Syllogimous does seem pretty legit though. I've got some research articles on relational training protocols and expected results lined up. Ideally, I think a perfect brain training protocol incorporates regular & strenuous n-back training, syllogistic or relational training, meditation, and cardiovascular exercise. Probably some supplements like creatine and omega-3 fatty acids, nutrition like choline from eggs, and consistent sleep hygiene like a regular bedtime and wake-up time.
That all might sound like a lot, but I think the cognitive benefits are worth it.