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 redbird-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.
Default reasoning has been widely studied in artificial intelligence. One of the the most influential piece of work within this area is that of Kraus et al. (1990). Kraus et al. investigated the properties of different sets of Gentzen-style proof rules for non-molmtonic consequence relations, and related these sets of rules to the model-theoretic properties of the associated logics. Their major result was that a particular set of proof rules generated the same set of consequences as a logic in which there is a preference order over models. This system of proof rules was termed System P by Kraus et al.. the P standing for "preferential".
Clearly, the second approach is more cautious. Intuitively, it demands that there is a specific argument for τ that is contained in each rational stance a reasoner can take given Γ, DRules, and SRules. The first option doesn't bind the acceptability of τ to a specific argument: it is sufficient if according to each rational stance there is some argument for τ. In Default Logic, the main representational tool is that of a default rule, or simply a default.