Towards declarative comparabilities: application to functional dependencies

TL;DR

This paper introduces a lattice-based declarative framework to handle context-dependent equality testing in databases, generalizing functional dependencies to accommodate various interpretations of equality.

Contribution

It proposes a novel high-level framework for specifying multiple semantics of equality and extends functional dependencies within this context, including complexity analysis.

Findings

Defined abstract functional dependencies generalizing classical FDs

Introduced notions of possible and certain FDs based on realities

Provided complexity results for the new framework

Abstract

In real life, data are often of poor quality as a result, for instance, of uncertainty, mismeasurements, missing values or bad inputs. This issue hampers an implicit yet crucial operation of every database management system: equality testing. Indeed, equality is, in the end, a context-dependent operation with a plethora of interpretations. In practice, the treatment of different types of equality is left to programmers, who have to struggle with those interpretations in their code. We propose a new lattice-based declarative framework to address this problem. It allows specification of numerous semantics for equality at a high level of abstraction. To go beyond tuple equality, we study functional dependencies (FDs) in the light of our framework. First, we define abstract FDs, generalizing classical FDs. These lead to the consideration of particular interpretations of equality: realities. Building upon realities and possible/certain answers, we introduce possible/certain FDs and give some related complexity results.