Formal logic AI systems have existed and were popular in the 1980s. One of the problems is that they don't work - in the real world there are no firm facts, everything is squishy, and when you try to build a large system you end up making tons of exceptions for special cases until it becomes completely untenable.

Non-deterministic systems that work probabilistically are just superior in function to that, even if it makes us all deeply uncomfortable.

I don't know what definition of AI you're using, but plenty of ML algorithms operate deterministically, let alone most other logic programmed into a computer. I don't see how your statement can be right given that these other software systems also operate in the real world.

Actually they do very well at medical diagnosis but the doctors union banned them.