SPO-Representable Inductive Inference Operators Extending Rational Closure

Rational closure, as introduced by Lehmann or via Pearl’s system Z, exhibits desirable characteristics of nonmonotonic inference relations. The property (RC Extension), formalizing that an inductive inference operator extends rational closure, has recently been investigated for basic defeasible entailment relations. In this article, we explore (RC Extension) for more general classes of inference relations. We semantically characterize (RC Extension) for preferential inference relations in general by a specific type of preferential models. Then we focus on operators that can be represented with strict partial orders (SPOs) on possible worlds and characterize SPO-representable inductive inference operators. We show that for SPO-representable inference operators, (RC Extension) is semantically characterized by refinements of the Z-rank relation on possible worlds. Finally, we explore several examples of inference operators satisfying (RC Extension) and their interrelationships.