Past exam of the computer science course of the University of Oxford / 2015 / Knowledge representation and reasoning / 1 / c / iv / Solution

In ALC, $\boxed{\text{only (ii)}}$ is representable over the given symbols. It is the general concept inclusionEquivalently, 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.