Relation And Extension In Nonmonotonic Inheritance Systems

An inheritance system is a representation system founded on the hierarchical structuring of knowledge. The primary advantage of hierarchical structuring is that it is an efficient method of representation. A second advantage of hierarchical structuring, after representational compactness, is that it makes searching more efficient. Its primary aim is to present a formal mathematical theory of a popular reasoning strategy that to date has been defended mostly by appeals to intuition: multiple inheritances with exceptions to defeasible inheritance properties. Reasoning with exceptions is complicated because it involves operations outside of classical first order logic. The formalism that have developed to express the nonstandard inference rules that underlie inheritance bears some relation to default and nonmonotonic logics, but it includes an important hierarchical notion these other systems lack.About the research of nonmonotonic inheritance system, it was developed by Tourtzky initially, along with the more research, now we focus on two aspects, one is a direct way and the other is not direct. But the direct way is more intuitive. A number of different accounts, in the semantic analysis of nonmonotonic inheritance systems, both direct and translational,have been developed with a variety of theoretical frameworks, and it would be impossible to treat them all with any care. Instead, this chapter concentrates on only a few theories developed within a single framework—roughly, those based on tourtzky's original ideas or their close relatives. The goal of this chapter is to present the work that added inheritable relations to the nonmonotonic inheritance systems. The thing that we researched in inheritance systems is only for individuals and properties, so first I transformed the binary relation into unitary property, and dealt it with accordingly. And we will research three extensions in the defeasible inheritance systems. The concept of knowledge is expanded and the description language of computer is enriched when add the relation to inheritance system, it is significantly in the research of artificial intelligence.