Is it not true that the brain process in ternary?
From the point of view of perception, I believe that we process the world in terms of pairwise comparisons. For example, the atomic indivisible of visual processing is figure/ground separation.
Back in ancient CS classes my prof said that was a Russian attempt of building ternary processors with +1, 0, -1 represented as voltages.
Another strike in for-ternary column is that it's the most efficient in the number of digits for representing numbers. Pi is optimally efficient but non-integer bases would break anyone's brain, I think.
The author also made a more approachable miniseries in Russian: https://habr.com/ru/articles/496366/
It can arduously crank through simple logic problems with its ludicrously tiny memory (around 8 bytes). Everything else is intuition and guesswork.
You can try to model those heuristics with various logics. Some logics work better in certain situations. Classical first order logic is actually really bad at modeling brain work, but it's simple to automate, so we use it even where it's wildly inappropriate.