I mention the intuition in passing (you have an object graph with complex bidirectional and derived relationships). Any example that would truly show the benefit would be too big to show on a blog post. Treat it like the world's smartest database, that's the key.

Another example would be something like an Entity Component System. The moment it starts getting complex (i.e., you have fancy queries and joins), then you're actually implementing a really shitty relational programming engine, and you might as well just implement Datalog instead at that point and reap the benefits.

Other kinds of search problems are probably better tackled by constraint programming instead.

The only production experience I have with logic programming is OPA Rego for writing security policies (not sure it's a "pure" logic language but feels like the primary paradigm).

I found it pretty interesting for that use case, although the learning curve isn't trivial for traditional devs.

https://www.openpolicyagent.org/

I've been reading a bit about it, and it seems easier to make goal-driven backwards chaining AI from it, like the block world example. You could in theory use that for something like a video game AI (like GOAP, Goal-Oriented Action Planning, which is based on STRIPS). Whenever I read about GOAP though, they seem to have used a graphical editor to declaratively input rules rather than a logic programming language.

Note that I'm not an expert in any of this, I've just been reading about this kind of AI recently. I haven't actually done this myself.

Generally speaking, the advantage of logic programming is that it's (more) declarative: you describe the problem and it derives a solution.