Re: Guessing?

From: Brian Selzer <brian_at_selzer-software.com>
Date: Thu, 24 Jul 2008 22:57:01 -0400
Message-ID: <2ibik.15318$xZ.4416@nlpi070.nbdc.sbc.com>

"David BL" <davidbl_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.

> Does the CWA merely relate to the trivial association between a
> relation (formalised as a set of tuples) and its internal predicate
> (which is just the relation's boolean-valued characteristic
> function).

>

> See http://en.wikipedia.org/wiki/Indicator_function
>

> Alternatively does the CWA relate to an assumed association between a
> relation and an external predicate? If it is the latter then the CWA
> is clearly outside the RM formalism.
>
Received on Thu Jul 24 2008 - 21:57:01 CDT

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