Non-cumulative Reasoning: Rules and Models

摘要

Many abstract studies of non-monotonic consequence relations (such as the one by Kraus, Lehmann and Magidor) have focused on logics which, in addition to satisfying some other properties, are cumulative. A number of concrete non-monotonic logics that have been proposed in the literature, however, are not cumulatie. Furthermore, the restriction of smootheness that has to be imposed on preferential models to ensure that their consequence relation satisfies Cautious Monotonicity is a strange condition from an ontological point of view. We argue that cumulativity is not a necessary property for non-monotonic logics, and we will give a number of representation results for non- cumulative consequence relations. This paper thus complements the results of Kraus. Lehmann and Magidor for the non-cumulative case.