I'm reminded of the interview where a researcher asks firemen how they make decisions under pressure, and the fireman answers that he never makes decisions because there's never time for that.
Or in other words, people can use implicit logic to solve puzzles. Similarly LLMs can implicitly be fine-tuned into logic models by asking them to solve a puzzle, insofar as that logic model fits in their weights. Transformers are very flexible that way.
When LLMs are presented with a problem they search for a solution based on the language model. And when they can't find a solution, there's always a match for something that looks like a solution.