Completeness of Relational Algebra via Cylindric Algebra

Jan Laštovička

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arXiv · 2603.15099

Completeness of Relational Algebra via Cylindric Algebra

Jan Laštovička

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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.

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Jan Laštovička. 2026-03-16. Completeness of Relational Algebra via Cylindric Algebra. https://arxiv.org/abs/2603.15099

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