With respect to a simulative engine in terms of a cognitive mind-map, the mentioned parallel universe does not exist in the beginning of the mind-map life-cycle. Consequently, any relevance values of any entity cell is not initially given. Undoubtedly, the change of dynamic value is to be handled in internally, whereas the initialization step must be examined explicitly.

So far, several alternatives have been identified, which do either use an a-priori knowledge or demand an ex-posterior information. A first (and in our opinion the most appropriate)
approach is to randomize each relevance value, which has the advantage that a-priori less/no efforts must be investigated. The belief that more important entity cells adapt to a higher relevance value (and less interesting entity cells to lower relevance values) can not be dismissed. The idea, to initially differ between entity cells explicitly is a tedious concern. Also it does not correspond to the evolution of mind-maps per se. An ex-posterior initialization of relevance values, for example by guessing or communicating with the conversing partner, may be feasible but is less applicable.

Then, we propose the function match(Mp, M∗
pq, t) as follows:

$$match(M_{p},M_{pq}^{*},t)=\sum_{i=1}^{k}\sum_{j=1}^{l}\frac{|\rho^{M_{p}}(e_{i},t)\cap\rho^{M_{pq}^{*}}(e_{j},t)|}{|\rho^{M_{p}}(e_{i},t)|}\tag{1}$$  Here $M_{p}$ is the self mind-maps for the person $p$ and $M_{pq}^{*}$
pq is the outer mind-maps for the person p, developed by the person q. Where k and l are the number of entity cells that contain the corresponding relevance values ρMp (ei, t) and ρ M∗
pq (ej , t) during the time slice t. The trust function is then to be evaluated as

$$gtrust(M_{p},M_{pq}^{*},t)=\left\{\begin{array}{l l}{{y e s,}}&{{i f\ m a t c h(M_{p},M_{p q}^{*},t)\geq\alpha}}\\ {{n o}}&{{e l s e}}\end{array}\right.\tag{2}$$

Please note that the function *match* is time varying and the trust threshold α is individual and given to each conversational partner solely. In this context the trust threshold α is a determinable parameter, which can be influenced by several factors : for instance by the number of entity cells, present inside the mind-maps.

## 3.3. An Example

Assume, that *Alice*'s/Bob's own mind-maps look like Figure 3. Assume furthermore, that the following conversation between Bob and *Alice* takes place:
Bob: The sun is shining, what a beautiful day.

Alice:
The sun is very hot.

## Bob: That Is Right, But I Like Sunny Days.

Taking into account the mind-maps of *Alice* and Bob, does Alice now trust Bob? Figure 3 shows the different mindmaps after Bob's reply to *Alice* - both for *Alice* (what she thinks about Bob) and Bob (what he thinks about *Alice*).

The nouns and verbs are filtered out and reduced to their morphological basis. Bob's affirmation is inherited to *Alice*'s mind-map. Please also note that the entity cell "day" is activated twice (because of the merge process) and that the learning principle has strengthened the connection between
"day" and "sunny".

Alice's match value after the conversation concerning Bob is low (0.2), because only one entity cell ("sun") appears during the conversation with some relevance, but neither
"Fresh air", "warm", "beach" nor "swimming". Concerning Bob, his match value is 1.0 because "hot" and "sun" occur during the conversation. For this, depending on each trust threshold α, (s)he trusts or not.

![0_image_0.png](0_image_0.png)

![0_image_1.png](0_image_1.png)

