There is a lot of work on neurosymbolic systems, see this review
https://arxiv.org/pdf/2305.00813.pdf
I'd note that it would be much more powerful to produce code to run in an SMT solver
https://en.wikipedia.org/wiki/Satisfiability_modulo_theories
as opposed to Prolog. It's clear to me how you can get the LLM to generate code for such a system but many of the tough problems about decidibility are as tough as they ever were. On top of that there is the problem of efficient logical inference. For instance the Cyc system
https://cyc.com/platform/
has more than 1000 specialized inference engines for particular kinds of problems, which doesn't seem like a terribly sustainable route.