# Restriction in description logic

$$Human ⊓ ¬Female ⊓ (∃married.Doctor) ⊓ (∀hasChild.(Doctor ⊔ Professor))$$

Here, $$∃married.Doctor$$ means if there exists an individual who is married to Bob belongs to $$Doctor$$ concept.

But my confusion is what if I use $$∀$$ instead of $$∃$$ will this mean:

1. Bob is married to individuals all of them belongs to $$Doctor$$ concept or

2. Bob is married to all from $$Doctor$$ concept. (like FOL if I pick anyone from Doctor domain married to Bob)

Below is the usual definition of $$\forall$$ and $$\exists$$ in description logic:
$$\forall R.C=\{x \in \Delta | \forall y, (x,y) \in R \to y \in C \}$$
$$\exists R.C=\{x \in \Delta | \exists y, (x,y) \in R \land y \in C \}$$
So apparently in your case if you use $$\forall$$ instead of $$\exists$$ and assuming your Bob is a concept assertion of your above recursively constructed concept, then your interpretation 1 is the right one. Also note strictly speaking in DL Doctor as a concept name is not a domain, but a subset of the domain of a certain language of DL.