What the Lottery Paradox Tells Us About Default Reasoning

In this paper I argue that we donotunderstand the process of default reasoning. A number of examples are given which serve to distinguish di erent default reasoning systems. It is shown that if we do not make our assumptions explicit we get into trouble with disjunctive knowledge, and if we make our assumptions explicit, we run foul of the lottery paradox. None of the current popular default reasoning systems work on all of the examples. It is argued that the lottery paradox does arise in default reasoning and can cause problems. It is also shown that some of the intuitively plausible requirements for default reasoning are incompatible. How different systems cope with this is discussed.