On the Interaction of Inclusion Dependencies with Independence Atoms

Abstract

Inclusion dependencies are one of the most important database constraints. In isolation their finite and unrestricted implication problems coincide, are finitely axiomatizable, PSPACE-complete, and fixed-parameter tractable in their arity. In contrast, finite and unrestricted implication problems for the combined class of functional and inclusion dependencies deviate from one another and are each undecidable. The same holds true for the class of embedded multivalued dependencies. An important embedded tractable fragment of embedded multivalued dependencies are independence atoms. These stipulate independence between two attribute sets in the sense that for every two tuples there is a third tuple that agrees with the first tuple on the first attribute set and with the second tuple on the second attribute set. For independence atoms, their finite and unrestricted implication problems coincide, are finitely axiomatizable, and decidable in cubic time. In this article, we study the implication problems of the combined class of independence atoms and inclusion dependencies. We show that their finite and unrestricted implication problems coincide, are finitely axiomatizable, PSPACE-complete, and fixed-parameter tractable in their arity. Hence, significant expressivity is gained without sacrificing any of the desirable properties that inclusion dependencies have in isolation. Finally, we establish an efficient condition that is sufficient for independence atoms and inclusion dependencies not to interact. The condition ensures that we can apply known algorithms for deciding implication of the individual classes of independence atoms and inclusion dependencies, respectively, to decide implication for an input that combines both individual classes.