A number of years ago we were designing a way to specify insurance claim adjudication rules in natural language, so that "the business" could write their own rules. The "natural" language we ended up with was not so natural after all. We would have had to teach users this specific English dialect and grammar (formal and precise syntax, as you said).

So, in the end, we abandoned that project and years later just rewrote the system so we could write claim rules in EDN format (from the Clojure world) to make our own lives easier.

In theory, the business users could also learn how to write in this EDN format, but it wasn't something the stakeholders outside of engineering even wanted. On the one hand, their expertise was in insurance claims---they didn't want to write code. More importantly, they felt they would be held accountable for any mistakes in the rules that could well result in thousands and thousands of dollars in overpayments. Something the engineers weren't impervious to, but there's a good reason we have quality assurance measures.