# Re: Guessing?

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