On Sun, 04 Feb 2007 07:52:02 -0500, Pei Wang <[EMAIL PROTECTED]> wrote:
However, the axioms of probability theory and interpretations of probability (frequentist, logical, subjective) all take a consistent probability distribution as precondition.
Also I think the meaning of 'probabilistic consistency' might change according to the interpretation of probability. For example two subjectivist-like AGI's might arrive at different conclusions, at least early in the learning process, without probabilistic inconsistency. Such apparent inconsistencies are however prohibited under the logical interpretation.
This I think may also go to the question of resources. I'm thinking a subjectivist (De Finetti-Ramsey inspired) AGI should require a different amount of resources than a logical (Keynes-Jaynes-Cox inspired) AGI. At the moment my conjecture is that implementations of the logical interpretation would require the greater resources in that it imposes more restraints, but I can also see some possible rationale for the converse.
Ben, this is also why I was wondering why your hypothesis is framed in terms of both Cox and De Finetti. Unless I misunderstand Cox, their interpretations are in some ways diametrically opposed. De Finetti was a radical subjectivist while Cox is (epistemically) an ardent logical/objectivist (or so I gather). Apparently you see their ideas as complementary rather than mutually exclusive, which is interesting... is it because De Finetti's subjective interpretation gives a theoretical foundation to your use of [U,L] ranges in your quadruples?
Another question on my mind is if and how it might be possible to design an AGI based entirely on the subjectivist ideas of De Finetti, an idea that I find very attractive. However I am at the moment stumped on that question; it may be true that no matter the philosophy of the programmer, he must for practical reasons implement something like a logical/objective interpretation of bayes' rule. Comments?
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