I don't agree. Even without any assumption on /how/ the states are
interpreted, there is still the bald fact that they are subject to
interpretation. If one state asserts that the employee operating welder #4
is being paid at the overtime rate, and another state asserts that the
employee operating welder #4 is being paid at the standard rate, would it be
valid to infer that 'the employee operating welder #4' denotes the same
employee at both states? I think not. Bottom line: the same term can
denote different things at different states, consequently, any conclusion
drawn from an algebraic expression, such as R' JOIN R, which in essence
relies upon the identity of terms, would be faulty, since identity of terms
at differnt states does not necessarily imply identity of the terms'
referents.
> And as Walter Mitty already wrote, it is not in fact necessary that
> databases are inpeepreted in such a way that tuples are about "things"
> in the universe of discourse.
>
> I think you are overstating your point, which was, if I understand
> you correctly, that while relational algebra and calculus may be used
> to express the contents of a database change, they do not express the
> fact that the contents change; and this does need to be expressed in
> some way when reasoning about database updates.
>
>>But since that isn't a requirement of the RM, the RM must be
>>in trouble! If different keys at different states map to the same thing
>>in
>>the universe of discourse, or if the same key at different states maps to
>>different things in the universe of discourse, then how is it possible to
>>describe exactly what is different between two states of a database.
>
> It is really simple. However, you are right in that mutability of
> keys and other aspects of the relationship between database contents
> and its interpretation will fall outside the scope of that description.
>
> --
> Reinier
