# Re: Guessing?

"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:
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*> > "David BL" <davi..._at_iinet.net.au> wrote in message
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*> >
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*> > news:c89ae2a9-5880-4b96-bf7e-adf8f2a899e1_at_j22g2000hsf.googlegroups.com...
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*> >
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*> >
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*> >
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*> >
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*> >
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*> > > On Jul 31, 10:01 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:
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*> > > > "David BL" <davi..._at_iinet.net.au> wrote in message
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*> >
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*> > > > > Given relation r, let X(r) be the boolean valued characteristic
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*> > > > > function of r.
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*> >
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*> > > > > Consider the following definitions
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*> >
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*> > > > > 1. OnTheTeam_r : the relation value recorded by the DB
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*> > > > > 2. OnTheTeam_i : the internal predicate recorded by the DB
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*> > > > > 3. OnTheTeam_e : the external predicate meant to represent
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*> > > > > reality
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*> >
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*> > > > > Is CWA associated with saying:
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*> >
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*> > > > > a) OnTheTeam_i = X(OnTheTeam_r) or
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*> > > > > b) OnTheTeam_i = OnTheTeam_e?
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*> >
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*> > > > > You appear to suggest CWA implies both a) and b). Is that right?
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*> >
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*> > > > The closed world assumption involves what can be proved rather than
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*> > > > what
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*> > > > something means; an external predicate involves what something
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*> > > > means;
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*> > > > therefore, the closed world assumption is not associated with saying
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*> > > > b).
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*> > > > On
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*> > > > the other hand, it is associated with saying:
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*> >
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*> > > > c) OnTheTeam_i --> OnTheTeam_e
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*> >
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*> > > > since whenever ~OnTheTeam_e, ~OnTheTeam_i.
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*> >
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*> > > I think you have that arse about. c) is assumed under OWA or CWA.
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*> >
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*> > You're right. I got it backwards:
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*> >
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*> > OnTheTeam_e --> OnTheTeam_i
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*> > since whenever ~OnTheTeam_i, ~OnTheTeam_e
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*> >
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*> > And when combined with
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*> >
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*> > OnTheTeam_i --> OnTheTeam_e
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*> >
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*> > becomes
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*> >
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*> > OnTheTeam_i iff OnTheTeam_e
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*> >
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*> > Which is not the case under the OWA.
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*> >
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*> > > If anything the CWA means that a missing tuple in the DB implies the
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*> > > negation of the proposition in reality.
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*> >
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*> > Since a database is a proposition under the closed world, domain closure
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*> > and
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*> > unique name assumptions, I prefer to refer to what a tuple corresponds
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*> > to as
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*> > a formula instead of a proposition, since it is just a small part of the
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*> > whole.
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*> >
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*> > > Also, you say CWA is concerned with what can be proved, and therefore
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*> > > isn’t related to an external predicate (because it is informal) and
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*> > > yet c) refers to an external predicate.
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*> >
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*> > The CWA does indeed involve what can be proved instead of what something
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*> > means, but that doesn't mean that it isn't related to the external
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*> > predicate. The internal predicate is related to the external predicate,
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*> > and
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*> > the CWA is related to the internal predicate; therefore the CWA is
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*> > related
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*> > to the external predicate. While the internal predicate is related to
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*> > the
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*> > external predicate, that doesn't mean that they are identical as is
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> > stated

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

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*> In what sense do you say '=' and 'iff' are different when comparing a
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*> pair of boolean valued functions? Two functions are equal when they
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*> have the same domain and each element of the domain maps to the same
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*> value. That seems equivalent to 'iff' where all the domain variables
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> are free and by convention would be universally quantified over their

> domains.

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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
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*> encoding of a relation value (or equivalently an internal predicate
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*> which is simply the boolean valued characteristic function) according
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*> to the RM formalism, irrespective of whether or not there exists any
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> 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
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> begs the question of whether the CWA is associated with a) or b).

> You seem closer to a).

Received on Fri Aug 01 2008 - 16:14:18 CEST

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