Database Reference
In-Depth Information
5. The translation of the Data integration framework into the functorial sketch's
based semantics, provided in example in Sects.
4.2.2
and
4.2.3
, is not an equiv-
alent representation because in Data Integration framework we do not provide
the materialization of its global schema, while in the functorial semantics each
schema is mapped into an instance data base of such a schema. Is it a unique
semantic difference? How is the problem with incomplete information in Data
Integration (with a class of possible models) resolved in the functorial seman-
tics? The certain answers to the queries over a global schema in Data Integration
framework are true in all models of the global schema. How can the certain an-
swers be provided in the functorial semantics with SOtgds (with the introduction
of the Skolem constants)?
6. Provide an example by modification of Example
27
of Data Integration in
Sects.
4.2.3
and
4.2.4
by dividing the global schema into two separate databases,
one containing only the binary relation
r
and the second only the binary relation
s
, and by substituting the FK constraints by two corresponding mappings be-
tween these two databases. The operational semantics for these two data mapping
representations will be equal (by considering that in Example
27
we obtained an
acyclic mapping graph, while in this new setting we obtain a cyclic graph) and,
if not, why?
7. Consider the modified version of Example
27
. Why can't the fixpoint operator for
a finite solution be used in a standard Data Integration framework, while, instead,
it can be realized in the functorial semantics with the operational semantics based
on the fixpoint operator for such a cyclic database mapping system?
Clearly, the model of such a mapping system will be composed by two
databases above, with relations containing an infinite number of tuples. Is this
fixpoint semantics, which do not produce a finite model of the database map-
ping system (but is equivalent for the certain-answer semantics for the query-
answering system, where the Skolem constants are eliminated from resulting
views), the way to resolve the cyclic database mapping systems containing in-
complete information (and hence with the possibly infinite models) in practice?
Is there another equivalently valid solution?
8. Can we obtain in this framework the infinite databases without using infinite
number of Skolem constants? Why is it necessary to theoretically consider the
infinite databases also for the cyclic database mapping systems, if we have the
fixpoint semantics provided above in order to obtain only the finite databases with
the same power to provide the certain-answers to the database queries? (Consider
the whole process of the algebraization of the SOtgds and the logic semantics of
the mappings.)
References
1. M. Barr, C. Wells,
Toposes, Triples and Theories
. Grundelehren der math. Wissenschaften,
vol. 278 (Springer, Berlin, 1985)
