The formal definition of Attribute Language with Complement (ALC) allows that complex Classes to be constructed. There can be an Atomic Class, the upper or Lower Class, the can be a Negation complex Class, they can be the Conjunction or Disjunction of complex Classes or Roles in Combination with complex Classes ad existential or universal Quantification.
To put it all together one can form a TBox with the transactional Knowledge which contains all Assertions of the form of
Class Inclusion or
Class Equivalence where C and D are complex Classes. This is the Terminological Knowledge.
Both TBox and ABox form an ALC Knowledge Base
ALC: (A is an Atomic Class, C and D are complex Classes and R is a Role)
ALCTBox contains Assertions of the form
C ⊑ Dand
C ≡ D, where C, D are complex Classes.
contains Assertions of the formC(a)
andR(a,b)``, where C is a complex Class, R a Role and a,b Individuals.
ALC-**Knowledge Basecontains an ABox and a TBox.