This is joint work with Floris Geerts of Edinburgh.
A schema-mapping is a high-level specification of a data-exchange
setting with source-to-target dependencies (encoding basic operations
such as copy, selection, join or union)
and target dependencies (such as inclusion dependencies and key
constraints over the target schema).
The first part of the talk will focus on the standard implication
problem which consists in checking whether a given property holds for
every source database and every solution of a given schema-mapping.
While the problem is in general undecidable, we will see that some
reasonable termination conditions can be used to ensure a good
data-complexity. We will also observe that this framework can be
generalized to strong schema-mappings which, unlike standard
schema-mappings, allow to express disjunctive dependencies and
complete views. In turn, this generalized framework will be shown
useful to decide, in a given schema-mapping, whether a target query is
relatively complete and/or determined by the source.
The second part of the talk focuses on a more involved problem of
implication which also takes in account the fact that the solutions
computed by standard data-exchange tools are not arbitrary. Two
particular settings will be discussed that allow to reach decidability
for this second implication problem: a first setting relying on a
notion of core-semantics (the solutions are assumed to be of minimal
size), and a second setting relying on a more flexible notion of
closed-world semantics.
