Re: Guessing?

From: Brian Selzer <>
Date: Sat, 31 May 2008 05:11:34 -0400
Message-ID: <aD80k.1977$>

"David BL" <> wrote in message
> On May 30, 9:14 pm, "Brian Selzer" <> wrote:
>> "David BL" <> wrote in message
>> > It seems to me that every base relvar will in practice have some
>> > defined intensional definition outside the RM formalism and
>> > inaccessible to the DBMS.
>> I thought the intension of a relation states what can be while the
>> extension
>> states what is: wouldn't that place the intensional definition inside the
>> RM
>> formalism? I understand what you're driving at, though, but I think it
>> is
>> indeed a part of the RM formalism. Let me explain. Suppose you have
>> predicate symbols P and Q. Isn't it true that under a first order logic
>> interpretation, not only constant symbols are assigned meaning, but also
>> predicate symbols? Isn't one of the assumptions under which the
>> Relational
>> Model operates the Unique Name Assumption? Wouldn't that assumption
>> apply
>> with equal force to predicate symbols as it does to constant symbols?
>> What
>> I mean by that is that it should not be possible for two predicate
>> symbols
>> to be assigned exactly the same meaning in the same way that it should
>> not
>> be possible for two constant symbols to be assigned exactly the same
>> meaning. Now, a predicate can be a conjunction of other predicates, and
>> the
>> components of that conjunction can appear in other predicates, but if two
>> predicates are composed of the exact same components, then they are
>> really
>> just one, and the Unique Name Assumption would require that only one
>> predicate symbol be used to represent that particular conjunction of
>> components. Bottom line: the name assigned to a relation is significant
>> because it is a symbol for a distinct predicate.
> Very informally I think an intensional definition of a finite relation
> should be sufficient to allow an omniscient being to calculate the
> corresponding extension. Therefore both intensional and extensional
> definitions state "what is". The difference comes down to whether the
> elements are explicitly enumerated.
> In some cases an intensional definition of a set can be mathematically
> precise. Eg
> X = { x in Z | x < 100 and exists y in Z st x = y^2 }
> which has an equivalent extensional definition
> X = { 0,1,4,9,16,25,36,49,64,81 }
> However such mathematically defined sets aren't of primary interest to
> the RM - because the RM is mostly interested in recording finite sets
> that cannot be algorithmically compressed. Therefore extensional
> definitions are more important than intensional definitions. [On a
> side note - it seems to make sense to allow mathematically defined
> relations as read only first class citizens so that selection is just
> a join].
> In practise the base relvars have intensional definitions that relate
> back to the real world and are outside our mathematical formalisms.
> Therefore a formal definition of the set is necessarily extensional.
> That being said I generally agree with your above comments except I
> think it is more accurate to say that the assumption that base relvars
> have distinct associated intensional definitions is part of the RM
> formalism whereas the intensional definitions themselves are not.
> Does that make sense?

Sort of, but correct me if I'm wrong: the intension of a relation shouldn't, and barring schema evolution, doesn't, change with time, whereas the extension usually can and does as what is to be represented in the relation comes into being, changes in appearance or ceases to exist. The determination that something /actually/ exists exceeds what the intension by itself can provide but not what the extension due to Domain Closure can provide; on the other hand, the intension does specify what can be represented and indirectly, therefore, again due to Domain Closure whether something /can/ exist. To determine from the intension whether something /actually/ exists would require an interpetation. So yes, the intension relates back to the real world. It should be noted here that the extension also relates back to the real world but that Domain Closure makes it possible to draw conclusions from the data without resorting to interpretation. I would argue, therefore, that the intensional definition /is/ part of the RM formalism, and that the mechanism of interpretation is also part of the RM formalism, but that any particular interpretation is not. The predicate of a database, including all state constraints, determines the set of all possible database values, but it is only under an interpretation that one of those possibilities can be designated to be actual. Received on Sat May 31 2008 - 11:11:34 CEST

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