LLMs generate text, and they do not use any system of logic or syllogisms to do so. It's a pretty cut-and-dry obvsious statement of fact, no need to muddy the conversation here.
https://rintintin.colorado.edu/~vancecd/phil201/Searle.pdf
People have been having these discussions since 1980 at least. I'm not going to bother rehashing the issue endlessly in shortform internet comments, but this paper exists if you're really interested in the subject.