Abstract
We discuss the structure of nonmonotonic reasoning. We suggest that an important aspect of nonmonotonic reasoning systems is the ordering relationship (preference structure) on the propositions in the knowledge. We suggest that this ordering relationship must be a weak order, a complete and transitive relationship. We provide a comprehensive discussion of some central issues in preference theory. In most real applications of nonmonotonic knowledge bases the ordering relationship available is often not complete. We suggest a mechanism for completing these relationships. The basic imperative used in providing this completion is to do it in such a manner as to add as few unjustified inferences as necessary. To formally accomplish this task we introduce a measure of buoyancy associated with a weak order and suggest that the preferred completion is the one with the maximal buoyancy.
Published Version
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