[JamesP81]

In fact, I would make the observation that just about everyone that uses the term "non-deterministic" with respect to computers really means "non-axiomatic".

Point taken. I remember my AI professor talking about some new research that cast doubt on the Axiom of Choice, the implications of which were huge.

[tortoise]

I remember my AI professor talking about some new research that cast doubt on the Axiom of Choice, the implications of which were huge.

That is something quite different, but yes, there are actually two different maths that depend on whether or not one assumes the Axiom of Choice. It is not a strictly necessary axiom in math apparently, and I expect mathematicians will be arguing about it for the foreseeable future.

Non-axiomatic computational models are something else, derived from non-axiomatic term logics (in the same way that classical computers use classic first-order logic), which has really only been fully formalized in the last decade or so. There are some interesting theorems that have been published in recent years that show that fully general intelligence is only expressible on non-axiomatic computational models, a kind of computational model with which we have very little experience with.