# Re: Guessing?

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