What does it mean for humans to understand? There are many times in the past where i thought i understood something and then i grow older and i see the holes.
One definition of "understand" would be "have or obtain an internal model of Thing-or-process-to-be-understood which is close enough to reality that it allows you to reasonably predict what will happen and make effective decisions regarding that thing". It does not have to be a perfect model - if it would, then I'll be the first to say that I don't understand anything according to that definition, but it's a bit more tricky than it sounds on the surface. For example, for a self-driving car, "understanding pedestrians" according to this definition does require an ability to predict how they will behave and thus "know" what factors affect that - that the likelihood of a kid suddenly springing towards the middle of the road is highly dependent on the presence of a ball or a pet in that direction; that certain wobbly and jagged movements are indicators that the person might behave in a less predictable manner than the average person, etc, etc; and if a system does have this practical knowledge (measured by how well it is able to effectively apply it for its goals) then I'd say that it does have some understanding.
Yeah, I feel this question is important to understand before we worry about what it means for the AI to understand.
My thought is that we've got three types of "understanding":
1) social understanding
2) intuitive understanding
3) structural understanding
Social understanding is something the society we live in knows, but the individual only knows in so far as the individual is doing something to fit in or via peer pressure. So for example, some high latitude countries eat fish for breakfast. Supposedly the statistics show that this helps them be more healthy than countries at similar latitudes which do not eat fish for breakfast ... probably because of problems due to lack of vitamin D due to lack of sunlight for certain parts of the year (the fish oil helps with this). However nobody actually "knows" this. They just eat fish because everyone else eats fish.
Intuitive understanding is anything where we start to use flowery language like "experience" or "gut". You're really good at it, but just giving someone a flow chart isn't good enough. They have to have gone through the experience themselves. Driving is a good example. We make people take a test, but if just giving them diagrams and rules was good enough, then we wouldn't need a test where you actually drive and requirements about a certain number of hours of supervised driving.
Structural understanding is anything that can be put to rules. So there's a lot of mathematics and algorithm stuff here. A simple example might be playing tic tac toe. The game is simple enough that you can write down a few rules that allow you to never lose.
EDIT:
My categories don't really answer the question, but they do give profiles and categories to look out for.
Social understanding is good because it statistically learns to avoid lethal pitfalls. Like, if there's a dangerous well in the forest that people fall down and die in. A society might start telling people to not go in the forest because other people go in there and die. However, the society doesn't know why this is good advice.
Intuitive understanding is good because it allows you to quickly statistically learn how to deal with imperfect and chaotic systems while getting good results.
Structural understanding is good because it allows you to break free of the statistics of the previous two understandings. You can get exact results. Also it lets you break free of issues that come from distantly causal action + consequence. A person's intuition might not tell them that dumping toxic waste into the water is a good idea because things don't go bad until a lot of waste has already been dumped. Similarly a society might make a similar judgement if the failure is far enough away from the actions that kick it off. However, if you understand the structural relationships between things then you'll have an idea that toxic waste should not be consumed.
I would use "experiential understanding" instead of "intuitive understanding", but I think we mean the same thing. I am not sure I agree with your hierarchy, however. I would rather have an experiential understanding of marital arts if I was faced with a would-be attacker than I would have a "structural understanding" as you put it. In other words, for many domains of interaction with the world, an experiential knowledge is far superior to a "structural" or as I understood what you were saying a "propositional" understanding of a topic or subject.
Here's another way of putting what I'm saying: when we want to learn about a tree, in the West, our first inclination is to cut it down, categorize/classify the parts, and count the rings. We think we know what a "tree" is at that point. In the East (and I'm learning this perspective from Eastern Orthodox Christianity), if you want to learn about a tree, you plant one. Maybe more than one. Nurture it. Prune it. Fertilize it. Watch it grow. Watch it change with the seasons. Build a treehouse in it for your kids. Watch your daughter get married in the shade of the tree. In other words, instead of dissecting something (which kills the thing itself) in order to categorically "understand" something propositionally, in the East, they focus on having a relationship with something in order to understand it.
It's not a hierarchy, it's just a list. Structural isn't meaningfully better than anything else. It just "works" for different reasons.
Intuitive is often faster to react and faster to get off the ground and producing results. So in a fight intuition is probably going to be better. That being said, supposedly the boxing fight that the movie 'cinderella man' was based off of involved Braddock analyzing Baer's fighting style and figuring out some foot work that kept him from getting pummeled. There's no reason that structural, intuitive, and social understanding can't all work together to get a result.
I misunderstood what you said as a hierarchy because of how you worded your last paragraph, but I would agree with you that synthesizing the different types of knowledge is the best way to interact with the world.