Database Reference
In-Depth Information
Our approach is very close to the model management approach, however, with
denotational semantics based on the theory of category sketches. In fact, here we
define a composition of database schema mappings and two principal algebraic op-
erators for DBMS composition of database schemas (data separation and data fed-
eration), which are used for composition of complex schema mappings graphs. At
the instance database level, we define also the matching and merging algebraic op-
erators for databases and the perfect inverse mappings.
Most of the work in the data integration/exchange and peer-to-peer (P2P) frame-
work is based on a logical point of view (particularly for the integrity constraints,
in order to define the right models for certain answers) in a 'local' mode (source-
to-target database) where proper attention to the general 'global' problem of the
compositions
of complex partial mappings which possibly involve a high number of
databases has not been given. Today, this 'global' approach cannot be avoided be-
cause of the necessity of P2P open-ended networks of heterogenous databases. The
aim of this work is a
definition of a
DB
category for the database mappings
which
has to be more suitable than a generic
Set
domain category since the databases are
more complex structures w.r.t. the sets and the mappings between them are so com-
plex that they cannot be represented by a
single
function (which is one arrow in
Set
). Why do we need an enriched categorical semantic domain for the databases?
We will try, before an exhaustive analysis of the problem presented in next two
chapters, to give a partial answer to this question.
•
This work is an attempt to give a proper solution for a general problem of com-
plex database-mappings and for the high-level algebra operators of the databases
(merging, matching, etc.), by preserving the traditional common practice logical
language for schema database mapping definitions.
•
The schema mapping specifications are not the integral parts of the standard
relational-database theory (used to define a database schema with its integrity
constraints); they are the
programs
and we need an enriched denotational se-
mantics context that is able to formally express these programs (derived by the
mappings between the databases).
•
Let us consider, for example, the P2P systems or the mappings in a complex
data warehouse. We would like to have a synthetic graphical representations of
the database mappings and queries, and to be able to develop a graphical tool
for the meta-mapping descriptions of complex (and partial) mappings in various
contexts, with a formal mathematical background.
Only a limited amount of research has been reported in the literature [
2
,
14
,
22
,
42
,
43
,
62
,
67
] that addressed the general problem presented in this topic. One of these
works uses category theory [
2
]. However, it is too restrictive: institutions can only
be applied to the simple
inclusion
mappings between databases.
A lot of work has been done for a sketch-based and fibrational formulation of de-
notational semantics for databases [
16
,
31
,
32
,
37
,
70
]. But all these works are using
the elements of an ER-scheme of a database, such as relations, attributes, etc., as the
objects of a sketch category but not the
whole databases
as a single object. Hence
we need a framework of inter-database mappings. The main difference between the
previous categorial approaches to databases and this one is the
level
of abstraction
used for the prime objects of the theory.
