James P. Delgrande
An approach to nonmonotonic inference, based on preference orderings between possible worlds or states of affairs, is presented. We begin with an extant weak theory of default conditionals; using this theory, orderings on worlds are derived. The idea is that if a conditional such as "birds fly" is true then, all other things being equal, worlds in which birds fly are preferred over those where they don’t. In this case, a red bird would fly by virtue of red-bird-worlds being among the least exceptional worlds in which birds fly. In this approach, irrelevant properties are correctly handled, as is specificity, reasoning within exceptional circumstances, and inheritance reasoning. A sound proof-theoretic characterisation is also given. Lastly, the approach is shown to subsume that of conditional entailment.