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

"Cimode" <cimode_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&creative=327641&linkCode=as1&creativeASIN=0486669807&adid=0RBVCPR6S96MA9VPBKCB&
>
>> 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. Received on Tue May 01 2007 - 15:55:04 CEST