The above mentioned concept specifications are only a subset of all possible specifications. The expressiveness and tractability of a particular DL depends on the type and allowed combinations of connectives and restrictions. There exist several theorem provers for special types of DLs. DL systems usually distinguish two separate reasoning components. Assertional reasoners support a query language as access to their state.
Some query languages offer the expressiveness of the full first-order calculus.
Concrete Domains Existing DL systems usually cannot deal with concepts defined with the help of algebra. For instance, it is not possible to specify a defined concept SmallCircle that resembles every circle whose radius is less than 10mm . However, these functions and their related concepts escape the DL semantics and prevent any reasoning. The above mentioned concepts SmallCircle and VerySmallCircle can be easily specified in CTL as defined concepts. CTL would immediately recognize the subsumption relationship between these concepts.