Question about semantics of existential restriction and universal restriction

(\forall R.C)^I contains domain elements that have R successor to domain elements that interpret C and also the domain elements that don't have R successor.

(\exists R.C)^I contains domain elements that have at least one R successor to domain elements that interpret C.

One thing we should notice when we try to write DL axioms to model a statement is that, it is better to make sure that this DL statement should work for every interpretation.

For example, if we want to model a statement that a woman is a person who has only female gender. It is not sufficient to write "Woman \subseteq Person \sqcap \forall hasGender.Female". Because if, in the interpretation, we have a person that don't have any gender information. In this case, the reasoner will think this person is a woman. But in fact, this person might be a man. On the other hand, It is also not sufficient to write "Woman \subseteq Person \sqcap \exists hasGender.Female". Since, for example, if there is a person who is intersex, which means he or she has both female and male gender. In this case, if you just write "Woman \subseteq Person \sqcap \exists hasGender.Female", then this person will be classified as a woman, which is not what we want. Instead, it is better to model it like: "Woman \subseteq Person \sqcap \forall hasGender.Female \sqcap \exists hasGender. Female".