Animation scientifique

In this presentation, we study implication bases, specifically, their optimization (i.e. obtaining an equivalent implication base with as few elements as possible).
This is a well-known NP-complete problem, it is tractable for several classes of closure systems, in particular in convex geometry.
However and interestingly, it was shown to be NP-complete in that case as well. 
The study of the conditions which make a convex geometry tractable is a natural and intriguing follow-up question.
After some definition, we will present a characterization of optimum bases of convex geometry relying on specific hypergraph, which we call "quasi-closed hypergraph".
We prove that when these hypergraphs have disjoint edges, optimization becomes tractable and show how it fit in with previous results. 
Finally, we will look at a new tractable class, acceptant convex geometry.