decidability of artificial intelligence
For a problem to be approachable using what we presently call "AI methods", it has to be, at least theoretically, also solvable using "regular" methods (writing a set of instructions that solves it, line by line). Thus, decidable.

AI systems may create effective algorithms whose operation no human can understand. Also, by using AI methods we may find solutions to new problems, by accident, or discover that problems are decidable. These things do not contradict the affirmative above.

An algorithm exists that solves the problem.