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This first property P1 is crucial in our model, as it links together the agents' internal
states: each one is modified by speech depending on its own parameter
u
i
. In the present
model, we assume that for a given agent, understanding of its productions and of its
perceptions are similar: for Agent
i
,
u
i
=
u
i
.
2.2
Non-verbal Behaviours Reflect Internal State
The second property P2, claims that “non-verbal behaviours reflect internal state”. That
is to say, agent's arousal, mood, satisfaction, awareness, are made visible thanks to
facial expressions, gaze, phatics, backchannel, prosody, gestures, speech pauses. To
make visible the internal properties of Agent
i
, a non-verbal signal,
NV
Act i
, is triggered
depending on its internal state,
S
i
.When
S
i
reaches the threshold
β
, the agent produces
non-verbal behaviours with
th
β
the threshold function (see Fig.2):
NV
Act i
(
t
)=
th
β
(
S
i
(
t
))
(3)
S
NV
1
Act
1
th
β
u
1
u
1
V
V
Agent1
Per
1
Act
1
S
NV
2
Act
2
th
β
u
2
u
2
V
V
Agent2
Per
2
Act
2
Fig. 2.
Each agent produces non-verbal behaviours
NV
Act i
when
S
i
reaches the threshold
β
.
NV
Act i
depends on how much the internal state
S
i
has been influenced by what has been said.
We suggest here that pitch accents, pauses, head nods, changes of facial expressions
and other non-verbal cues are, for a certain part, produced by agents when a particu-
larly important idea arises, when the explanation reach a certain point, when an idea or a
concept starts to be outlined. We assume that the phenomenon is similar in both speaker
and listener, it is driven by the evolution of what is wanted to be expressed in one case
and it is driven by what is heard in the other case. If speaker and listener understand
each other, these peaks of arousal and understanding should co-occur: they appear to
be temporally linked. These peaks will be the bases of entrainment for intentional co-
ordination between partners. And then this coordination could be seen as a marker of
interaction quality.
Considering these two first points, that is to say, equations 2 and 3 we have the fol-
lowing system of equations :
NV
Act
1
(
t
1
)=
th
β
(
t
t
0
u
1
V
Act
1
(
t
))
NV
Act
2
(
t
1
)=
th
β
(
t
t
0
u
2
V
Act
1
(
t
))
(4)
