Re: Guessing?
From: Brian Selzer <brian_at_selzer-software.com>
Date: Wed, 30 Jul 2008 22:01:56 -0400
Message-ID: <M29kk.15214$cW3.2934_at_nlpi064.nbdc.sbc.com>
>> "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.
Date: Wed, 30 Jul 2008 22:01:56 -0400
Message-ID: <M29kk.15214$cW3.2934_at_nlpi064.nbdc.sbc.com>
"David BL" <davidbl_at_iinet.net.au> wrote in message news: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: > > a) OnTheTeam_i = X(OnTheTeam_r) or > b) OnTheTeam_i = OnTheTeam_e? > > You appear to suggest CWA implies both a) and b). Is that right? >
The closed world assumption involves what can be proved rather than what something means; an external predicate involves what something means; therefore, the closed world assumption is not associated with saying b). On the other hand, it is associated with saying:
c) OnTheTeam_i --> OnTheTeam_e
since whenever ~OnTheTeam_e, ~OnTheTeam_i. Received on Thu Jul 31 2008 - 04:01:56 CEST