I'm trying to define the Uniqueness quantification ∃! in description logic. I am aware that it is possible to define it in predicate logic, as the Wikipedia page (and many answers here) shows, but as description logic is weaker, can we define this quantification in description? If not, why not?
I am talking about description logic ALC without any extensions.
I think my answer would be that it is not possible due to the fact there are no free variables in Description Logic. Am I right?