On managing nonmonotonic transitive relationships

Efficient representation of knowledge, under a multiple inheritance scheme with exceptions, plays an important role in artificial intelligence. Fast verification of the existence of a transitive relationship in such a hierarchy is of great importance. This paper presents an efficient algorithm for computing transitive relationships with exceptions. It is based on a known transitive closure compression technique that uses a labeled spanning tree of a directed acyclic graph. It is a very fast algorithm compared to graph-search algorithms that solve the same problem, without sacrificing some desirable properties that nonmonotonic multiple inheritance schemes should, in general, possess. Moreover it satisfies low storage requirements.