Information Technology Reference
In-Depth Information
4.4.3.1.
Complementarity
Two modalities -
m
1
and
m
2
- are called complementary for task
T
to be carried
out if the next formula is verified by the system:
G
((
state
=
stateI
)=
⇒
((
mod
=
m
1
∨ mod
=
m
2
)
∪
(
state
=
stateF
)))
[4.1]
∧
G
(
not
((
state
=
stateI
)=
⇒
((
mod
=
m
1
)
∪
(
state
=
stateF
))))
[4.2]
∧
G
(
not
((
state
=
stateI
)=
⇒
((
mod
=
m
2
)
∪
(
state
=
stateF
))))
[4.3]
This formula means that in the system of transitions of the multimodal HCI (all
the traces of execution):
(1) if a state is identified as being the initial state of the task
T
(
state
=
stateI
),
then all the states that follow it are reached either by modality
m
1
or
m
2
(
mod
=
m
1
∨ mod
=
m
2
) until (
∪
) the end of the realization of this task
T
(
state
=
stateF
);
(2) there is no execution where if a state is identified as being the initial state then
all the states that follow it are reached with
m
1
modality until (
∪
) the final state of the
task
T
;
(3) there is no execution so if a state is identified as being the initial state then all
the states that follow it are reached with the
m
2
modality until (
∪
), the final state of
the task
T
.
4.4.3.2.
Assignation
A modality
m
i
is assigned to task
T
if the following formula is verified by the
multimodal HCI system:
G
((
state
=
stateI
)=
⇒
((
mod
=
m
i
)
∪
(
state
=
stateF
)))
This formula means that in the transition system of the HCI (all the execution
traces), if
stateI
is identified as being the initial state of task
T
(
state
=
stateI
), then
all the states that follow it are reached by modality
m
i
until the end of the realization
of task
T
(
state
=
stateF
).
4.4.3.3.
Equivalence
Two modalities -
m
1
and
m
2
- are said to be equivalent for the realization of task
T
if the following formula is verified by the system:
G
((
state
=
stateI
)=
⇒
(((
mod
=
m
1
)
∪
(
state
=
stateF
))
∨
((
mod
=
m
2
)
∪
(
state
=
stateF
))))
