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In-Depth Information
∧
Student
(x
n
,y)
⇒
Enrolment
(y,x
c
)
M
AC
=
∀
x
c
Takes
(x
n
,x
c
)
⇒
Learning
x
n
,x
c
,f
2
(x
n
,x
c
)
,
x
n
∀
M
CD
=
∀
x
p
Learning
(x
n
,x
c
,x
p
)
⇒
Teaching
(x
p
,x
c
)
.
x
n
∀
x
c
∀
Hence, their composition is equal to the following mappings:
M
AD
=
M
BD
◦
M
AB
=
∃
f
1
∀
x
2
Takes
(x
1
,x
2
)
⇒
Enrolment
f
1
(x
1
),x
2
,
x
1
∀
M
AD
=
M
CD
◦
M
AC
=
∃
f
2
∀
x
2
Takes
(x
1
,x
2
)
⇒
Teaching
f
2
(x
1
,x
2
),x
2
,
x
1
∀
which are not logically equivalent.
However, we obtain from Definition
13
,for
A
=
α
∗
(
A
),B
=
α
∗
(
B
)
and
C
=
α
∗
(
C
)
:
Flux
α,
MakeOperads(
M
AB
)
M
BD
)
◦
MakeOperads(
Flux
α, MakeOperads(
M
AB
)
∩
Flux
α, MakeOperads(
M
BD
)
=
T
Takes
(x
n
,x
c
)
A
,π
x
n
Takes
(x
n
,x
c
)
A
∩
=
T
π
x
c
,y
Takes1
(x
n
,x
c
)
∧
Student
(x
n
,y)
B
,
and
Flux
α,
MakeOperads(
M
AC
)
M
CD
)
◦
MakeOperads(
Flux
α, MakeOperads(
M
AC
)
∩
Flux
α, MakeOperads(
M
CD
)
=
T
Takes
(x
n
,x
c
)
A
∩
T
π
x
p
,x
c
Learning
(x
n
,x
c
,x
p
)
C
.
=
In the case when in the given universe
dom
, the domain
dom(y)
for the at-
tribute
y
of the atom
Student
(x
n
,y)
is disjoint from
dom(x
n
)
and from
dom(x
c
)
of the atom
Takes
(x
n
,x
c
)
, and if
dom(x
p
)
for the attribute
x
p
of the atom
Learning
(x
n
,x
c
,x
p
)
is disjoint from
dom(x
n
)
and from
dom(x
c
)
of the atom
Takes
(x
n
,x
c
)
, then it is easy to verify that
Flux
α,
MakeOperads(
U
=
M
AB
)
M
BD
)
◦
MakeOperads(
Flux
α,
MakeOperads(
M
AC
)
=
M
CD
)
◦
MakeOperads(
T
Takes
(x
n
,x
c
)
A
.
=
M
AD
have the
Consequently, in this case, the two composed mappings
M
AD
and
same information fluxes from
, so that, from the strict
semantics point of view, they are equal instance-level mappings.
A
into the target schema
D
