Class Axioms
Class Axioms are used to define classes, e.g in <owl:class/> defines the existence of a class and is a class axiom, likewise is the ID of the class a class axiom.
The set of individuals linked to the class is called class extension.
SubClassOf axiom
It means the class expression is an instance of another classes expression, it is used to display hierarchy. It follows that the set of individuals in the class 1 are a subset of the set of individuals of class 2. Due to that the the first class expression which is the subclass of the other is more specific than the other.
Equivalent classes axiom
Equivalent class axioms state that multiple class expressions are equivalent to each other. Thus these class expressions can be used as synonym, when the meaning of the ontology won't be changed.
Disjoint classes axiom
These axioms state that class expressions are disjoint,thus they have no instances in common.
