A Preference-Based Approach to Default Reasoning: Preliminary Report

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.