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Dialectics and specificity: conditioning in logic-based hypothetical reasoning (preliminary report)

In this paper we start with defaults as possible hypotheses and prediction as membership in all extensions. It is argued that this is too conservative and does not allow many intuitive answers. We show how viewing membership in all extensions as a form of di-alectic, and adding a notion of conditioning can produce more intuitive answers. Defaults are possible hypotheses for a logical argument that contain a pragmatic component that is a context in which we know the default is applicable. This context is used to ignore counter arguments that follow from the context of the default. The conditioning that is presented is very close to the irrelevance that Geener added to-semantics, and the resulting solutions turn out to be very similar.