Re: Guessing?

From: Brian Selzer <brian_at_selzer-software.com>
Date: Sun, 22 Jun 2008 00:51:51 -0400
Message-ID: <HTk7k.11571$mh5.9313@nlpi067.nbdc.sbc.com>

"paul c" <toledobysea_at_ac.ooyah> wrote in message news:%yf7k.23319$Jx.3424_at_pd7urf1no...
> Brian Selzer wrote:

>> "paul c" <toledobysea_at_ac.ooyah> wrote in message

> ...
>>>> ... In a first order language, you have constant symbols and
>>>> predicate symbols, and under an interpretation, meaning is assigned not 
>>>> only to the constant symbols but also to the predicate symbols.  The 
>>>> way I see it, the only way you can have overlapping meanings is if a 
>>>> relation has a disjunctive predicate. ...
>>>
>>> Not sure if that's so, but willing to assume it is for now.  It reminds 
>>> me that I have doubts about whether any relation should be allowed to 
>>> disjunctions within individual propositions, at least if we want 
>>> 'interchangeability'.  For example, a base relvar that has been inserted 
>>> to with "union" certainly doesn't have a disjunctive predicate so why 
>>> should a view that is manifested the same way be different?
>>
>> Because one involves two database states and the other involves only one. 
>> Any mutating operation necessarily involves two database states (or 
>> instances, or values--whichever nomenclature you prefer): there is what 
>> was then supposed to be the case and what is now supposed to be the case. 
>> But a view simply presents information contained in one database 
>> state--what is now supposed to be the case--in a different way.  The 
>> connection between what is presented by a view and what is in the 
>> underlying relations is the expression that defines the view.  If that 
>> happens to be a union, then the predicate of the view is the disjunction 
>> of the predicates of the two operands of the union.  This is inescapable.
>> ...
>

> One may choose one's starting point so as to conclude that it is
> 'inescapable' (sorry, not trying to mimic Bob B's high tones), but I feel
> that escape from this consequence is rather necessary!

Why is it necessary?

> (seems a pedantic consequence to me which usually signals to me that
> something basic is just wrong, also I'm not saying I have the IQ
> wherewithal to show how, but am wondering whether a more complete POOD
> might argue that the presence of any non-disjunctive tuple in a db, no
> matter whether it's in a base or 'virtual' relation, trumps any
> disjunctive operator that might have produced/manifested it.)
>

Consider the following statements:

  1. Susan is an electrical engineer.
  2. Susan is a mechanical engineer.
  3. Susan is an electrical engineer or Susan is a mechanical engineer.

Now, suppose you have a base relation P whose members map to individuals that exemplify the property of being an electrical engineer, a base relation Q whose members map to individuals that exemplify the property of being a mechanical engineer, and a virtual relation (a view) R (P UNION Q) whose members map to individuals that exemplify either the property of being an electrical engineer or the property of being a mechanical engineer or both. The presence of a tuple in the virtual relation with a value that maps to Susan tells us only that Susan exists and that she is either an electrical engineer or a mechanical engineer or both. It does not tell us which. It is only the fact that the value that maps to Susan appears also in both of the base relations that tells us that in fact Susan is both an electrical engineer and a mechanical engineer. So here we have three relations, two base, one derived, that draw their values from the same domain, but it is where a particular value appears that imparts different aspects of meaning to that value. Note that there is no overlap in meaning for relations P and Q--even though they draw their values from the same domain: whether an individual is an electrical engineer or not has no bearing whatsoever on whether that individual is a mechanical engineer or not. Received on Sat Jun 21 2008 - 23:51:51 CDT

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