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From: jbarnett@shomase.NoSubdomain.NoDomain (Jeff Barnett)
Subject: Re: Axioms of Probability
Message-ID: <Dvu6GB.EE3@gremlin.nrtc.northrop.com>
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Reply-To: jbarnett@charming.nrtc.northrop.com
Organization: Northrop Automation Sciences Laboratory
References:  <199608061919.PAA24323@age.cs.columbia.edu>
Date: Thu, 8 Aug 1996 20:33:47 GMT
Lines: 23

In article <199608061919.PAA24323@age.cs.columbia.edu>, laila@news.cs.columbia.edu ("Laila C. Khreisat") writes:
|> 
|> 
|> I am looking for literature that provides the proof of 
|> completeness of the Axioms of Probability. Any suggestions
|> would be appreciated.
|> 
|> Laila

I suggested that you look at the works of Rudolph(?) Carnap.  He
spent much of his career generating models of rationality and
proving that probability measures were used.  However, I'm not
sure what you mean by completeness.  If what you mean is that
  As the probabilities of certain propositions approach 1, so
  will the probabilities of all the propositions they imply,
  etc.
Then I'm not sure of what's a good reference.  However, the proof
for propositional logic is trivial because p(a|b), the conditional
probability of a given b is 1 if and only if b implies a.  If you
are thinking of first-order theories, I'm not sure of the status
of things.

Jeff Barnett
