Abstract
Data exchange is the problem of transforming data structured according to a source schema into data structured according to a target schema, via a mapping specified by means of rules in the form of source-to-target tuple generating dependencies – rules whose body is a conjunction of atoms over the source schema and the head is a conjunction of atoms over the target schema, with possibly existential variables in the head. With this formalization, given a fixed source database, there might be more than one target databases satisfying a given mapping. That is, the target database is actually an incomplete database represented by a set of possible databases. Therefore, the problem of query answering the target data is inherently complex for general (non-positive) relational or aggregate queries.