Databases Reference
In-Depth Information
3.2
Correspondences
The first step toward the creation of mappings between two schemas was to under-
stand how the elements of the different schemas relate to each other. This relation-
ship had to be expressed in some high level specification. That specification was
materialized in the form of correspondences.
A
correspondence
maps atomic elements of a source schema to atomic elements
of the target schema. This specification is independent of logical design choices
such as the grouping of elements into tables (normalization choices), or the nesting
of records or tables (for example, the hierarchical structure of an XML schema). In
other words, one need not specify the logical access paths (join or navigation) that
define the associations between the elements involved. Therefore, even users that
are unfamiliar with the complex structure of the schema can easily specify them.
Correspondences can be represented graphically through simple arrows or lines that
connect the elements of the two schemas.
The efficacy of using element-to-element correspondences is greatly increased
by the fact that they need not be specified by a human user. They could be in fact the
result of an automatic component that matches the elements of the two schemas, and
then the mapping designer simply verifies the correctness of the results. This task
is found in the literature under the name
schema matching
and has received consid-
erable attention, and has led into a variety of methodologies and techniques [
Rahm
and Bernstein
2001
].
A correspondence can be formally described as a tgd with one and only one
existentially quantified variable being equal to one of the universally quantified vari-
ables, and one term on each side of the dependency (for the case of the relational
schemas). The correspondence states that every value of the source schema element
represented by the first variable should also exist in the instance values of target
schema element represented by the second.
In certain cases, correspondences that involve more than one source schema
elements may exist, but there should always be one existentially quantified vari-
able whose value is determined as a function of the universally quantified variables
representing the participated source schema elements.
Consider the example of Fig.
5.4
a, which is a variation of the example presented
previously. Here, the first source consists of only the three relational tables
Public-
Company
,
Public-Grant
,and
Contact
, while the target consists of only the table
Company
. As before, the intra-schema lines represent schema constraints, and in
the particular example are foreign key constraints. The red dotted inter-schema
lines represent the correspondences. Note that the appearance of an attribute with
the same or similar name in both schemas does not necessarily mean that the two
attributes represent the same fact. For instance, consider the attributes
symbol
and
id
. Although in the companies world these terms may be used interchangingly, in
the specific example, the lack of a line among them may be justified by a case in
which the attribute
id
may represent the fiscal number of the company while the
attribute
symbol
may be the symbol with which the company appears in the stock
exchange.
