One way to make AI to believe in a claim that we know is false, is a situation than disproving the claim requires much more computational complexity that suggesting it. Fo example, it is very cheap thought for me to suggest that we live in a vast computer simulation with probability 0.5. But to disprove this claim with probability one, AI may need a lot of thinking, may be more than total maximum possible computational power of the universe allows.
One way to make AI to believe in a claim that we know is false, is a situation than disproving the claim requires much more computational complexity that suggesting it. Fo example, it is very cheap thought for me to suggest that we live in a vast computer simulation with probability 0.5. But to disprove this claim with probability one, AI may need a lot of thinking, may be more than total maximum possible computational power of the universe allows.