Re: A new proof of the superiority of set oriented approaches: numerical/time serie linear interpolation
Date: Tue, 1 May 2007 14:10:38 -0400
Message-ID: <yoLZh.3354$HX7.204_at_newssvr19.news.prodigy.net>
"Cimode" <cimode_at_hotmail.com> wrote in message
news:1178028682.007857.36200_at_p77g2000hsh.googlegroups.com...
> 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*? >
A database value. Received on Tue May 01 2007 - 20:10:38 CEST