So, if I'm understanding right:

• Backwards chaining is an old classical algorithm for logic proving.

• They've implemented backwards chaining using a bunch of language models, so it works well with natural text.

• Given a knowledge base (which are available as datasets these days), it can decompose a statement and check if it's logically consistent with that knowledge.

• The reason they're interested in this is to use it as a training function to make language models more accurate.

This is effectively an old "expert system" from the 70s built out of neural networks. I wonder what other classical algorithms you can implement with neural networks.

I also wonder if you could use this to create its own knowledge base from internet data. Since the internet is full of contradicting information, you would have to compare new data against existing data somehow and decide which to keep.