There are 10 levels in the logic skill. This is one of the few skills that children can start learning once they reach max level in the mental skill. If a child completes the mental aspersion, as an adult, the sim will have a +20% boost in learning the logic skill. Also to make sure that the lot has the lot trait "Science Lair" , as this gives a +50% to skill gains.
The logic skill can be start by either buying a chess table, a telescope or buying the logic books from the bookshelf. There are several jobs and one aspiration that require the logic skill, so you can level up a sim while also working towards that next promotion.
I found the easiest way to get a sim maxed out in logic is to have them play chess whenever they can and to have the lot trait set to science lair. I didn't use a child since I don't have one yet in the game and it took about 3 hours of playing (real world).