I agree with your comment "In many languages, if you choose any of those supposed rules you can probably construct an algorithm to generate odd, but understandable words that defy that rule." - it comes many forms, from Goodhart's Law to the "hot dog vs. sandwich" debate.

I do mention this in my blog post - although I think Generalization is Language, I don't think it's possible to create a formal framework of language, for precisely because of "adversarial examples" that can be supplied for any formal definition.

Natural language itself, ignorant of formality, is able to account for these exceptions insofar as language is sufficient for people to convey a bare minimum of meaning. I am proposing to define language and generalization via the implicit understanding of large language models, in the same way you might use an image classifier to define "cat images" or "hot dogs"