Recovery from Inconsistency in Incomplete Relations

It is not always possible to avoid inconsistency of a set of constraints in a database, for example in a legacy database where we are given an out of date set of constraints which may have changed due to maintenance. Thus we need some mechanism to reassess the set of constraints in order to recover from this inconsistency. We tackle this problem concentrating on the situation when the constraints are a set of functional dependencies (FDs) and the database may be incomplete. The approach we take to alleviate this problem is to consider as the correct semantics the maximally consistent subsets of the given set of FDs in the incomplete relation. We show how to compute all the maximally consistent subsets, although, in general, this computation is shown to be intractable. We then investigate the dependency inference problem for FDs in incomplete relations, which can be viewed as a data mining application of our approach to dealing with inconsistency. Finally, we show that Lien and Atzeni's axiomatisation of FDs in incomplete relations can be given semantics in terms of a reened family of maximally consistent sets of FDs.