We present a model of nonmonotonic inheritance based on a process of dialectical argumentation applied to mixed inheritance networks. A mixed inheritance network consists of strict and default links between nodes representing kinds or properties of objects. Given an object, represented by strict or default connections to nodes of an inheritance network, and a goal node in the inheritance network, the model argues with itself to determine inheritability of the goal with respect to that object. Burden of proof is a key parameter to this dialectical argumentation process, allowing our model to allocate risk in a flexible manner. We apply our model to several examples from the nonmonotonic inheritance literature, demonstrating its key properties.