Description logics (DL) is a formalism for representing and reasoning about knowledge. OWL has three flavors, OWL Lite, OWL DL, and OWL Full. With our focus on OWL DL, because it is expressively powerful while still computationally feasible, some level of understanding of DL terminology is useful.
At a minimum, a DL representation consists of concepts and relationships between concepts. A concept is a set or grouping of individuals, also commonly called a class. The DL meaning of concept is very closely aligned with mathematical set theory--a concept is a set of similar things whose similarity is the criteria for set membership. Binary relationships between individuals are called roles or properties. Concepts and roles map quite naturally to a graphical representation as a network of nodes (concepts) and directed links between the nodes (roles or properties). A very important concept in DL is subsumption. A concept C is subsumed by a concept D if every instance of C is also an instance of D. This may also be expressed as concept C is a subclass of concept D. In set-theory terms, set C is a subset of set D. For example, the concept Dog is subsumed by the concept Animal--every dog is an animal. Some DL representations allow for attributes, which are simple characteristics of the individuals of a class. For example, Animals may be thought of as having the attribute Age, which is a number with an implicit unit.
The ability to represent relationships besides subsumption (i.e., roles) is an important characteristic of DL. These links between concepts can have value restrictions that express a limitation on either the types of objects that can fill the role or on the number of instances of that relationship which an instance of the concept may have. OWL DL permits number restrictions to express an exact required cardinality or to express minimum and/or maximum cardinality to constrain the number of values to a range.
A knowledge base may be thought of as consisting of two parts. The definition of concepts, roles, and subsumption hierarchies constitute the terminology of the knowledge base and is called the TBox. TBoxes may be thought of as having a lattice structure because of the inheritance implied by the subsumption relationships. TBox content is sometimes called intensional knowledge. The assertions about the individual things in the problem domain are called the ABox. For example, the assertion that "Lassie is a dog." is ABox content. ABox knowledge is sometimes called extensional.
The basic form of a TBox declaration is a definition of a concept in terms of other previously defined concepts. Definitions can be classified as:
DL terminologies usually make a set of assumptions which facilitate reasoning over the knowledge base.
When these assumptions are met, every defined concept can be expanded in a unique way into a complex expression containing only atomic concepts. An atomic concept is a primitive class or type which is not defined in terms of other concepts. An ABox assertion can assign an individual to an atomic concept. While DL research has invented and implemented representations which permit certain kinds of cycles, OWL DL appears to require that these conditions be met.
From these various OWL language elements may be used to construct other concepts and roles.