How should what one knows about an individual affect default conclusions about that individual? This paper contrasts two views of ``knowledge'' in default reasoning systems. The first is the traditional view that one knows just what is in one's knowledge base. It is shown how, under this interpretation, having to know an exception is too strong for default reasoning. It is argued that we need to distinguish ``background'' and ``contingent'' knowledge in order to be able to handle specificity, and that this is a natural distinction. The second view of knowledge is what is contingently known about the world under consideration. Using this view of knowledge, a notion of conditioning that seems like a minimal property of a default is defined. Finally, a qualitative version of the lottery paradox is given; if we want to be able to say that individuals that are typical in every respect do not exist, we should not expect to conclude the conjunction of our default conclusions. \n This paper expands on work in the proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning .
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