I think trying to accurately express natural language statements as values and logical steps as operators is going to be very difficult. You also need to take into account ambiguity and subtext and things like that.
I actually believe it is technically possible, but is going to be very hard.
What formal language can express this statement? What will the text be parsed into? Which transformations can you use to produce other truthful (and interesting) statements from it? Is this flexible enough to capture everything that can be expressed in English?
The closest that comes to mind is Prolog, but it doesn’t really come close.
You can get a model to write lean or something, but formal logic, while verifiable is not useful for everyday life since it's mostly incomplete and does not even take into account inductive logic.
It's doing so already. All code executed on a computer, especially neural networks w/o any loops are simply doing boolean arithmetic. In fact, the computer can't do anything else other than boolean arithmetic.