Abstract

ABSTRACT Reiter's default logic is one of the most prominent and well-studied approaches to nonmonotonic reasoning. Its evolution has resulted in diverse variants enjoying many interesting properties. This process however seems to be diverging because it has led to default logics that are difficult to compare due to different formal characterizations—sometimes even dealing with different objects of discourse. This problem is addressed in this paper in two ways. One the one hand, we elaborate on the relationships between different types of default logics and discuss their differences wrt some basic properties. In particular, we show how two recently proposed variants, namely rational and CA-default logic, are related to each other and existing default logics. As an interesting byproduct, we obtain a cumulative counterpart to Lukasiewicz' variant of default logic. The resulting system is insofar surprising since it necessitates to refine the canonical way of assuring cumulativity in default logics. On the other hand, we pursue an integrating approach. We give a translation embedding rational and CA-default logic into a recently developed framework for default logics. This allows us not only to classify these variants, but it moreover provides us with semantical underpinnings that have been lacking so far.