Nonmonotonic inference based on expectations

Abstract

We show how nonmonotonic inferences may elegantly be interpreted in terms of underlying expectations. The fundamental idea is that when we reason, we make use of not only the information that we firmly believe, but also expectations that guide our beliefs without quite being part of them. We propose two ways of modelling the expectations used in nonmonotonic reasoning: by expectation sets, equipped with selection functions, and by expectation relations. For each of these we prove representation theorems and establish relations with several other modellings in the area, including Poole systems and preferential models. We also show that by using the notion of expectation, one can unify the treatment of the theory of belief revision and that of nonmonotonic inference relations. This is accomplished by viewing the relation of “epistemic entrenchment” used in Gärdenfors [18] and Gärdenfors and Makinson [20] as a kind of expectation ordering. Thus we see belief revision and nonmonotonic reasoning as basically the same process, albeit used for two different purposes.