  Rational inference relations were introduced by Lehmann and Magidor as the
ideal systems for drawing conclusions from a conditional base. However, there
has been no simple characterization of these relations, other than its original
representation by preferential models. In this paper, we shall characterize
them with a class of total preorders of formulas by improving and extending
Gardenfors and Makinson's results for expectation inference relations. A second
representation is application-oriented and is obtained by considering a class
of consequence operators that grade sets of defaults according to our reliance
on them. The finitary fragment of this class of consequence operators has been
employed by recent default logic formalisms based on maxiconsistency.
