Handling Inconsistencies in Tables with Nulls and Functional Dependencies

In this paper we address the problem of handling inconsistencies in tables with missing values (or nulls) and functional dependencies. Although the traditional view is that table instances must respect all functional dependencies imposed on them, it is nevertheless relevant to develop theories about how to handle instances that violate some dependencies. The usual approach to alleviate the impact of inconsistent data on the answers to a query is to introduce the notion of repair: a repair is a minimally di?erent consistent instance and an answer is consistent if it is present in every repair. Our approach is fundamentally di?erent: we use set theoretic semantics for tuples and functional dependencies that allow us to associate each tuple with a truth value among the following: true, false, inconsistent or unknown. The users of the table can then query the set of true tuples as usual. Regarding missing values, we make no assumptions on their existence: a missing value exists only if it is inferred from the functional dependencies of the table. The main contributions of the paper are the following: (a) we introduce a new approach to handle inconsistencies in a table with nulls and functional dependencies, (b) we give algorithms for computing all true, inconsistent and false tuples, (c) we discuss how our approach relates to Belnap's four valued logic, (d) we de- scribe how our approach can be applied to the consolidation of two or more tables and (e) we discuss the relationship between our approach and that of table repairs.