Database Reference
In-Depth Information
3. The mapping
M
AC
={
Φ
}:
A
→
C
in Example
9
with
Φ
equal to SOtgd
f
Over
65
∃
f
1
∃
f
Emp
∃
1
∧
Local
(x
e
)
⇒
Office
x
e
,f
1
(x
e
)
∧∀
x
e
f
Emp
(x
e
)
.
x
e
f
Emp
(x
e
)
.
∀
=
1
∧
f
Over
65
(x
e
)
.
1
⇒
CanRetire
(x
e
)
.
=
=
Then
Φ
E
is equal to
f
Over
65
∃
f
Emp
∃
x
e
f
Emp
(x
e
)
.
1
∧
Local
(x
e
)
⇒
r
q
3
(x
e
)
∀
=
x
e
f
Emp
(x
e
)
.
1
∧
f
Over
65
(x
e
)
.
1
⇒
r
q
4
(x
e
)
∧∀
=
=
and
Φ
M
is equal to
f
Local
∀
x
e
r
q
3
(x
e
)
∧
f
Emp
(x
e
)
.
∃
f
1
∃
f
Emp
∃
f
Over
65
∃
1
∧
f
Local
(x
e
)
.
1
⇒
Office
x
e
,f
1
(x
e
)
=
=
x
e
r
q
4
(x
e
)
∧
f
Emp
(x
e
)
.
1
∧
f
Over
65
(x
e
)
.
1
⇒
CanRetire
(x
e
)
,
∧∀
=
=
C
=
with a new schema
(
{
r
q
3
,r
q
4
}
,
∅
)
composed of two unary relational symbols
r
q
3
and
r
q
4
.
Lets us define these two mappings,
Φ
E
}:
A
→
C
and
M
AC
={
M
C
C
=
Φ
M
}:
C
→
C
{
.
For any mapping-interpretation
α
such that
A
=
α
∗
(
A
)
and both schema map-
pings
M
AC
and
M
AC
are satisfied, we have that
Flux
α, MakeOperads(
M
AC
)
=
Flux
α, MakeOperads(
M
AC
)
.
If for such an interpretation (R-algebra)
α
,
π
x
e
f
Emp
(x
e
)
.
1
∧
Local
(x
e
)
A
=
α(r
q
3
)
=
=
α(
Emp
)
∩
α(
Local
)
and
π
x
e
f
Emp
(x
e
)
.
1
A
1
∧
f
Over
65
(x
e
)
.
α(r
q
4
)
=
=
=
=
α(
Emp
)
∩
α(
Over65
)
then also
Flux
α, MakeOperads(
M
C
C
)
=
Flux
α, MakeOperads(
M
AC
)
.
Based on this schema-mapping decomposition, we can obtain the instance-
mapping decomposition as well:
