Relational Algebra as non-Distributive Lattice

TL;DR

This paper shows that relational algebra can be simplified to two core operations, natural join and generalized union, which form a relationally complete non-distributive lattice, highlighting a fundamental algebraic structure.

Contribution

The paper introduces a minimal operator set for relational algebra that forms a non-distributive lattice, simplifying the theoretical framework.

Findings

Relational algebra operators can be reduced to natural join and generalized union.

The reduced operator set is relationally complete.

The operator set satisfies lattice axioms, including non-distributivity.

Abstract

We reduce the set of classic relational algebra operators to two binary operations: natural join and generalized union. We further demonstrate that this set of operators is relationally complete and honors lattice axioms.