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Matching dependencies were recently introduced as declarative rules for datacleaning and entity resolution. Enforcing a matching dependency on a databaseinstance identifies the values of some attributes for two tuples, provided thatthe values of some other attributes are sufficiently similar. Assuming theexistence of matching functions for making two attributes values equal, weformally introduce the process of cleaning an instance using matchingdependencies, as a chase-like procedure. We show that matching functionsnaturally introduce a lattice structure on attribute domains, and a partialorder of semantic domination between instances. Using the latter, we define thesemantics of clean query answering in terms of certain/possible answers as thegreatest lower bound/least upper bound of all possible answers obtained fromthe clean instances. We show that clean query answering is intractable in somecases. Then we study queries that behave monotonically wrt semantic dominationorder, and show that we can provide an under/over approximation for cleananswers to monotone queries. Moreover, non-monotone positive queries can berelaxed into monotone queries.

Data Cleaning and Query Answering with Matching Dependencies and Matching Functions