Database Reference
In-Depth Information
atom
Takes
(x
1
,x
2
)
with the equivalent to it equation
(f
Ta k e s
(x
1
,x
2
)
.
=
1
)
, be-
A
cause the relational symbol
Takes
is of schema
and not of the new schema
C
=
(
{
r
q
1
}
,
∅
)
with a unary relational symbol
r
q
1
. Let us define these two map-
pings,
M
AC
={
Φ
E
}:
A
→
C
and
M
CD
={
Φ
M
}:
C
→
D
.
α
∗
(
For any mapping-interpretation
α
such that
A
=
A
)
and both schema map-
M
AD
are satisfied, we have that
Flux
α, MakeOperads(
pings
M
AC
and
M
AC
)
=
Flux
α, MakeOperads
M
AD
.
If for such an interpretation (R-algebra)
α
,
π
x
2
Takes
(x
1
,x
2
)
A
=
π
x
2
α(
Takes
)
α(r
q
1
)
=
then also
Flux
α, MakeOperads(
M
CD
)
=
Flux
α, MakeOperads
M
AD
.
M
AD
={
2. The mapping
Φ
}:
A
→
D
in Example
5
with
Φ
equal to SOtgd
f
Student
∀
y
3
Takes
(x
1
,x
2
)
∧
f
Student
(x
1
,y
3
)
.
∃
x
1
∀
x
2
∀
1
⇒
Enrolment
(y
3
,x
2
)
.
=
Then
Φ
E
is equal to
∃
f
Student
∀
x
1
∀
x
2
∀
y
3
Takes
(x
1
,x
2
)
∧
f
Student
(x
1
,y
3
)
.
1
⇒
r
q
2
(y
3
,x
2
)
=
and
Φ
M
is equal to
f
Ta k e s
∀
y
3
r
q
2
(y
3
,x
2
)
∧
f
Ta k e s
(x
1
,y
2
)
.
1
∃
f
Student
∃
x
1
∀
x
2
∀
=
∧
f
Student
(x
1
,y
3
)
.
1
⇒
Enrolment
(y
3
,x
2
)
,
=
with a new schema
)
composed of a binary relational symbol
r
q
2
.
Let us define these two mappings,
C
=
(
{
r
q
2
}
,
∅
M
AC
={
Φ
E
}:
A
→
C
and
M
CD
=
{
Φ
M
}:
C
→
D
.
For any mapping-interpretation
α
such that
A
α
∗
(
=
A
)
and both schema map-
M
AD
are satisfied, we have that
Flux
α, MakeOperads(
pings
M
AC
and
M
AC
)
=
Flux
α, MakeOperads
M
AD
.
If for such an interpretation (R-algebra)
α
,
π
x
2
,y
3
Takes
(x
1
,x
2
)
f
Student
(x
1
,y
3
)
.
1
A
α(r
q
2
)
=
∧
=
then also
Flux
α, MakeOperads(
M
CD
)
=
Flux
α, MakeOperads
M
AD
.
