There's more to Cyc's contexts than what we've covered here. The rest is reserved for the more advanced course modules:
The nesting of one context within another, such as when Joe has a belief about Sue's beliefs. Or when Scheherezade tells a story about Hassan telling a story about the Green Djinn, telling a story about the Wise Parrot, telling a story about....
The #$ist predicate explicitly connecting a proposition with some context.
Decontextualization -- making explicit the things that are implied by a ``context-within-a-context'' for the outer, containing context.
Specific lifting rules for moving (and possibly transforming) assertions form one context into another context.
The Default Coreference Axiom (DCA) by which Cyc assumes that the meaning of symbols does not change from one context to another (unless we say so specifically), and that most rules can be ``lifted'' to another context without any transformation.
Relevance-ranking of contexts to solve a given problem.