I have no experience with logic programming (LP) and I have no time and reason to learn Prolog or other language that are canonical in the area of LP. By the way I’m very interested in the topic of LP and related paradigms. Could you please mention some OCaml libraries for logic programming and related things?
Check out https://github.com/c-cube/choice. It’s based on the LogicT library/paper (worth a read), which is closely related to miniKanren. The ideas are similar in that you construct nondeterministic programs by manipulating streams of solutions.