= 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>.
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