Relational Lattice Axioms
Marshall Spight, Vadim Tropashko
TL;DR
This paper explores the axiomatic foundations of relational lattice theory, simplifying relational algebra to two core operations and extending its formal properties with new axioms and practical applications.
Contribution
It introduces new axioms, an equational definition for set difference, and demonstrates how relational lattice theory can be applied to query transformations.
Findings
Added axioms for relational lattice
Equational definition for set difference (anti-join)
Case study on query transformation applications
Abstract
Relational lattice is a formal mathematical model for Relational algebra. It reduces the set of six classic relational algebra operators to two: natural join and inner union. We continue to investigate Relational lattice properties with emphasis onto axiomatic definition. New results include additional axioms, equational definition for set difference (more generally anti-join), and case study demonstrating application of the relational lattice theory for query transformations.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rough Sets and Fuzzy Logic · Logic, Reasoning, and Knowledge