Basics of Intersubjectivity Dynamics: Model of Synchrony Emergence When Dialogue Partners Understand Each Other - Agents and Artificial Intelligence - page 300

Then, in the subsections 2.3 and 2.4, we describe how this will give to a dyad of agents
coupling capabilities. That constitute the modelling of the third and fourth properties,
P3 and P4.

2.1 Speak and Listen Modifies Internal State
Let us consider a dyad of agents, Agent1 and Agent2. Each agent's state is represented
by one single variable, S 1 for Agent1 and S 2 for Agent2 (

1 , 1] ). Now, let us con-
sider the speech produced by each agent, the verbal signal V Act i (

∈ [ −

∈{ 0 , 1 } ), and the

speech heard by each agent, the perceived signal V Per i ( ).

P1 claims that each agent, either listener or speaker, has its internal state S i modi-
fied by verbal signals: the listener's internal state is modified by what it hears, and the
speaker's internal state is modified by what it says. Two “level of understanding”, the
weights u i and u i , are defined for each agent of the dyad. u i modulates the perceived
verbal signal V Per i ,and u i modulates the produced verbal signal V Act i (see fig.1). To

∈{ 0 , 1 }

S

1

u 1

u

1

V V

Agent1

Per 1 Act 1

S

2

u 2

u 2

V V Agent2

Per 2 Act 2

Fig. 1. Verbal perception, V Per i , and verbal action, V Act i , both influence the internal state S i .
These influences depend respectively on the level of understanding u i and u i .
model interaction in more natural settings these u i parameters should be influenced by
many variables, such as the context of the interaction (discussion topic, relation-ship be-
tween interactants), the agents moods and personalities. However in the present model
we combine all these parameters in the single variable u i (

1 , 1] ). The choice of the
values of u 1 and u 2 is arbitrary near 0 . 01 : it enables a well balanced sampling of the
oscillators' activations, the period last around 100 time steps; the other parameters of
the architecture are chosen depending on this one so as not to modify the whole systems
dynamics.
If t is the time we have the following equations:
S 1 ( t +1)= S 1 ( t )+ u 1 V Per 1 ( t +1)+ u 1 V Act 1 ( t +1)
S 2 ( t +1)= S 2 ( t )+ u 2 V Per 2 ( t +1)+ u 2 V Act 2 ( t +1)

∈ [ −

(1)

Assuming that communication is ideal, i.e. V Peri = V Actj , and that Agent1 is the only
one to speak, i.e. V Act 2 = V Per 1 =0 ,the system of equations 1 gives:
S 1 ( t +1)= S 1 ( t )+ u 1 V Act 1 ( t +1)
S 2 ( t +1)= S 2 ( t )+ u 2 V Act 1 ( t +1)

(2)