Plausibility measures and default reasoning

In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, ε-semantics, possibilistic structures, and κ-rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties (for Kraus, Lehmann, and Magidor). While this was viewed as a surprise, we show here that it is almost inevitable. We do this by giving yet another semantics for defaults that uses plausibility measures, a new approach to modeling uncertainty that generalize other approaches, such as probability measures, belief functions, and possibility measures. We show that all the earlier approaches to default reasoning can be embedded in the framework of plausibility. We then provide a necessary and sufficient condition on plausibilities for the KLM properties to be sound, and an additional condition necessary and sufficient for the KLM properties to be complete. These conditions are easily seen to hold for all the earlier approaches, thus expiring why they are characterized by the KLM properties.