>>12391320>>12391325Yeeeahh nah, this is just symbol manipulation, not a formal semantics at all. You're even defaulting back to the currently-used Tarski-correspondence notion of truth, so what you have at present is not even close to being a foundation for algebra, let alone all of math.
In your defence, you've admitted that it's still incomplete, but I'd strongly suggest you read up on existing systems like the lambda calculus (and its variants) and the sequent calculus, paying special attention to the semantics on top of the syntax. Otherwise, all you will have done is create a private language that no one else will use, since it offers zero benefit compared to what mathematicians (of all stripes) are currently using now.