# Re: Guessing?

Date: Fri, 1 Aug 2008 18:35:34 -0700 (PDT)

Message-ID: <2f568722-56b5-4e44-a3f8-7b4bdf85dc80@b2g2000prf.googlegroups.com>

On Aug 1, 10:14 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:

*> "David BL" <davi..._at_iinet.net.au> wrote in message*

*>*

*> news:dca3a676-7636-4ffa-962d-bd44f312da67_at_p31g2000prf.googlegroups.com...*

*>*

*>*

*>*

*>*

*>*

*> > On Jul 31, 7:53 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:*

*> > > "David BL" <davi..._at_iinet.net.au> wrote in message*

*>*

*> > >news:c89ae2a9-5880-4b96-bf7e-adf8f2a899e1_at_j22g2000hsf.googlegroups.com...*

*>*

*> > > > On Jul 31, 10:01 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:*

*> > > > > "David BL" <davi..._at_iinet.net.au> wrote in message*

*>*

*> > > > > > Given relation r, let X(r) be the boolean valued characteristic*

*> > > > > > function of r.*

*>*

*> > > > > > Consider the following definitions*

*>*

*> > > > > > 1. OnTheTeam_r : the relation value recorded by the DB*

*> > > > > > 2. OnTheTeam_i : the internal predicate recorded by the DB*

*> > > > > > 3. OnTheTeam_e : the external predicate meant to represent*

*> > > > > > reality*

*>*

*> > > > > > Is CWA associated with saying:*

*>*

*> > > > > > a) OnTheTeam_i = X(OnTheTeam_r) or*

*> > > > > > b) OnTheTeam_i = OnTheTeam_e?*

*>*

*> > > > > > You appear to suggest CWA implies both a) and b). Is that right?*

*>*

*> > > > > The closed world assumption involves what can be proved rather than*

*> > > > > what*

*> > > > > something means; an external predicate involves what something*

*> > > > > means;*

*> > > > > therefore, the closed world assumption is not associated with saying*

*> > > > > b).*

*> > > > > On*

*> > > > > the other hand, it is associated with saying:*

*>*

*> > > > > c) OnTheTeam_i --> OnTheTeam_e*

*>*

*> > > > > since whenever ~OnTheTeam_e, ~OnTheTeam_i.*

*>*

*> > > > I think you have that arse about. c) is assumed under OWA or CWA.*

*>*

*> > > You're right. I got it backwards:*

*>*

*> > > OnTheTeam_e --> OnTheTeam_i*

*> > > since whenever ~OnTheTeam_i, ~OnTheTeam_e*

*>*

*> > > And when combined with*

*>*

*> > > OnTheTeam_i --> OnTheTeam_e*

*>*

*> > > becomes*

*>*

*> > > OnTheTeam_i iff OnTheTeam_e*

*>*

*> > > Which is not the case under the OWA.*

*>*

*> > > > If anything the CWA means that a missing tuple in the DB implies the*

*> > > > negation of the proposition in reality.*

*>*

*> > > Since a database is a proposition under the closed world, domain closure*

*> > > and*

*> > > unique name assumptions, I prefer to refer to what a tuple corresponds*

*> > > to as*

*> > > a formula instead of a proposition, since it is just a small part of the*

*> > > whole.*

*>*

*> > > > Also, you say CWA is concerned with what can be proved, and therefore*

*> > > > isn’t related to an external predicate (because it is informal) and*

*> > > > yet c) refers to an external predicate.*

*>*

*> > > The CWA does indeed involve what can be proved instead of what something*

*> > > means, but that doesn't mean that it isn't related to the external*

*> > > predicate. The internal predicate is related to the external predicate,*

*> > > and*

*> > > the CWA is related to the internal predicate; therefore the CWA is*

*> > > related*

*> > > to the external predicate. While the internal predicate is related to*

*> > > the*

*> > > external predicate, that doesn't mean that they are identical as is*

*> > > stated*

*> > > in b). '=' and 'iff' are different relations.*

*>*

*> > In what sense do you say '=' and 'iff' are different when comparing a*

*> > pair of boolean valued functions? Two functions are equal when they*

*> > have the same domain and each element of the domain maps to the same*

*> > value. That seems equivalent to 'iff' where all the domain variables*

*> > are free and by convention would be universally quantified over their*

*> > domains.*

*>*

*> Are you equating the domains of the internal predicate with those of the*

*> external predicate?*

Yes

*> > I like to think that a database relvar can be understood as an*

*> > encoding of a relation value (or equivalently an internal predicate*

*> > which is simply the boolean valued characteristic function) according*

*> > to the RM formalism, irrespective of whether or not there exists any*

*> > corresponding external predicate. The latter is informal and*

*> > completely outside the formalism.*

*>*

*> A relvar is a container. A relvar is analogous to a relation schema. A*

*> relation is a value that can be contained within a relvar or conforms to a*

*> relation schema. How can a container encode that which might be contained*

*> within it?*

I agree that a variable is nothing more than a container for holding a value. A variable normally exists in time and space, and a value is "encoded" (ie represented) in order for a variable to "hold it".

*> > I think of a) and b) as quite independent options. Therefore it still*

*> > begs the question of whether the CWA is associated with a) or b).*

*> > You seem closer to a).*

Received on Fri Aug 01 2008 - 20:35:34 CDT