On the Interaction of Functional and Inclusion Dependencies with Independence Atoms

TL;DR

This paper investigates the logical implications of combined database dependencies, showing that certain classes, including independence atoms and unary dependencies, are decidable and axiomatizable efficiently in both finite and unrestricted cases.

Contribution

It establishes that implication problems for combined classes of independence atoms, unary functional, and unary inclusion dependencies are decidable and axiomatizable in polynomial time.

Findings

Implication problems for combined classes are decidable in polynomial time.

Finite and unrestricted implication problems are axiomatizable.

Independence atoms and unary dependencies form a tractable fragment.

Abstract

Infamously, the finite and unrestricted implication problems for the classes of i) functional and inclusion dependencies together, and ii) embedded multivalued dependencies alone are each undecidable. Famously, the restriction of i) to functional and unary inclusion dependencies in combination with the restriction of ii) to multivalued dependencies yield implication problems that are still different in the finite and unrestricted case, but each are finitely axiomatizable and decidable in low-degree polynomial time. An important embedded tractable fragment of embedded multivalued dependencies are independence atoms that stipulate independence between two attribute sets. We establish a series of results for implication problems over subclasses of the combined class of functional and inclusion dependencies as well as independence atoms. One of our main results is that both finite and unrestricted implication problems for the combined class of independence atoms, unary functional and unary inclusion dependencies are axiomatizable and decidable in low-degree polynomial time.