Monoidal functional dependencies

TL;DR

This paper develops a complete logical framework for reasoning about advanced functional dependencies that incorporate similarity and ordering, extending traditional FDs with richer semantic expressiveness.

Contribution

It introduces a novel logic for functional dependencies based on ordered monoids and residuated lattices, providing a complete axiomatization and exploring semantic and computational aspects.

Findings

Complete axiomatization of the logic using Armstrong-like rules

Expressiveness of dependencies for similarity and ordering

Discussion of computational and semantic considerations

Abstract

We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express stronger relationships between attribute values than the ordinary FDs. In our setting, the dependencies not only express that certain values are determined by others but also express that similar values of attributes imply similar values of other attributes. We show complete axiomatization using a system of Armstrong-like rules, comment on related computational issues, and the relational vs. propositional semantics of the dependencies.