The non-monotonic logics offer a formal framework to deal with exception within a logical formalization. Those logics are very general; they offer a representation power equivalent to that of first order predicate logic. However, the automatic proof procedures are very inefficient within this too general framework. For now more than 20 years, there are several restrictions to first order logic, which have been proved to be very inefficient. That is particularly the case with Description Logics for which there are very efficient theorem provers. It has then be proposed to extend the notion of non-monotonicity to the description logics. It means that the "IS-A" links, which play a key role in description logics may be defeasible.
We are interested in defeasible description logics for two reasons, which gives birth to two internship subjects

Subject 1: for a few years now, we are developing, in the ACASA team, a new approach for evolutionary ontology, with a topological approach. It is now time to precisely compare the topological approach and the defeasible description logics to ontology with exception

Subject 2: extension of formal concept analysis with defeasible description logics. To be more precise, we are working, in the ACASA team, on the extension of formal concept analysis to description logics. Our goal, with this subject, is to go further, with defeasible description logics.

Remark: there might be a scholarship for a thesis on the first subject