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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 inR, we introduce the preferred structure relation on worlds. The preferredstructure relation is the core ingredient of a new inference relation calledsystem W inference that inductively completes the knowledge given explicitly inR. We show that system W exhibits desirable inference properties likesatisfying system P and avoiding, in contrast to e.g. system Z, the drowningproblem. It fully captures and strictly extends both system Z and skepticalc-inference. In contrast to skeptical c-inference, it does not require to solvea complex constraint satisfaction problem, but is as tractable as system Z.

Nonmonotonic Inferences with Qualitative Conditionals based on Preferred Structures on Worlds