Abductive consequence relations

In this paper we present a systematic study of abductive consequence relations. We show that a monotone abductive consequence relation satisfies the properties of a cumulative monotonic system as defined by Kraus, Lehmann and Magidor when the disjunction of all abductive explanations is the explanation used to justify the observations, We also show that, in general, for this class of abductive consequence relations the Or rule does not hold, We present an example that shows that when there are preferences between different abductive explanations monotonicity does not hold. We show that nonmonotonic abductive systems preserve a partial version of rational monotonicity and in fact are very similar to rational relations. We also present semantic characterizations of both monotonic and nonmonotonic abductive systems in terms of cumulative models as defined by Kraus, Lehmann and Magidor.