Description Logics (DLs) are a
Family of Logics that are Fragments of First Order Logic. In general what one does in Description Logics is from simple Descriptions to create more complex Descriptions with the help of Constructors. The different Variants of Description Logics differ in the applied Constructors as there are Constructors with different Exprissivity. Originally these Description Logics have been developed from Semantic Networks. Description Logics have been developed to be decidable most times and some times they are also feasible which means that they do not have too high complexity.
DLs are related to Modal Logics
The Web Ontology Language considers more complex Description Logics that go beyond ALC. If all the roles that are considered in ALC are transitive, then the Letter ALC changes to S. Datatypes are for example Strings or Integers.
The Constructors form and build up single Languages in Description Logics.
ALC: Attribute Language with Complement
S: ALC + Transitivity or Roles
H: Role Hierarchies
I: Inverse Roles
N: Number restriction ≤ n R etc.
Q: Qualified number restrictions ≤ R.C etc.
F: Functional Roles
R: Role Constructors
There are also qualified number Restriction. For instance a String Quartet would be for Persons that all play String. Therefore a qualified number restriction has alos a Class Restriction on the Range of that Role or Property.
Role Hierarchies are given by subclass relations.