Re: Guessing?

From: Brian Selzer <brian_at_selzer-software.com>
Date: Fri, 1 Aug 2008 10:14:18 -0400
Message-ID: <mTEkk.15425$cW3.2392@nlpi064.nbdc.sbc.com>

"David BL" <davidbl_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
> > > 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.

>

Are you equating the domains of the internal predicate with those of the external predicate?

> 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 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 - 09:14:18 CDT

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