Functional and Logic Programming

What are some mathematics subfields that go well with these paradigms?

My final objective is in a broad sense, AI.

Lisps are good for algebra and other symbolic-transformations. If you invent a dialect of Lisp that works with fuzzy symbols, then it would be good for AI.

Prolog isn't really good at anything, as its functionality can be replaced with Lisp's AMB operator. In general, using logic programming for AI is a dead-end idea.