(Searching the internet I have noticed that different people have different perspectives on the idea of the trivium and apply it in different ways to education. I join the club, with no pretense that I am being faithful to the original concept.
)As for grammar, there is quite a bit of go knowledge: the basics of capture and ko, the need for two eyes for independent life, the different types of eyes, the different kinds of seki, basic shapes, basic haengma, basic tesuji, etc. Much of it is encapsulated in proverbs, such as eight live, six die and hane at the head of two stones.
I think that dialectic encompasses technique: tesuji, tsumego, much of the endgame. These types of problems have provable solutions. Reading would also go here. I think that joseki would, too. Not that they are provable, but they undergo a dialectical process.
Rhetoric would include strategy and creative application of knowledge and technique: fuseki and much of the middle game; attack and defense, reduction, invasion, sabaki, shinogi, sacrifice, furikawari, etc.; advanced concepts such as thick and thin, heavy and light, kikashi and kikasare. Also efficiency and positional judgement.
