A Clash of Intuitions: The Current State of Nonmonotonic Multiple Inheritance Systems

Early attempts at combining multiple inheritance with nonmonotonic reasoning were based on straight forward extensions of tree-structured inheritance systems, and were theoretically unsound. In The Mathematics of Inheritance Systems, or TMOIS, Touretzky described two problems these systems cannot handle: reasoning in the presence of true but redundant assertions, and coping with ambiguity. TMOIS provided a definition and analysis of a theoretically sound multiple inheritance system, accompanied by inference algorithms. Other definitions for inheritance have since been proposed that are equally sound and intuitive, but do not always agree with TMOIS. At the heart of the controversy is a clash of intuitions about certain fundamental issues such as skepticism versus credulity, the direction in which inheritance paths are extended, and classical versus intuitive notions of consistency. Just as there are alternative logics, there may be no single "best" approach to nonmonotonic multiple inheritance.