Nonmonotonic Inferences with Qualitative Conditionals based on Preferred Structures on Worlds

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