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With today's hype about large language models, I was wondering if there is any research about mathematical structures for describing sets of words or sentences from a "semantics perspective".

Some web searches led to nothing – probably because I use wrong keywords. On StackExchange I found this question and this question of interest, but one doesn't have an answer, the other takes more of a formal-logic perspective (well-formed formulae), and both are somewhat old.

pglpm
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    Not an answer, but possibly of interest: Randall Munroe's take on the number of meaningfully-distinct 140-character tweets https://what-if.xkcd.com/34/ <> Also not an answer: The meaning of language is not contained in language, but is necessarily tied to things like "context" and "experience in the external world." In my view this is one reason LLMs are ... profoundly unskillful ... at writing proofs, and part of why relying on them, or even construing them as "intelligent," is Misguided and Dangerous. – Andrew D. Hwang Sep 13 '23 at 15:11
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    @AndrewD.Hwang Great link, thank you! :) Completely agree with you about "meaning" and current LLMs – they're just word-predictors, they don't "understand" or "know". But this is why I'm asking for literature – in general I was wondering if any kind of "structural" mathematical research is being done on these matters. – pglpm Sep 14 '23 at 10:17
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    In my view it's an interesting question, though it may more naturally fall under linguistics rather than math. <> Offhand, I expect there is not any mathematical work along these lines: There is no fiscal imperative (cf. LLMs), and semantics are Difficult to model mathematically. (To be honest, my opinion and hope is that semantics are impossible to model mathematically. I see technological civilizations doing deep, widespread systemic harm under believies [sic] that Everything In The World Can Be Quantified And Controlled, and that Doing So Is Optimal And Imperative. But I digress. :) – Andrew D. Hwang Sep 14 '23 at 12:00

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