Re: Guessing?

From: David BL <davidbl_at_iinet.net.au>
Date: Sun, 27 Jul 2008 18:21:28 -0700 (PDT)
Message-ID: <7302ef07-2063-46f7-b88d-dc5d2a188194_at_b30g2000prf.googlegroups.com>


On Jul 25, 10:57 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> "David BL" <davi..._at_iinet.net.au> wrote in message
>
> news:8f91db82-8f47-40b4-be47-d54eb4451e91_at_v1g2000pra.googlegroups.com...
>
>
>
>
>
> > On Jul 24, 9:25 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> >> "David BL" <davi..._at_iinet.net.au> wrote in message
>
> >>news:cf134a05-1096-4a43-b1fb-c4c45e03eb42_at_c65g2000hsa.googlegroups.com...
>
> >> > On Jul 24, 10:56 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:
>
> >> >> > In a database encoding there is only a single defined interpretation
> >> >> > of the encoded attributes as values in the RM formalism. Therefore
> >> >> > there is no distinction between symbol and value that can be made.
>
> >> >> I don't agree. Under the domain closure, unique name and closed world
> >> >> assumptions, a database is a proposition that is supposed to be true.
> >> >> How
> >> >> the database is physically implemented is irrelevant.
>
> >> > A relation is formally defined as a set of tuples. Nothing more!
>
> >> There are several definitions, but that is neither here nor there.
> >> Relations were chosen because they look and behave a lot like the
> >> extensions
> >> of first order predicates. Of course the extension of a predicate
> >> includes
> >> both positive and negative formulae, but the closed world assumption
> >> enables
> >> the elimination of the negative formulae.
>
> > Well I'm not sure what the CWA actually means...
>
> The way I understand it, CWA is simply:
>
> If there ain't no row, then it ain't so.
>
> What that means is if there is a tuple that conforms to a relation's schema,
> but isn't in the relation, then the formula that the tuple embodies is
> false. For example, if you have a domain of players,
>
> Players {Bill, Bob, Joe, John, Mike, George, Raymond, Brian, Mark, Frank}
>
> and a relation for the property of being on the team,
>
> OnTheTeam {{Joe}, {John}, {Mike}, {Raymond}, {Mark}}
>
> Then due to the closed world assumption we can infer that neither
>
> Bill, Bob, George, Brian nor Frank are on the team.
>
> The first order sentence,
>
> Exists x in Players OnTheTeam(x)
> extends to the disjunction
>
> OnTheTeam(Bill) \/
> OnTheTeam(Bob) \/
> OnTheTeam(Joe) \/
> OnTheTeam(John) \/
> OnTheTeam(Mike) \/
> OnTheTeam(George) \/
> OnTheTeam(Raymond) \/
> OnTheTeam(Brian) \/
> OnTheTeam(Mark) \/
> OnTheTeam(Frank)
>
> where
>
> OnTheTeam(Joe)
> OnTheTeam(John)
> OnTheTeam(Mike)
> OnTheTeam(Raymond)
> OnTheTeam(Mark)
>
> each evaluates to true, and
>
> OnTheTeam(Bill)
> OnTheTeam(Bob)
> OnTheTeam(George)
> OnTheTeam(Brian)
> OnTheTeam(Frank)
>
> each evaluates to false.

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:

  1. OnTheTeam_i = X(OnTheTeam_r) or
  2. OnTheTeam_i = OnTheTeam_e?

You appear to suggest CWA implies both a) and b). Is that right? Received on Mon Jul 28 2008 - 03:21:28 CEST

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