  We seek to find normative criteria of adequacy for nonmonotonic logic similar
to the criterion of validity for deductive logic. Rather than stipulating that
the conclusion of an inference be true in all models in which the premises are
true, we require that the conclusion of a nonmonotonic inference be true in
``almost all'' models of a certain sort in which the premises are true. This
``certain sort'' specification picks out the models that are relevant to the
inference, taking into account factors such as specificity and vagueness, and
previous inferences. The frequencies characterizing the relevant models reflect
known frequencies in our actual world. The criteria of adequacy for a default
inference can be extended by thresholding to criteria of adequacy for an
extension. We show that this avoids the implausibilities that might otherwise
result from the chaining of default inferences. The model proportions, when
construed in terms of frequencies, provide a verifiable grounding of default
rules, and can become the basis for generating default rules from statistics.
