Database Reference
In-Depth Information
with
f
1
(b,ω
1
)
=
ω
2
and
α
2
(v
1
)
:{
(b,ω
0
),(ω
1
,ω
2
)
}→{
(b,ω
0
)
}
is not an
M
AB
is not satisfied. Consequently,
α
2
injection, and hence
is not a model of
the database-mapping program in
G
.
Step 3.
=
:{
}→{
}
Here
f
α
3
(q
1
)
(a,b),(b,ω
1
)
(b,ω
0
),(ω
1
,f
1
(b,ω
1
))
where
=
={
}
f
1
(b,ω
1
)
ω
2
,
α
3
(r
q
)
(b,ω
0
),(ω
1
,ω
2
)
and
:
(b,ω
0
),(ω
1
,ω
2
)
→
(b,ω
0
),(ω
1
,ω
2
)
α
3
(v
1
)
is an injection. and hence
M
AB
is satisfied. However,
=
(b,ω
1
),
ω
1
,f
1
(ω
1
,ω
2
)
α
3
(s
q
)
with
f
1
(ω
1
,ω
2
)
=
ω
3
and
α
3
(v
2
)
:{
(b,ω
1
),(ω
1
,ω
3
)
}→{
(a,b),(b,ω
1
)
}
is
M
BA
is not satisfied. Consequently,
α
3
not an injection, and hence
is not a
model of the database-mapping program in
G
.
...
It is easy to verify that no mapping interpretation (i.e., a functor)
α
i
∈
Int(G)
DB
Sch
(G)
for a finite
i
1
,
2
,...
is a model of
G
, and each one of
them satisfies only one of the two schema mappings in
G
. We will see the unique
solution of this Strong Data Integration semantics for the database mapping pro-
gram in the sketch
Sch
(G)
, based on the unique final colagebra semantics in the
next section. From the fact that the solution of
G
in the Strong Data Integration
Semantics has to be a model of
G
, clearly, the databases
⊆
=
of such a
solution cannot be finite, so that this semantics is not applicable in practice.
2.
Weak Data Integration semantics.
In this case, the SOtgds in the database-
mappings in
G
are considered as the default rules used to generate the recom-
mendations for an updating of the peer databases. Thus it is not necessary that at
the end of the forward chaining process all schema SOtgds mappings be satisfied.
For example, we will consider the case when the peer databases do not accept
the inserting in their local knowledge the tuples composed by only the Skolem
marked null values. In fact, in this case, the forward-chaining will be finite:
A
and
B
α
i
∈
Int(G)
r
∈
A
s
∈
B
Transition
Equations
α
1
(p
0
=
nil),(p
1
={{
b
}
,
⊥}
.p
2
)
1
b,ω
0
α
2
2
b,ω
1
(p
2
={{
b
}
,
⊥}
.p
3
)
=
α
3
(
A
))
α
3
=
α
2
3
∅
(p
3
The first two steps are equal to those in the previous case for Strong Data
Integration semantics. In the third step, the tuple
(ω
1
,ω
2
)
is refused by peer
B
M
AB
⇒
, so that the transition (in Definition
54
)
α
2
====
α
3
will have
α
3
=
α
2
and hence
Y
, so that the algorithm '
DBprog
' will reach the
end with the final equation
(p
3
=
=
S
(A,α
∗
)
=∅
α
3
(
))
, where
α
3
(
α
2
(
A
A
)
=
A
)
={⊥
,α
2
(r)
}
