Clarifying Mixed Bipolar Multiple Inheritance with Exceptions

The inheritance problem can be simply stated: for any instantiation of an inheritance network , say a speciic hierarchy ? nd a conclusion set for ?. In other words nd out what is logically entailed by ?. This can be done in two ways: either by deening a deductive or proof theoretic deenition to determine what paths are entailed by a network; or by translating the individual links in the network to a more general nonmonotonic logic and using its model and proof theory to generate entailments that correspond to what one would expect from \viewing" the inheritance hierarchy. Two approaches to a solution to the inheritance problem structure this paper. The rst is widely known as the \path-based" or \proof theoretic" and the second, the \model-based" or \model theoretic". The two approaches result in both a diierent interpretation of default links as well as a variation in the entailment strategy for a solution to the inheritance problem. In either case the entailments produced need some intuitive interpretation which can be either credulous or skeptical. The semantics of both skeptical and credulous inheritance reasoners are examined.