I feel like some sort of Deep Learning oriented programming might be the "new logic programming". Instead of the horn clause engine you get the DL engine. Essentially you have a "universal mapping function" and "parameter fitting". Instead of defining facts you provide data, instead of rules you provide mappings and you also get the "inference for free" (which is sort of the battle cry of Prolog). Instead of logical deductions you get probabilistic deductions. Are there any dedicated machine learning/deep learning languages or DSLs that work at this level of abstraction?
I reckon that's closer to "goal-based programming" (the proposed "missing" fourth programming paradigm on that page). Basically (as I interpret it at least) defining test cases / behavior specifications for what you want the software to do, then letting an artificially-intelligent sort of "autoprogrammer" automagically generate a program that conforms to that specification.
Software like Cucumber [0] might be part of that particular paradigm once the missing pieces around AI/ML take proper form.
