Credulous Reasoning About Defaults

In this paper we propose a preference-based conditional logic for credulous reasoning about defaults. A conditional default “if β then by default α” is either formalized by the strong preference “βΛ¬α is not preferred to or equivalent to β Λ α”, or by the weak preference “the preferred β is an α”. We show that these two expressions, instances of what we call the ordering and minimizing usages of preference orderings, can be considered as duals of each other. Moreover, we give a formalization of ordering and minimizing in Boutilier's modal logic CT40 and we show how to combine them in a two-phase default logic.