= Solution
$\boxed{\text{No.}}$ A <disjunctive Datalog> <knowledge base> can have several incomparable minimal <Herbrand models> without a <least Herbrand model>. Take the single disjunctive fact
$$
\top\to P(a)\lor Q(a).
$$
Both $M_1=\{P(a)\}$ and $M_2=\{Q(a)\}$ are <Herbrand models>. Any <least Herbrand model> would have to be contained in both, hence contained in $M_1\cap M_2=\varnothing$. But the empty <Herbrand interpretation> falsifies the disjunctive fact. This is a contradiction. Taking the intersection of all models therefore fails because that intersection need not itself be a model.
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