Editing Description logic (section)

====Examples====
As an example, <math>\mathcal{ALC}</math> is a centrally important description logic from which comparisons with other varieties can be made. <math>\mathcal{ALC}</math> is simply <math>\mathcal{AL}</math> with complement of any concept allowed, not just atomic concepts. <math>\mathcal{ALC}</math> is used instead of the equivalent <math>\mathcal{ALUE}</math>.

A further example, the description logic <math>\mathcal{SHIQ}</math> is the logic <math>\mathcal{ALC}</math> plus  extended cardinality restrictions, and transitive and inverse roles. The naming conventions aren't purely systematic so that the logic <math>\mathcal{ALCOIN}</math> might be referred to as <math>\mathcal{ALCNIO}</math> and other abbreviations are also made where possible.

The Protégé ontology editor supports <math>\mathcal{SHOIN}^\mathcal{(D)}</math>. Three major biomedical informatics terminology bases, [[SNOMED CT]], GALEN, and GO, are expressible in <math>\mathcal{EL}</math> (with additional role properties).

OWL 2 provides the expressiveness of  <math>\mathcal{SROIQ}^\mathcal{(D)}</math>, OWL-DL is based on <math>\mathcal{SHOIN}^\mathcal{(D)}</math>, and for OWL-Lite it is <math>\mathcal{SHIF}^\mathcal{(D)}</math>.