Structure identification in relational data

This paper presents several investigations into the prospects for identifying meaningful structures in empirical data, namely, structures permitting effective organization of the data to meet requirements of future queries. We propose a general framework whereby the notion of identifiability is given a precise formal definition similar to that of learnability. Using this framework, we then explore if a tractable procedure exists for deciding whether a given relation is decomposable into a constraint network or a CNF theory with desirable topology and, if the answer is positive, identifying the desired decomposition. Finally, we address the problem of expressing a given relation as a Horn theory and, if this is impossible, finding the best k-Horn approximation to the given relation. We show that both problems can be solved in time polynomial in the length of the data

On the Interaction of Inclusion Dependencies with Independence Atoms

Proceeding volume: 46Inclusion 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 de- pendencies 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 inter- act. 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.Peer reviewe