People are already using Prolog for this;
1) A series of excellent and detailed blog posts by Eugene Asahara Prolog in the LLM Era - https://eugeneasahara.com/category/prolog-in-the-llm-era/
2) Previous HN discussion Use Prolog to improve LLM's reasoning - https://news.ycombinator.com/item?id=41831735
3) User "bytebach" gives a nice example of using Prolog as an intermediate DSL in the prompt to an LLM so as to transform English declarative -> Imperative code - https://news.ycombinator.com/item?id=41549823
There's also [1], containing further bibliography references along with practical applications in discrete planning.
Prolog is quite popular and successful as a target for LLMs. And it's no accident considering Prolog was introduced to represent natural language statements in (predicate) logic.
[1]: https://quantumprolog.sgml.net/llm-demo/part1.html
That is pretty neat!
As big Prolog fan, thanks for sharing those resources.