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Re: In an RDBMS, what does "Data" mean?

From: Anthony W. Youngman <wol_at_thewolery.demon.co.uk>
Date: Mon, 14 Jun 2004 23:24:28 +0100
Message-ID: <ZoGxRIEcWizAFwDp@thewolery.demon.co.uk>


In message <An3yc.2600$FE6.1451_at_newssvr15.news.prodigy.com>, Eric Kaun <ekaun_at_yahoo.com> writes
>"Anthony W. Youngman" <wol_at_thewolery.demon.co.uk> wrote in message
>news:8jbIDPPhC7xAFwHy_at_thewolery.demon.co.uk...
>> In message <lgGxc.6818$eP2.1437_at_newssvr32.news.prodigy.com>, Eric Kaun
>> <ekaun_at_yahoo.com> writes
>> >And as stated elsewhere, those aren't axioms anyway... he used the word
>> >"representation", and the context fully suggests that he's not
>correlating
>> >it with the real world.
>> >
>> I know. After writing that I thought rather more about what C&D's twelve
>> rules actually are. And that they don't seem to contain any axioms at
>> all.
>>
>> Which leads to the conclusion that relational theory is axiom-free.
>> Which means that it cannot be a valid model.
>
>Some possibilities (I'm running too short on time to explore them):
>- The axioms may be simply implicit in his rules
>- What are MV's axioms? If it has them, then we could map at least some of
>them to relational (since there are commonalities)

If they're implicit, then they need to be made explicit (hence my comment about mathematicians "fleshing out" the theory).
>
>> Which means that its
>> application to the real world has no basis in anything whatsoever.
>
>Maybe, but again, what sort of data model would have axioms? I'm not sure
>this is possible... and if it is, again, relational would somewhat-similar
>ones. Surely there's at least a partial homomorphism between data models?

The generic always trumps the specific. I suspect Pick axioms are very similar to relational. But just as C&D's first rule says that data comes in 2-dimensional tables (or arrays), I've defined "Pick's first rule" that says data comes in n-dimensional arrays. So relational is the specific subset of Pick where n=2. :-)
>
>> Okay, I'm sure that the mathematicians who've built on it have fleshed
>> out the fundamentals somewhat, but it certainly means that if your sole
>> criteria for defining a "relational database" is that "it complies with
>> C&D's 12 rules", then such a database has no grounding in formal logic
>> whatsoever.
>
>Mathematics requires axioms - does logic? I thought it was purely symbolic
>manipulation, which is defined for relational.
>

Logic is used to manipulate axioms to give theorems. The result is a model.

So no, if you're being pedantic, maybe logic doesn't require axioms. But in the same way as an axe doesn't *require* wood. Just as an axe with nothing to chop is useless, so is logic without axioms to manipulate.

Cheers,
Wol

-- 
Anthony W. Youngman - wol at thewolery dot demon dot co dot uk
HEX wondered how much he should tell the Wizards. He felt it would not be a
good idea to burden them with too much input. Hex always thought of his reports
as Lies-to-People.
The Science of Discworld : (c) Terry Pratchett 1999
Received on Mon Jun 14 2004 - 17:24:28 CDT

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