Inaccessible Worlds and Irrelevan

Recently, the relationship between several forms of default reasoning based on conditional defaults has been investigated, In particular, the systems based on e-semantics, preferential models t and (fragments of) mod ally-defined conditional logics have been shown to be equivalent. These systems form a plausible core for default inference, but are too weak in general, failing to deal adequately with irrelevance. We propose an extension of the (modal) conditional logics in which one can express the truth of sentences at inaccessible possible worlds and show how this logic can be used to axiomatize a simple preference relation on the modal structures of this logic. This preferential semantics is shown to be equivalent to 1-entailment and rational closure. We suggest that many metalogical systems of default inference can be axiomatized within this logic, using the notion of inaccessible worlds.