Interpolation and Beth Definability in Default Logics

We investigate interpolation and Beth definability in default logics. To this end, we start by defining a general framework which is sufficiently abstract to encompass most of the usual definitions of a default logic. In this framework a default logic DL is built on a base, monotonic, logic L. We then investigate the question of when interpolation and Beth definability results transfer from L to DL. This investigation needs suitable notions of interpolation and Beth definability for default logics. We show both positive and negative general results: depending on how DL is defined and of the kind of interpolation/Beth definability involved, the property might or might not transfer from L to DL.