A Framework for Part-of Hierarchies in Terminological Logics

There is a growing recognition that part-whole hierarchies are a very general form of representation, widely used by humans in commonsense reasoning. This paper develops a terminological logic, and related inference mechanisms for representing and reasoning about composite concepts and individuals. A basic terminological logic language is extended with constructs for describing composite concepts in terms of their parts and the relationships between them. A part-of hierarchy is deened, based on the relationship of compositional inclusion. This part-of hierarchy is analogous to, but diierent from, the \is-a" hierarchy. Compositional in-ferencing is deened as a process which infers the existence of a whole, based on the existence of the required parts, where the parts are in the necessary relationship to each other. Three stable states are deened with respect to compositional inferencing-compo-sitional extensions, credulous compositional extensions and skeptical compositional conclusions. This framework signiicantly enhances and is complementary to, knowledge representation and reasoning based on is-a hierarchies .