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

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)

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1 Answer 1

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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.

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