> This metalanguage must have some kind of constructs to describe unknown things, or things that are deliberately simplified in favor of exposition.

Perhaps you're thinking of mathematics.

If you have to be able to represent arbitrary abstract logical constructs, I don't think you can formalized the whole language ahead of time. I think the best you can do is allow for ad-hoc formalization of notation while trying to keep any newly introduced notation reasonably consitent with previously introduced notation.