Nonmonotonic Inferences with Qualitative Conditionals based on Preferred Structures on Worlds

TL;DR

This paper introduces system W, a new inference method for qualitative conditionals based on preferred structures, which extends existing systems while avoiding complex computations and maintaining desirable logical properties.

Contribution

The paper presents system W, a novel inference relation that extends system Z and skeptical c-inference, based on preferred structures, with improved tractability and logical properties.

Findings

System W satisfies system P and avoids drowning problem.

System W extends system Z and skeptical c-inference.

System W is as tractable as system Z.

Abstract

A conditional knowledge base R is a set of conditionals of the form "If A, the usually B". Using structural information derived from the conditionals in R, we introduce the preferred structure relation on worlds. The preferred structure relation is the core ingredient of a new inference relation called system W inference that inductively completes the knowledge given explicitly in R. We show that system W exhibits desirable inference properties like satisfying system P and avoiding, in contrast to e.g. system Z, the drowning problem. It fully captures and strictly extends both system Z and skeptical c-inference. In contrast to skeptical c-inference, it does not require to solve a complex constraint satisfaction problem, but is as tractable as system Z.