Nonmonotonic inheritance of class membership
This thesis describes a formal analysis of nonmonotonic inheritance. The need for such an understanding of inheritance has been apparent from the time that multiple inheritance and exceptions were mixed in the same representation with the result that the meaning of an inheritance network was no longer clear. Many attempts to deal with the problems associated with nonmonotonic multiple inheritance appeared in the literature but, probably due to the lack of clear semantics there was no general agreement on how many of the standard examples should be handled. This thesis attempts to resolve these problems by presenting a framework for a family of path based inheritance reasoners which allows the consequences of design decisions to be explored. Many of the major theorems are therefore proved without the need to make any commitment as to how conflicts between nonmonotonic chains of reasoning are to be resolved. In particular it is shown that consistent sets of conclusions, known as expansions, exist for a wide class of networks. When commitment is made to a method of choosing between conflicting arguments, particular inheritance systems are produced. The systems described in this thesis can be divided into three classes. The simplest of these, in which an arbitrary choice is made between conflicting arguments, is shown to be very closely related to default logic. The other classes each of which contain four systems, are the decoupled and coupled inheritance systems which use specificity as a guide to choosing between conflicting arguments. In a decoupled system the results relating to a particular node are not affected in any way by derived results concerning other nodes in the inheritance network, whereas in a coupled system decisions in the face of ambiguity are linked to produce expansions which are more intuitively acceptable as a consistent view of the world. A number of results concerning the relationship between these systems are given. In particular it is shown that the process of coupling will not affect the results which lie in the intersection of the expansions produced for a given network.