The Budget-Constrained Functional Dependency

TL;DR

This paper extends Armstrong's axioms for functional dependencies to include attribute costs, providing a complete logical system for reasoning under budget constraints in database attribute dependencies.

Contribution

It introduces a novel extension of Armstrong's axioms with cost considerations and proves the completeness of this new logical system.

Findings

Proposed a cost-augmented logical system for functional dependencies.

Proved the completeness theorem for the new system.

Enhanced reasoning capabilities under budget constraints.

Abstract

Armstrong's axioms of functional dependency form a well-known logical system that captures properties of functional dependencies between sets of database attributes. This article assumes that there are costs associated with attributes and proposes an extension of Armstrong's system for reasoning about budget-constrained functional dependencies in such a setting. The main technical result of this article is the completeness theorem for the proposed logical system. Although the proposed axioms are obtained by just adding cost subscript to the original Armstrong's axioms, the proof of the completeness for the proposed system is significantly more complicated than that for the Armstrong's system.