Re: Guessing?
- From: "Brian Selzer" <brian@xxxxxxxxxxxxxxxxxxx>
- Date: Sun, 1 Jun 2008 22:19:54 -0400
"David BL" <davidbl@xxxxxxxxxxxx> wrote in message
news:b7d01d30-8f85-406a-a07f-6801809a1a97@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On May 31, 5:11 pm, "Brian Selzer" <br...@xxxxxxxxxxxxxxxxxxx> wrote:
"David BL" <davi...@xxxxxxxxxxxx> wrote in message
news:5dc1c57d-8508-4180-a26c-38f944cf2779@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On May 30, 9:14 pm, "Brian Selzer" <br...@xxxxxxxxxxxxxxxxxxx> wrote:
"David BL" <davi...@xxxxxxxxxxxx> 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?
No. The intension states what can be. It cannot by itself state what is
unless what is represented is necessarily the case.
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?
Though there may be many possible database values, only one can represent
what is actually the case. And only that which is represented in that
database value actually exists. If you're curious, look up Domain Closure.
.
- Follow-Ups:
- Re: Guessing?
- From: Brian Selzer
- Re: Guessing?
- References:
- Re: Guessing?
- From: David BL
- Re: Guessing?
- Prev by Date: Re: Guessing?
- Next by Date: Re: Guessing?
- Previous by thread: Re: Guessing?
- Next by thread: Re: Guessing?
- Index(es):
Relevant Pages
|
