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P
,
i
are reflexive), it can be taken:
is not empty (all
Primary meaning of P on X f or the group G
=
P
,
G
.
Notice that provided all
P
,
i
are preorders,
P
,
G
is also a preorder.
μ
(
i
)
P
If
mL
−
degrees
are known for each primary meaning
P
,
i
, since
•
x
=
P
,
G
y
⃔
x
=
P
,
1
y
&
...
&
x
=
P
,
m
y
,
•
x
P
,
G
y
⃔
x
P
,
1
y
&
...
&
x
P
,
m
y
,
L
m
for each function
:
ₒ
L
, non-decreasing in each place
i
between 1 and
m
(for example, if
a
b
then
(
a
,
x
2
,...,
x
m
)
(
b
,
x
2
,...,
x
m
))
, or aggregation
function, it results
•
⃒
(μ
(
1
)
P
),...,μ
(
m
)
P
))
(μ
(
1
)
P
), . . . , μ
(
m
)
P
x
P
,
G
y
(
x
(
x
(
y
(
y
)),
that allows to take
)
=
(μ
(
1
)
P
),...,μ
(
m
)
P
G
μ
P
(
X
(
x
(
x
)),
for all
x
∈
X
,
as an
aggregate L
degree
of
P
on
X
for the group
G
. The meaning for G results
from aggregating its people's meanings.
−
1.4.5 Synonims
In the language, synonymy is a complex problem whose roots are possibly to be
searched for in the apparition of new facts or concepts for which there is not yet a
word for their designation. Then, what is sometimes done is to designate the new
fact/concept by means of an old word whose meaning is considered, for some rea-
sons, similar to that of the new fact/concept. That is, for example, that in which
the old word was already used in situations judged similar to those where the new
fact/concept appears/applies.
Synonymy is related with some kind of similarity or proximity of meaning but
here we will only try to present some previous treats of it.
Let
P
be a predicate on
X
with
P
, and
Q
a predicate on
Y
with
Q
. If there
exists a bijective function
u
:
X
ₒ
Y
such that,
•
x
2
),
predicates
P
and
Q
are
u-primary-synonyms
. Notice that when
X
x
1
P
x
2
⃔
u
(
x
1
)
Q
u
(
id
X
,
what results is that
P
and
Q
are
id
X
-primary synonyms, or
primary synonyms
for
short, if and only if
=
Y
, with
u
=
P
=
Q
, that is, if and only if
Primary meaning of
P
on
X
=
Primary meaning of
Q
on
X
If
P
and
Q
are
id
X
-primary synonyms, it is said that they are exact or perfect
synonyms when
μ
P
=
μ
Q
, and it results
(
P
,
μ
P
)
=
(
Q
,
μ
Q
)
.
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