Unfortunately, computer programs mean what they actually do, not what you wish they did. The field of formal semantics of programming languages exists to study the real meaning of programming languages, not the “intended” one, whatever the latter might be.
> If this is your way of saying that the only thing a DBMS does (and can ever be expected to do) is algebraic computation (e.g. to verify constraint satisfaction of a given update to a given existing db state)
The programmer is expected to make the DBMS enforce business rules. A database schema is a model (in the informal, everyday sense of the word) of the real world to the extent the real world's rules are enforced constraints in the schema. Otherwise, it's just wishful thinking.