In this SYSTeMS dialogue, I have two main goals. 

The first is to introduce some concepts of the theory of imprecise 
probabilities for the (new) people in our group that are not so 
(un-)familiar with this subject. Trying out yet another approach, I will 
try to emphasize the dialogue part of our seminar series' name. My goal 
will be attained, and the first part of the seminar complete when a 
sufficient level of understanding of what a lower probability is, and 
acceptance of its aptness for modelling uncertainty, is reached.

We will then be sufficiently prepared for the second part, about "extreme 
lower probabilities" (on finite possibility spaces). These extreme lower 
probabilities are to other lower probabilities what the vertices of a 
triangle are to the other points and the inside of that triangle. I will 
talk about some different `triangles' that are of interest for imprecise 
probabilities, and about (the difficulties) in obtaining their vertices. 
The second goal will be reached when it is clear how conceptually simple 
these extreme lower probabilities are, and at the same time realize the 
different reasons for how hard it can be to get to them.