A structural base for conditional reasoning

There are several approaches implementing reasoning based on conditional knowledge bases, one of the most popular being System Z [1]. We look at ranking functions [2] in general, conditional structures and crepresentations [3] in order to examine the reasoning strength of the different approaches by learning which of the known calculi of nonmonotonic reasoning (System P and R) and Direct Inference are applicable to these inference relations. Furthermore we use the recently proposed Enforcement-postulate [4] to show dependencies between these approaches.