Information Technology Reference
In-Depth Information
Let
T
be the temporal relation which associates the start and end instant with each
information:
T
:
I −→ Time× Time
∀i
i
∈ I ∃
(
deb
(
i
i
)
, end
(
i
i
))
∈ Time× Time
such as
deb
(
i
i
)
< end
(
i
i
) and
T
(
i
i
)=
(
deb
(
i
i
)
, end
(
i
i
)).
4.5.2.4.
Dynamic semantics
The dynamic semantics of the fission model describe the temporal ordering of
i
i
.
It defines the temporal operators by means of the temporal relation
T
:
∀op
temp
∈{An,Sq,Ct,Cd,Pl,Ch,In}
∀i
i
,i
j
∈ I,
with
T
(
i
i
)=(
deb
(
i
i
)
, end
(
i
i
))
,T
(
i
j
)=(
deb
(
i
j
)
, end
(
i
j
))
∃i
k
∈ I
, with
i
k
=
i
i
op
temp
i
j
and:
T
(
i
k
)=(
deb
(
i
i
)
, end
(
i
j
)) iff
op
temp
=
An
and
end
(
i
i
)
<deb
(
i
j
)
T
(
i
k
)=(
deb
(
i
i
)
, end
(
i
j
)) iff
op
temp
=
Sq
and
end
(
i
i
)=
deb
(
i
j
)
T
(
i
k
)=(
deb
(
i
i
)
, end
(
i
j
)) iff
op
temp
=
Ct
and
deb
(
i
i
)
<deb
(
i
j
)
< end
(
i
i
)
< end
(
i
j
)
T
(
i
k
)=(
deb
(
i
i
)
, end
(
i
i
)) iff
op
temp
=
Cd
and
deb
(
i
i
)
<deb
(
i
j
)
< end
(
i
j
)
< end
(
i
i
)
T
(
i
k
)=(
deb
(
i
i
)
, end
(
i
i
)) iff
op
temp
=
Pl
and
deb
(
i
i
)=
deb
(
i
j
)
∧end
(
i
i
)=
end
(
i
j
)
i
k
=
i
i
∨ i
k
=
i
j
iff
op
temp
=
Ch
T
(
i
k
)=(
deb
(
i
k
)
, end
(
i
k
)) iff
op
temp
=
In
The binary temporal operator
It
is defined as follows:
∀i
i
∈ I, n ∈
N
∗
It
(
n, i
i
)=(
...
((
i
i
Sq i
i
)
S
q i
i
)
... Sq i
i
)
n
times
4.5.2.5.
Modeling of the CASE space
The formal model of the CASE space is based on the formal model that
was previously described, by defining the syntaxes relative to the four types of
multimodality of the space. We start by defining the temporal and semantic operators
authorized for each of the two values of the two axes of the space (use of media
and link between information). Then we give the grammar of the syntax of the four
axes resulting from crossing of the two axes (concurrent, alternated, synergistic and
exclusive):
