A common-ish trope in sci-fi movies/books is the bootstrapping of communication between alien beings using a sort of mathematics-based "primer", whereby atomic mathematical assertions (such as demonstrating truth and falsity), etc are used to "build up" a language for cross-alien being communications.

In these stories, it's taken for granted that doing this can indeed bootstrap language.

That said, has anyone actually developed such a proof-of-concept for actually bootstrapping a language based on atomic mathematical principles, or is this simply left as an exercise-to-the-readers'-imagination?