On Desirable Semantics of Functional Dependencies over Databases with Incomplete Information

Abstract

Codd's relational model describes just one possible world. To better cope with incomplete information, extended database models allow several possible worlds. Vague tables are one such convenient extended model where attributes accept sets of possible values (e.g., the manager is either Jill or Bob). However, conceptual database design in such cases remains an open problem. In particular, there is no canonical definition of functional dependencies (FDs) over possible worlds (e.g., each employee has just one manager). We identify several desirable properties that the semantics of such FDs should meet including Armstrong's axioms, the independence from irrelevant attributes, seamless satisfaction and implied by strong satisfaction. We show that we can define FDs such that they have all our desirable properties over vague tables. However, we also show that no notion of FD can satisfy all our desirable properties over a more general model (disjunctive tables). Our work formalizes a trade-off between having a general model and having well-behaved FDs.

Discovery of genuine functional dependencies from relational data with missing values

“…There has been some work on probabilistic FDs that might hold on the data with some probability [10,34]. Recently, there has been some proposals to extend the semantics of FDs under NULL markers [1,2]. However, none of the FD mining algorithms questions whether the discovered FDs are genuine FDs or not.…”