Sis estimated to average 1 hour 9eo eidorse. . incldiunq the time for reviewing. intrucions. searching exsting data This paper describes a theory of inheritance theories. We present an original theory of inheritance in nonmonotonic hierarchies. The structures on which this theory is based delineate a framework that subsumes most inheritance theories in the literature, providing a new foundation for inheritance. "* Our path-based theory is sound and complete w.r.t. a direct model-theoretic semantics."* Both the credulous and the skeptical conclusions of this theory are polynomial-time computable."* We prove that true skeptical inheritance is not contained in the language of path-based inheritance.Because our techniques are modular w.r.t. the definition of specificity, they generalize to provide a unified framework for a broad class of inheritance theories. By describing multiple inheritance theories in the same "language" of credulous extensions, we make principled comparisons rather than the ad-hoc examination of specific examples makes up most of the comparative inheritance work.
IntroductionInheritance reasoning is ubiquitous. Hierarchies provide a concise encoding of much of our comrmonsense knowledge. They appear in various guises in the literature of artificial intelligence, but also throughout the various arts and sciences. Open nearly any textbook, and some hierarchy is likely to appear. Reasoning with inheritance hierarchies is of particular interest to the artificial intelligence community because hierarchies are not only useful and native to human reasoning, but also simple and often tractable. The simplicity of the "inheritance problem" makes it attractive as a topic that can be considered in its entirety; its tractability makes it practical for the implementation of knowledge representation systems.In this paper, we present several equivalent formulations of inheritance reasoning. Each approach may be useful in a particular context; by demonstrating their equivalence, we show that the most appropriate definition may be chosen. The techniques that we develop here generalize to a broad class of existing systems, providing a unified foundation for inheritance theory and a basis for comparative analysis, as well as extending previous results.We begin, in section 2, by providing an intuitive description of what we intend by inheritance reasoning. We view inheritance hierarchies as representing primitive assertions in the knowledge base of some reasoning agent, and the inheritance problem as that of determining the agent's derived beliefs. The work in the remainder of this paper builds on this foundation.In section 3, we give a formal path-based definition of inheritance. A path-based inheritance theory gives rules describing the admissible conclusions of a hierarchy. The theory presented here combines rules concerning the transitivity of primitive assertions with an ambiguity-resolution criterion to be invoked when two paths conflict. We describe the transitivity component by the notion of reachability; ...