I am trying to understand the following axioms of OWL 2 but don't know what kind of axioms they are. here R is role and C is class
As far i think 1 gives information about Range of R,but i am not sure. Thanks
The only way to make sense of these axioms is to understand the semantics of the Description Logic constructors used:
∃R is the short form of ∃R.T (where T refers to the top concept which represents the complete domain). Mathematically
(∃R.T)^I = {x ∈ δ^I | A y exists such that (x, y) ∈ R^I and y ∈ T^I}
This states that ∃R.T represents the set of individuals consisting of x such that x is associated via relation R to at least 1 individual y that is in top (the domain of discourse). If we had ∃R.C rather than T, y will be in C.
C ⊑ D states that all individuals of type C are also of type D. That is C is a subset of D.
∃R ⊑ C means all the individuals linked to at least 1 individual via relation R is a subset of C. That is why ∃R ⊑ C is also known as a domain axiom because it enforces that for all relations (x, y) in R, that x will be of type C.
¬C defines all the individuals that are not of type C in the domain of interpretation.
Going through the rest of these axioms in a similar way will help you to understand their meaning.