What the Lottery Paradox Tells Us About Default Reasoning

In this paper I argue that we do not under stand the process of default reasoning A number of examples are given which serve to distinguish di erent default reasoning sys tems 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 para dox 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 dif ferent systems cope with this is discussed