their professor) and the credibility that each individual grants to each other. These influences are described by a *structure matrix* $\Gamma \in {\mathcal{M}}_N({\mathbb{R}})$ and a *credibility matrix* $C \in {\mathcal{M}}_N({\mathbb{R}})$, respectively. Knowledge-like functions also evolve by *individual learning* which is described as a stochastic process that we will detail in the following. The learning algorithm then takes into account *both* social and individual learning.

Let us first start with some useful notations that we shall use in the following:

-   The space of square matrices of size $N >0$ with coefficients in $\mathbb K$ will be denoted by $\mathcal M_N(\mathbb K)$.

-   The vector of ${\mathbb{R}}^N$ composed of $1$s will be denoted by $\mathbf e$: $$\label{def:eqVector}
                \mathbf e = (1, \ldots, 1)^T \in {\mathbb{R}}^N.$$

-   The distance from a function $f$ to a set $\mathcal{X}$ is defined by $$d(f,\mathcal X) = \inf_{g \in \mathcal{X}} d(f,g).$$

Modeling Knowledge
------------------

A *knowledge setting* $\mathcal{K}$ is a triple $(\mathcal{E},\mathcal{C},\mathcal{F})$ where :

1.  $\mathcal{E}$ is a closed and bounded subset of $\mathbb{R}^n$.

2.  $\mathcal{C} \subset \mathbb{E}^l$ with $l\in \mathbb{N}^*$, $\mathbb{E}$ an euclidean space, and $0 \in \mathcal{C}$.

3.  $\mathcal{F}$ is a subset of the set of the functions from $\mathcal{E}$ to $\mathcal{C}$.

The set 