(u, v) ∈ E(T ) is described by the presence function ρ : E(T ) × T → {0, 1} **such**
that ∀t ∈ T , e ∈ E(T ):

$$\forall:t_{1}\leq t$$

ρ(e, t) = 1 ⇐⇒ ∃(u, v, t1, t2) ∈ C : t1 ≤ t < t2 (2)
The triplet G = (V, E, ρ) is called an epistemic representation graph**, and the**
temporal domain T = [ta, tb) of the function ρ, is the lifetime of G**. We denote by**
G[t,t′) the mental representation subgraph of G covering the period [ta, tb) ∩ [**t, t**′)
Hence, a sequence of couples J = {(e1, t1),(e2, t2), ...}, with ei ∈ E and ti ∈ T
for all i, is called a journey in G iff {e1, e2, ...} is a walk in G and for all i, ρ(ei, ti**) = 1**
and ti+1 ≥ ti. Journeys can be thought of as paths over time **from a source node to**
a destination node (if the journey is finite).

Let us denote by J
∗
G
the set of all possible journeys in an epistemic representation system G. We will say that G admits a journey from a node u to a node v**, and note**
∃J(u,v) ∈ J ∗
G
, if there exists at least one possible journey from u to v in G.

## 4.4. **Opinion Dynamics And Society**

One of the most famous formalisms aimed at describing the process of persuasion is the "Bounded Confidence Model" (BCM) where agents exchanging **information** are modeled as likely to adjust their opinions only if the preceding and the received information are close enough to each other. Such an aspect is modeled by introducing a real number ǫ **, which stands for tolerance or uncertainty such that an agent**
with opinion x **interacts only with agents whose opinions is in the interval ]x** ǫ ,
x + ǫ **[. Neverthless the wide, massive and cross-disciplinary use of the BCM ([19,**
15]) ranging from "viral marketing" to to the Italians' opinions distortion played by controlled mass media ([25, 4, 5, 15]). Such a model does not provide **an explanation of the phenomena yielding to the tolerance value, it is just assumed as a static**
value.

In this work we will outline which are the factors affecting the acceptance or the refuse of one another opinion. In particular, how can we formalize comparison of two or more opinions? Recalling that a mental representation is a preposition with the truth value defined by two variable To, Ts ∈ R and dc ∈ R **respectively quantifying**
the "real" and the perceived truth value and the degree of confidence with respect to a given object or proposition. And considering that such mental **representations**
are modeled as set of time connected entities of the form G = (V, E, ρ**) we can now**
provide some definitions aimed at describing the process of persuasion.

Assuming that an epistemic representation system, which is by nature adaptive, when facing with external events, reacts to the stimulus by activating only a subset of its components. For instance, consider the example where an agent x **is questioned**
by an agent y **about his opinion on a given target.**
What does happen in the x**'s mental representation system? How can we quantify**
x's attitudes to change or not is opinions regarding a given matter of fact?