Database Reference
In-Depth Information
•
Semantics.
The lack of semantic description in traditional approaches to data modeling is a strong
limiting factor for the effective use of data and this significantly decreases its value including pos-
sibility of information exchange, integration, consistency, interoperability and many other func-
tions. Semantics in databases “should enable it to respond to queries and other transactions in a
more intelligent manner” (Codd, 1979). Currently, semantics is supposed to exist at conceptual
level while logical data models have rather limited possibilities for representing semantic relation-
ships. In this context, the goal of COM is to make semantics integral part of the logical data model
so that the database can be directly used for reasoning about data. To reach this goal, COM makes
a principled assumption that database is a
partially ordered set
(as opposed to a set without any
structure). Partial order is supposed to be represented by references which are used as an elemen-
tary semantic construct in COM.
CONCEPT-ORIENTED MODEL
The smallest unit of data in COM is a
primitive value
like integer or text string. They are normally
provided by DBMS and therefore their structure is not part of the model. More complex elements are
produced by means of
tuples
which are treated in their common mathematical sense as a combination
of primitive values or other tuples. Each member of a tuple has its unique position which is referred
to as a
dimension
. If
e
=(
x
=
a
,
y
=
b
,
z
=
c
,…) is a tuple then
x
,
y
and
z
are dimensions while
a
,
b
and
c
are
members of this tuple. According to the duality principle, an element in COM is defined as a couple of
two tuples: identity tuple and entity tuple. Identity tuples are values which are passed by-copy while
entity tuples are passed by-reference. Identity tuples are used as locations or addresses for entity tuples.
If tuple
a
is a member within tuple
b
then only identity part of
a
is included by-value in
b
. It is assumed
that it is always possible to access entity tuple if its identity tuple is available. In terms of conventional
computer memory, identity tuple has the structure of memory addresses and entity tuple has the structure
of memory cells.
Inclusion principle in COM is implemented via
extension operator
denoted by semicolon. If
a
and
b
are two elements then
e
=
a
:
b
is a new element where
a
is a base and
b
is an extension (so
b
is said to
extend
a
). It is analogous to object-oriented extension with the difference that this operation is applied to
couples of identity-entity tuples rather than to individual tuples. If entity tuple is empty then this opera-
tion can be used to extend values and model value domains. If identity tuple is empty then it is used to
extend objects or records. With the help of extension any element can be represented as a sequence of
couples starting from some common root element and ending with the last extension. Extension opera-
tor induces
strict inclusion relation
∧
among elements by assuming that extended element is included
in its base element, that is, if
e
=
a
:
b
then
a
∧
e
. All elements from set
R
in this case are represented as a
nested set (
R
,
∧
) where parents are referred to as
super-elements
and children (extended elements) are
referred to as
sub-elements
. Inclusion relation among elements is analogous to the nested structure of
elements in XML.
According to the order principle, elements in COM are (strictly) partially ordered by assuming that
a tuple is less than any of its members, that is, if
e
=(…,
a
,…) is a tuple then
e
<
a
. All elements of set
R
in
this case are represented as a partially ordered set (
R
,<). If
a
<
b
then
a
is said to be a
lesser
element and
b
is referred to as a
greater
element. In particular, this assumption means that a tuple cannot have itself
as a member directly or indirectly, that is, cycles are prohibited. According to the duality principles,
