Properties of System W and Its Relationships to Other Inductive Inference Operators

Abstract

AbstractSystem W is a recently introduced inference method for conditional belief bases with some notable properties like capturing system Z and thus rational closure and, in contrast to system Z, fully satisfying syntax splitting. This paper further investigates properties of system W. We show how system W behaves with respect to postulates put forward for nonmonotonic reasoning like rational monotony, weak rational monotony, or semi-monotony. We develop tailored postulates ensuring syntax splitting for any inference operator based on a strict partial order on worlds. By showing that system W satisfies these axioms, we obtain an alternative and more general proof that system W satisfies syntax splitting. We explore how syntax splitting affects the strict partial order underlying system W and exploit this for answering certain queries without having to determine the complete strict partial order. Furthermore, we investigate the relationships among system W and other inference methods, showing that, for instance, lexicographic inference extends both system W and c-inference, and leading to a full map of interrelationships among various inductive inference operators.