A concept language extended with di erent kinds of transitive

Motivated by applications that demand for the adequate representation of part-whole relations, diierent possibilities of representing transitive relations in terminological knowledge representation systems are investigated. A well-known concept language, ALC, is extended by three diierent kinds of transitive roles. It turns out that these extensions diier largely in expressiveness and computational complexity, hence this investigation gives insight into the diverse alternatives for the representation of transitive relations such as part-whole relations, family relations or partial orders in general.