= Solution
In <ALC>, $\boxed{\text{only (ii)}}$ is representable over the given symbols. It is the <general concept inclusion>
$$
\boxed{\mathit{Undergrad}\sqcup\mathit{Masters}\sqsubseteq\exists\mathit{SupervisedBy}.\top.}
$$
Equivalently, use one <general concept inclusion> for each category. Unary predicates become <description logic concepts> and the supervision predicate becomes a <description logic role>.
Sentence (i) depends on a ternary predicate evaluated at two named constants. Basic <ALC> has unary <description logic concepts> and binary <description logic roles>, with no constructor for that course-and-year slice of a ternary predicate. Sentence (iii) uses a counting function and a comparison relation that basic <ALC> cannot express. Replacing these conditions by freshly named <description logic concepts> would give an informal encoding, but would not define their meanings or establish equivalence in the supplied vocabulary.
Back to article page
