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.

翻译：本文提出了关系代数相对于一阶逻辑允许公式完备性的另一种证明。该证明基于关系代数到柱体代数的著名嵌入，这使得以更代数化的方式建立完备性成为可能。基于此证明，我们提出了一种替代算法，可生成与给定允许公式等价的关系表达式。本研究的主要动机在于建立一种适合推广到处理不完整或模糊信息的关系模型的完备性证明。