When one constructs a Knowledge Base one has to define Classes. One does this with help of [Class](/blog/619/) Inclusion and [Class](/blog/619/) [Equivalence](/blog/776/).
In a Class Inclusion one says that one Class is Subclass of another Class. Here it meas the the Professor class is a Subclass of Faculty Member. One can also describe this with an Equal Expression in First Order Logic, which states for all Variables X it holds that if X a Professor, then X is also a Faculty Member.
Alternatively one can have a Class Equivalence as the Professor might be equivalent to a Faculty Member which equals the first Order Logic that uses and universal Quantifier and equivalence, instead of Implication. This both methods are quite the same.
Professor ⊑ FacultyMember
every Professor is a Faculty Member
equals (∀x)(Professor(x) → Faculty Member
Professor ≡ FacultyMember
the Factuality Members are exactly the Professors
(x)(∀x)(Professor(x) FacultyMember