2009/02/20 by Vadim Tropashko, Tropashko, Vadim
Computer Science · #Advanced Algebra and Logic #Advanced Database Systems and Queries #Databases (cs.DB) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.0902.3532
openalex publication_date 2009/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Relational Lattice is a succinct mathematical model for Relational Algebra. It reduces the set of six classic relational algebra operators to two: natural join and inner union. In this paper we push relational lattice theory in two directions. First, we uncover a pair of complementary lattice operators, and organize the model into a bilattice of four operations and four distinguished constants. We take a notice a peculiar way bilattice symmetry is broken. Then, we give axiomatic introduction of unary negation operation and prove several laws, including double negation and De Morgan. Next we reduce the model back to two basic binary operations and twelve axioms, and exhibit a convincing argument that the resulting system is complete in model-theoretic sense. The final parts of the paper casts relational lattice perspective onto database dependency theory and into cylindric algebras.