Modern AI, things like AlphaGo are examples of applied AI. "Common sense" falls within the realm of artificial general intelligence, which is a line of research that's largely abandoned now in favor of applied AI. Modern AI solutions are engineered to solve very very specific problems. You are never going to see attempts to teach "common sense".
https://arxiv.org/abs/1705.08807
With that said, the above is what the world's AI researchers think is possible hopefully within my lifetime using just applied AI without the notion of "common sense".
Common sense is AGI. That's not the goal anymore. The goal is to do things like self driving cars. Both Google and Tesla have placed vehicles on the road that have driven for literally millions of miles.
The idea is to build a bunch of classifiers and regression models and use them together in an ensemble to solve your problem. The same approach is being applied successfully to a lot of unrelated fields where deep learning is concerned.
Also, modern AI doesn't even pretend to be biological in nature, in fact we'll known researchers like Andrew Ng make a point in saying that they are only biologically inspires and that's where the commonalities end.
There are other models like HTM that are way more ambitious and want to come up with a single generalized scheme to solve a broad range of problems, AGI style. These guys think biology is important and are trying to emulate the neocortex. They ARE going for AGI, common sense, etc.
