Terminological Cycles : Semantics and Computational

Terminological knowledge representation formalisms are intended to capture the analytic relationships between terms of a vocabulary intended to describe a domain. A term whose deenition refers, either directly or indirectly, to the term itself presents a problem for most terminological representation systems because it is obvious neither whether such a term is meaningful, nor how it could be handled by a knowledge representation system in a satisfying manner. After some examples of intuitively sound terminological cycles are given, diierent formal semantics are investigated and evaluated with respect to the examples. As it turns out, none of the diierent styles of semantics seems to be completely satisfying for all purposes. Finally, consequences in terms of computational complexity and decidability are discussed.