Rational Closure Extension in SPO-Representable Inductive Inference Operators

Jonas Haldimann, Thomas Meyer, Gabriele Kern-Isberner, Christoph Beierle

Abstract: The class of inductive inference operators that extend rational closure, as introduced by Lehmann or via Pearl’s system Z, exhibits desirable inference characteristics. The property that formalizes this, known as (RC Extension), has recently been investigated for basic defeasible entailment relations. In this paper, we explore (RC Extension) for more general classes of inference relations. First, we semantically characterize (RC Extension) for preferential inference relations in general. Then we focus on operators that can be represented with strict partial orders (SPOs) on possible worlds and characterize SPO-representable inductive inference operators. Furthermore, we show that for SPO-representable inference operators, (RC Extension) is semantically characterized as a refinement of the Z-rank relation on possible worlds.