The T-Box contains specifications of concepts and roles . There is no direct modal logic correspondence for A-Box entries. From a modal logic point of view, A-Box instances are names for worlds. On the T-Box level there are two major reasoning problems. First of all, one wants to know whether a newly introduced concept definition is consistent with the previously introduced ones.
Subsumption relations are very useful for structuring a knowledge base.
Finding out all subsumption relations between all concepts is called classification , and this is the basic operation of all T-Boxes. In this paper we investigate problems which have been discussed more in the description logic context than in the modal logic context. Therefore we prefer using the description logic notions. Table 1 compares the different notions used by the modal logic community with the corresponding notions used by the description logic community. Since most of them are decidable, they represent proper fragments of FOL, but they are usually more expressive than propositional logic.