Database Reference
In-Depth Information
•
We consider a finitary
view
as a union of a finite set
S
of conjunctive queries
with the same head
q(
x
)
over a schema
, and from the equivalent algebraic
point of view, it is a “select-project-join+union” (SPJRU) finite-length term
t(
x
)
which corresponds to a union of the terms of conjunctive queries in
S
. In what
follows, we will use the same notation for an FOL formula
q(
x
)
and its equivalent
algebraic SPJRU expression
t(
x
)
. A materialized view of an instance-database
A
is an
n
-ary relation
R
A
=
q(
x
)
∈
S
A
. Notice that a finitary view can also
have an infinite number of tuples. We denote the set of all finitary materialized
views that can be obtained from an instance
A
by
TA
.
q(
x
)
•
Given two autonomous instance-databases
A
and
B
, we can make a
federation
of them, in order to be able to
compute
the queries with relations of both au-
tonomous instance-databases. A federated database system is a type of meta-
database management system (DBMS) which transparently integrates multiple
autonomous database systems into a single federated database. The constituent
databases are interconnected via a computer network, and may be geographi-
cally decentralized. Since the constituent database systems remain autonomous,
a federated database system is a contrastable alternative to the task of
merging
together several disparate databases. A federated database, or virtual database, is
a fully-integrated, logical composite of all constituent databases in a federated
database system. McLeod and Heimbigner [
61
] were among the first to define a
federated database system. Among other surveys, Sheth and Larsen [
73
] define a
Federated Database as a collection of cooperating component systems which are
autonomous and are possibly heterogeneous.
We consider the views as a universal property for databases: they are the possible
observations of the information contained in an instance-database. We can use them
in order to establish an equivalence relation between databases. Database category
DB
, which will be introduced in Chap.
3
,isatthe
instance level
, i.e., any object
in
DB
is an instance-database. The connection between a
schema level
and this
category is based on the
interpretation
functors. Thus, each rule-based conjunctive
query at the schema level over a schema
A
will be translated (by an interpretation
functor) in a morphism in
DB
, from an instance-database
A
(a model of the schema
A
) into the instance-database
TA
(composed by all materialized views of
A
).
1.4.1 Basic Theory about Database Observations: Idempotent
Power-View Operator
We will introduce a class of coalgebras for database query-answering systems for
a given instance-database
A
of a schema
in Sect.
2.4.2
. They will be presented
in an algebraic style by providing a co-signature. In particular, the sorts include a
single “hidden sort”, corresponding to the carrier of a coalgebra, and other “visible”
sorts for the inputs and outputs with a given fixed interpretation. Visible sorts will
be interpreted as the sets without any algebraic structure defined on them. For us,
the coalgebraic terms, built by operations (destructors), are interpreted by the basic
observations
which one can make on the states of a coalgebra.
A
