Re: Guessing?

From: David BL <davidbl_at_iinet.net.au>
Date: Thu, 31 Jul 2008 06:46:51 -0700 (PDT)
Message-ID: <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
> > isnít 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.

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.

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 Thu Jul 31 2008 - 15:46:51 CEST

Original text of this message