 Solution

For ordinary function-free Datalog, $\boxed{\text{none of the three sentences}}$ has the required form. Sentence (i) is not a definite first-order Horn clause: the category choice gives two positive alternatives, and its second clause is a negative constraint. Even allowing constraints would not remove the positive choice. Semantically, the category-choice condition fails closure under intersection of interpretations with fixed domain and functions: one model can choose only the undergraduate category, another only the masters category, and their intersection chooses neither.

Sentence (ii) needs an existentially supplied supervisor. Function-free Datalog cannot demand such a witness without naming or otherwise fixing it in the rule. Its Skolemized form is a first-order Horn clause with a function, rather than a Datalog rule. Sentence (iii) also contains a nonconstant function. Being Horn is therefore insufficient for membership in Datalog.