Comment by mbbbackus

Good point. You can create a formal definition of hallucinations in formal language, like math and logic, but probably not for natural language. There are bound to be edge cases where natural language defies the rules of formal logic without being incoherent. But, while you might not be able to have a simple formal definition, maybe you could create a model that's trained to recognize these edge cases, and the model would be a sort of approximation of a formal definition.