof of the completeness of relational algebra using cylindric algebra and introduces an algorithm for generating equivalent relational expressions, aiming to extend to incomplete or vague information models.

Contribution

It offers a new algebraic proof of relational algebra's completeness and an algorithm for expression generation, facilitating future work on incomplete or vague data models.

Findings

Algebraic proof of relational algebra completeness

Algorithm for generating equivalent relational expressions

Potential extension to incomplete or vague information models

Abstract

An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it possible to establish completeness in a more algebraic way. Building on this proof, we present an alternative algorithm that produces a relational expression equivalent to a given allowed formula. The main motivation for the present work is to establish a proof of completeness suitable for generalisation to relational models handling incomplete or vague information.