Re: a union is always a join!

On Apr 5, 2:06 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> "rpost" <rp..._at_pcwin518.campus.tue.nl> wrote in message
>
> news:gq8e2h$1ujr$1_at_mud.stack.nl...
>
>
>
> > Brian Selzer wrote:
>
> >>>> The mathematics of relational calculus and relational algebra are fully
> >>>> capable, AFAIK, of describing the difference between two states of a
> >>>> database.
>
> > [...]
>
> >>The algebra is capable of that if and only if each and every tuple has a
> >>key
> >>that permanently identifies the thing in the universe of discourse that
> >>the
> >>tuple maps to.
>
> > No, the algebra can describe the difference between database states
> > without any assumption on how these states are interpreted.
>
> 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

I would like to make the following note. In my model (see www.dbdesign11.com) I didn’t use terms as “possible worlds”, “state of affairs” or “temporal”. Especially I didn’t use the mentioned terms as basic. They are undefined terms. For example, nobody knows what “world” is. However I precisely defined the state of entity and state of relationship which are some of my basic terms. Reinier for example doesn’t distinguish “state of affairs” from the state of entity. He wrote about my model the following: “The database records not only present state of affairs, but also all past state…” - meaning that db records something like “possible worlds” + all past states.
You intensively used terms “possible world” and “rigid designator” but you carefully made transformation and now you are using term the state. In the above message, you went further and you mentioned term - the state of “the employee”.
You seem to spending a lot of energy using basic terms and ideas from my db model.
But you proclaim superiority of the relational model and it is unclear to me why you don’t use basic terms from relational model or maybe from a combination of “temporal” data and relational model?

Vladimir Odrljin Received on Tue Apr 07 2009 - 09:15:54 CEST