Skeptical Inference Relations

Abstract

In this chapter we are going to consider the notion of a skeptical inference, which constitutes a most important and studied kind of nonmonotonic inference. As we said in Chapter 3, our semantic interpretation of such an inference is derived from the traditional understanding of conditionals suggested by Ramsey and Mill. From a purely technical point of view, the representation of such an inference in terms of epistemic states could also be seen as a ‘fusion’ of the two main approaches to describing such inference suggested in the literature, namely possible worlds-based preferential models of [KLM90], and expectation-based models of [GM94]. We have already seen that possible worlds models constitute a very special case of epistemic states. On the other hand, our representation provides a generalization of the approach suggested in [GM94] that extends the latter to a broader class of nonmonotonic logics. Moreover, it shares with the latter the change of gestalt consisting in viewing preferences between worlds as merely a by-product of more basic relations holding between our beliefs. As a special case of this representation, we will establish a direct correspondence between preferential inference relations and supraclassical Tarski consequence relations.