I think the interface of LLM with formalized languages is really the future. Because here you can formally verify every statement and deal with hallucinations.
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For example, how might an arbitrary statement like "Scholars believe that professional competence of a teacher is a prerequisite for improving the quality of the educational process in preschools" be put in a lean-like language? What about "The theoretical basis of the October Revolution lay in a development of Marxism, but this development occurred through three successive rounds of theoretical debate"?
Or have I totally misunderstood what people mean when they say that developments in automatic theorem proving will solve LLM's hallucination problem?
> This takes for granted a formal setting, which is what I'm questioning in any of these 'real world' contexts.
A formal model of semantics would likely be a low-level physical representation of possible states augmented with sound definitions of higher-level concepts and objects. I don't think humans are capable of developing a formal semantics that would work for your sentences (it's taken us hundreds of years to approach formalization of particle physics), but I think that an automated prover with access to physical experiments and an LLM could probably start building a more comprehensive semantics.