It's not as common any more, but there's still things using logic programming languages (Prolog and similar) even today.
Java uses it in the type checker. From the JVM spec:
The type checker enforces type rules that are specified by means of Prolog clauses.
There's some other compiler and NLP (natural language processing) use cases for it too. I've seen some companies use it to define restraints for their business logic, which isn't too different from the type checker rules use case.
We did Prolog in university - actually it was one of the two languages we had to learn in CS, the other one being Pascal.
I always considered Prolog a pain in the ass and unsuitable for anything bigger than a piece of homework due to the "we don't do loops, we have tail recursion" making the code unnecessary complex and hard to read. On a list of Write-Only languages I'd rate it a few steps below Perl.