Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema. Given a source instance, there may be many solutions - target instances that satisfy the constraints of the data exchange problem. Previous work has identified two classes of desirable solutions: canonical universal solutions, and their cores. Query answering in data exchange amounts to rewriting a query over the target schema to another query that, over a materialized target instance, gives the result that is semantically consistent with the source. A basic question is then whether there exists a transformation sending a source instance into a solution over which target queries can be answered.
In this talk, we show that the answer is negative for many data exchange transformations that have structural properties similar to the canonical universal solution and the core. Namely, we prove that many such transformations preserve the "local" structure of the data. Using this notion, we further show that every target query rewritable over such a transformation cannot distinguish tuples whose neighborhoods in the source are similar. This gives us a first tool that helps check whether a query is rewritable.
This is joint work with Pablo Barcelo, Ronald Fagin and Leonid Libkin.