Database Reference
In-Depth Information
q
C,k
+
1
t
1
∧···∧∀
y
m
q
B,m
(
y
m
)
⇒
q
C,k
+
m
t
m
,
⇒
(3.1)
≤
i
≤
k
, and
t
i
the tuple of terms
with
t
i
the tuple of terms with variables in
x
i
,for1
with variables in
y
i
,for1
≤
i
≤
m
. Consequently, this mapping is the graph:
with
M
AC
=
∃
f
A
∀
x
1
q
A,
1
(
x
1
)
q
C,
1
(
t
1
)
∧···∧∀
x
k
q
A,k
(
x
k
)
q
C,k
(
t
k
)
⇒
⇒
and
M
BC
=
∃
f
B
∀
y
1
q
B,
1
(
y
1
)
q
C,k
+
1
t
1
∧···∧∀
y
m
q
B,m
(
y
m
)
⇒
q
C,k
+
m
t
m
,
⇒
and
f
A
,
f
B
⊆
such a decomposition
is not possible because we can have a query mapping
q(
x
)
⇒
q
C
(
x
)
in the SOtgd of
M
f
, while in the case of mapping
M
:
A
⊕
B
→
C
with relational symbols in
q(
x
)
from both databases
A
and
B
.
M
1
={
{∀
If we introduce the mappings
x
i
(r
Ai
(
x
i
)
⇒
r
Ai
(
x
i
))
|
r
Ai
∈
A
}}
and
M
2
={
{∀
⇒
|
r
Bi
∈
B
}}
y
i
(r
Bi
(
y
i
)
r
Bi
(
y
i
))
then we obtain the mapping graph
that can be seen as a cocone diagram for schema database mappings.
Let us consider another dual example, a mapping
M
:
C
→
A
†
B
. In this case,
in any query mapping
q
C
(
x
)
⇒
q(
x
)
∈
M
, all relational symbols in the query
q(
x
)
must be of database
A
or (mutually exclusive) of database
B
. That is,
M
=
∃
f
∀
x
1
q
C,
1
(
x
1
)
q
A,
1
(
t
1
)
∧···∧∀
x
k
q
C,k
(
x
k
)
⇒
q
A,k
(
t
k
)
∧∀
y
1
q
C,k
+
1
(
y
1
)
⇒
