Re: A new proof of the superiority of set oriented approaches: numerical/time serie linear interpolation

On 1 mai, 15:55, "Brian Selzer" <b..._at_selzer-software.com> wrote:
> "Cimode" <cim..._at_hotmail.com> wrote in message
>
> news:1178005261.553981.294010_at_y80g2000hsf.googlegroups.com...
>
>
>
> > On 30 avr, 18:08, "Brian Selzer" <b..._at_selzer-software.com> wrote:
> >> "Cimode" <cim..._at_hotmail.com> wrote in message
>
> >>news:1177938789.949723.62480_at_h2g2000hsg.googlegroups.com...
> >> [snip]
>
> >> > I am aware of that article but thank you for reminding it. It simply
> >> > a negation of previous work and has been demonstrated since as wrong
> >> > by Codd's disciples (Date, Darwen). The induction of NULL 3VL simply
> >> > breaks the POCW (Principle of Closed World) redefining the meaning of
> >> > a database as a collection of facts. I think of this tolerance as one
> >> > of Codd's errors.
>
> >> In a closed world, there is no such thing as "missing information." Can
> >> you
> >> provide a reference that states that Codd adopted the closed world
> >> assumption? I've never read that he did, and in light of his views on
> >> missing information, I would be surprised if he had. In an open world,
> >> the
> >> focus is on what has been stated, and the contents of a database is a
> >> collection of recorded facts, not a collection of all of the facts.
> >> D&D's
> >> interpretation of the RM differs from Codd's in several substantive ways.
> >> Aside from missing information, Codd never described a database as a
> >> collection of relvars.
> > I have to admit that I neither agree with *all* of what either Codd or
> > D&D wrote as I found some unclear areas in both their writings. For
> > instance, I disagree with Codd's choice of table/attribute based
> > structuralism to caracterize relations (I do not either agree with
> > definition of database as a collection of relvars).
>
> > In case of doubt I prefer to get back to fundamental set theory who
> > necessarily tends to support better the closed world assumption.
> > I suggest you take a closer look at this. It is the heart of the
> > subject we are discussing.
>
> >http://www.amazon.com/dp/0486669807?tag=databasede095-20&camp=14573&c...
>
> >> In everything I've read, he has always referred to
> >> database modifications as inserts, updates and deletes. This would
> >> follow,
> >> since inserts, updates and deletes are statements that specify how what
> >> is
> >> known about the universe now differs from what has already been recorded.
> >> D&D's interpretation posits that insert, update and delete are simply
> >> instances of relational assignment, blissfully ignoring their inherent
> >> dependency on the current state.
> > I see your point. But keep in mind that RM is an application of a
> > mathematical set theory. As soon as it starts loosing touch with
> > math, lots of confusion arises.
>
> True. But even from a mathematical standpoint a closed world has its
> drawbacks. A closed world is great for describing and manipulating a single
> database state, whether you're issuing a query or verifying the consistency
> of a proposed state, but falls apart when trying to deal with more than one
> state at a time. In a closed world, a database modification is not so much
> a modification as it is a replacement. The entire content of the database
> must be stated during each transition because in a closed world there is no
> dependency on what is already known. This limits the granularity of a
> transition constraint to an entire relation, because a relation is a named
> set of sets of named values where each element of the relation is
> distinguishible from all others only by its component values. As a
> consequence, the number of possible mappings between the elements in one
> state and the elements in another can be huge. In fact, for a pair of
> relations (R, R'), the number of possible mappings is greater than |R| *
> |R'|. This makes it impractical if not impossible to define a transition
> constraint with a granularity smaller than an entire relation. The only
> solution I can think of that is in accord with the closed world assumption
> is to introduce surrogates. A surrogate transforms a relation into a named
> set of named sets of named values, where the surrogate value becomes the
> name for a tuple, and where all names are invariant. Those names can then
> be used to provide the 1:1 mapping between the elements in each state during
> a transition that is required to define a transition constraint with a
> granularity smaller than an entire relation. So either transition
> constraints must be enforced within the application that proposes a new
> database state, or surrogates must be defined on each relation schema so
> constrained. In an open world, this problem doesn't exist, because a
> database modification is a statement that describes the difference between
> what is known now and what has already been recorded. In effect, the user
> selects which of the possible mappings between states applies, and conveys
> that information in the modification statement.
I am sorry but I do not understand you anymore. What exactly is a *database state*? Received on Tue May 01 2007 - 16:11:22 CEST