What is a Default Priority?

The notion of default priority has played a central role in default reasoning research. We show that Pearl’s Z-ranking of default rules need not always correspond to priorities. System Z can still be used for priorities, but perhaps not in the obvious manner. Rather than the Z-ranking of rules, we show that the Zrankings of the negations of the material counterparts of rules correspond naturally to priorities. We also show that the priorities of default rules can be explained in terms of belief revision by appeal to the epistemic entrenchment of the material counterpart of a rule in a theory of expectations in the Theorist sense. Furthermore, Brewka’s notion of preferred subtheories provides a means of improving on Pearl’s 1-entailment, given this connection. These results are demonstrated within the modal logic CO*, a unifying framework for various types of default reasoning and belief revision.