Re: Guessing?

From: David BL <davidbl_at_iinet.net.au>
Date: Sun, 1 Jun 2008 18:16:48 -0700 (PDT)
Message-ID: <b7d01d30-8f85-406a-a07f-6801809a1a97@b5g2000pri.googlegroups.com>


On May 31, 5:11 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> "David BL" <davi..._at_iinet.net.au> wrote in message
>
> news:5dc1c57d-8508-4180-a26c-38f944cf2779_at_q24g2000prf.googlegroups.com...
>
>
>
>
>
> > On May 30, 9:14 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> >> "David BL" <davi..._at_iinet.net.au> 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.

An intensional definition can be a function of time. Eg

    S(t) = set of surnames of UK prime-ministers

           after Thatcher at time t

with (current) extension

    S(June 2 2008) = { Major, Blair, Brown }

Knowing the extension at a particular time doesn't tell you what the extension is at other times.

I guess you could say the intensional definition doesn't change with time because t is bound! Is that what you mean?

> 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.

Sorry I don't understand this. For example what does "actually exist" mean? Received on Sun Jun 01 2008 - 20:16:48 CDT

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