>> LLMs are inherently statistical interpolators. They operate beautifully in an Open World (where missing information is just "unknown" and can be guessed or left vague) and they use Non-Monotonic Reasoning (where new information can invalidate previous conclusions).
I think LLM reasoning is not so much non-monotonic as unsound, in the sense that conclusions do not necessarily follow from the premises. New information may change conclusions but how that happens is anyone's guess. There's some scholarship on that, e.g. there's a series of papers by Subarao Kamphampathi and his students that show how reasoning models' "thiking" tokens don't really correspond to sound reasoning chains, even if they seem to improve performance overall [1].
But it is difficult to tell what reasoning really means in LLMs. I believe the charitable interpretation of claims about LLM reasoning is that it is supposed to be informal. There is evidence both for and against it (e.g. much testing is in fact on formal reasoning problems, like math exam questions or Sokoban, but there's tests of informal reasoning also, e.g. on the bar exam). However, different interpretations are hard to square with the claims that "we don't understand reasoning"; not a direct quote, but I'm aware of many claims like that by people whose job it is to develop LLMs and that were made at the height of activity around reasoning models (which seems now to have been superseded by activity around "world models") [1].
If LLMs are really capable of informal reasoning (I'm not necessarily opposed to that idea) then we really don't understand what that reasoning is, but it seems we're a bit stuck because to really understand it, we have to, well, formalise it.
That said, non-monotonic reasoning is supposed to be closer to the way humans do informal reasoning in the real world, compared to classical logic, even though classical logic started entirely as an effort to formalise human reasoning; I mean, with Aristotle's Syllogisms (literally "rsasonings" in Greek).
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[1] Happy to get links if needed.