Re: Guessing?

From: Brian Selzer <>
Date: Thu, 24 Jul 2008 22:57:01 -0400
Message-ID: <2ibik.15318$>

"David BL" <> wrote in message
> On Jul 24, 9:25 pm, "Brian Selzer" <> wrote:

>> "David BL" <> wrote in message
>> > On Jul 24, 10:56 am, "Brian Selzer" <> 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) \/



each evaluates to true, and


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

> 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

Original text of this message