Completeness of Relational Algebra via Cylindric Algebra
Logic in Computer Science
2026-03-17 v1 Databases
Logic
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.
Cite
@article{arxiv.2603.15099,
title = {Completeness of Relational Algebra via Cylindric Algebra},
author = {Jan Laštovička},
journal= {arXiv preprint arXiv:2603.15099},
year = {2026}
}