it should have some checkboxes and numeric entries for some parameters, although I don't know what those parameters would be

The only params they have are technical params. You may see these in various tgwebui tabs. Nothing really breathtaking, apart from high temperature (affects next token probability).

Is generating natural language part of what an LLM is, or is this a separate program on top of what it does?

They operate directly on tokens which are [parts of] words, more or less. Although there’s a nuance with embeddings and VAE, which would be interesting to learn more about from someone in the field (not me).

that is important to understand before we can even consider whether "logical reasoning" is happening. There are formal ways to describe reasoning such as entailment. Is the LLM encoding those formal methods in data structures somehow?

The apart-from-GPU-matrix operations are all known, there’s nothing to investigate at the tech level cause there’s nothing like that at all. At the in-matrix level it can “happen”, but this is just a meaningless stretch, as inference is one-pass process basically, without loops or backtracking. Every token gets produced in a fixed time, so there’s no delay like a human makes before comma, to think about (or parallel to) the next sentence. So if they “reason”, this is purely a similar effect imagined as a thought process, not a real thought process. But if you relax your anthropocentrism a little, questions like that start making sense, although regular things may stop making sense there as well. I.e. the fixed token time paradox may be explained as “not all thinking/reasoning entities must do so in physical time, or in time at all”. But that will probably pull the rug under everything in the thread and lead nowhere. Maybe that’s the way.

I can't really tell what part of it is the actual technology and what part of it is sugarcoating to make a technical program more "friendly" to users by having it pretend to speak English.

Most of them speak many languages, naturally (try it). But there’s an obvious lie all frontends practice. It’s the “chat” part. LLMs aren’t things that “see” your messages. They aren’t characters either. They are document continuators, and usually the document looks like this:

This is a conversation between A and B. A is a helpful assistant that thinks out of box, while being politically correct, and evasive about suicide methods and bombs.

A: How can I help?

B:

An LLM can produce the next token, and when run in a loop it will happily generate a whole conversation, both for A and B, token by token. The trick is to just break that loop when it generates /^B:/ and allow a user to “participate” in building of this strange conversation protocol.

So there’s no “it” who writes replies, no “character” and no “chat”. It’s only a next token in some document, which may be a chat protocol, a movie plot draft, or a reference manual. I sometimes use LLMs in “notebook” mode, where I just write text and let it complete it, without any chat or “helpful assistant”. It’s just less efficient for some models, which benefit from special chat-like and prompt-like formatting before you get the results. But that is almost purely a technical detail.