The right tool might be Spiking Neural Networks. Due to their sparse activation, event driven computation, and temporal coding. This all depends on how good neuromorphic chips get.
Would depend on the implementation, I think. You could probably write one like that, but as usual there will be trade-offs. I suspect it would also matter if you're targeting booleans or numbers.
The typical, obvious case how these things work in Prolog is in list concatenation. If you only supply variables it'll start outputting lists of increasing length with placeholder variables. It's a somewhat simple engine for traversing a problem space and testing constraints that uses backtracking to step through it. Some implementations allow you to explicitly change the search strategy.
