What's a class?
A class is a set of entities. Each of the entities in a class is said to be an instance of the class. An entity can be an instance of multiple classes, which are called its types. A class can be an instance of a class. A class which has instances that are themselves classes is called a meta-class.
Entities that are not classes are referred to as individuals. Thus, the domain of discourse consists of individuals and classes. The unary relation class is true if and only if its argument is a class and the unary relation individual is true if and only if its argument is an individual. The following axiom holds:
(<=> (class ?X) (not (individual ?X)))
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