No, the thing you'd want the LLM to be learning would be the rules.

> But can they learn how to apply structured knowledge in precise ways?

I personally believe: clearly yes, already. You can already get a LLM to generate code for simple logical problems. You can ask ChatGPT to modify a solution in a particular way, showing it has some understanding of the underlying logic, rather than just regurgitating solutions it saw.

In other domains, you can already give IQ tests to GPT-N: https://lifearchitect.ai/ravens/. Others have written in more detail than I could do justice to: https://www.gwern.net/Scaling-hypothesis#scaling-hypothesis.

I'd just note that a lot of commentators make quite simple errors of either goalpost-moving or a failure to extrapolate capabilities a year or two ahead. Of course, no linear or exponential growth curve continues indefinitely. But betting against this curve, now, seems to me a good way of losing money.