In this paper, we analyze systematically the downward (property flow) and the upward (individual flow) views of inheritance for different categories of inheritance networks. We observe that both these views assign the same meaning to tree-structured hierarchies, and explain the divergence in the interpretation of more general networks in terms of their expressive power. This simple analysis sheds light on the inherent nature of nonmonotonic inheritance and can form the basis for the design of efficient algorithms for certain classes of queries. In addition, we describe the notion of preferential inheritance to specify additional conflict resolution information that can be integrated smoothly with the upward view of inheritance.