Adding Number Restrictions to a Four-Valued Terminological Logic

An intuitive four-valued semantics can be used to develop expressively powerful terminological logits which have tractable subsumption. If a fourvalued identity is also used, number restrictions can be added to the logic while retaining tracts bility. The subsumptions supported by the logic are a type of “structural” subsumption, where each structural component of one concept must have an analogue in the other concept. Structural subsumption captures an important set of subsumptions, similar to the subsumptions computed in KL-ONE and NIKL. This shows that the trade-off between expressive power and computational tractability which plagues terminological logics based on standard, two-valued semantics can be defeated while still retaining a useful and semantically supported set of subsumptions.