Axiomatizing approximate inclusion

TL;DR

This paper introduces two approximate inclusion dependency variants, analyzes their axiomatization and complexity, and provides decidability results under certain restrictions using team semantics.

Contribution

It presents novel approximate inclusion dependencies, explores their axiomatization, and establishes complexity and decidability results with team semantics.

Findings

Complete axiomatizations for both variants under arity restrictions

Implication problem for unary dependencies is decidable in PTIME

Formalization using team semantics for database interpretation

Abstract

We introduce two approximate variants of inclusion dependencies and examine the axiomatization and computational complexity of their implication problems. The approximate variants allow for some imperfection in the database and differ in how this degree is measured. One considers the error relative to the database size, while the other applies a fixed threshold independent of size. We obtain complete axiomatizations for both under some arity restrictions. In particular, restricted to unary inclusion dependencies, the implication problem for each approximate variant is decidable in PTIME. We formalise the results using team semantics, where a team corresponds to a uni-relational database.