Re: [agi] foundations of probability theory

2007-02-02 Thread gts
On Thu, 01 Feb 2007 14:00:06 -0500, Ben Goertzel [EMAIL PROTECTED] wrote: Discussing Cox's work is on-topic for this list... Okay, I'll get a copy and read it. Let me tell you one research project that interests me re Cox and subjective probability: Justifying Probability Theory as

Re: [agi] foundations of probability theory

2007-02-02 Thread Pei Wang
I don't know of any work explicitly addressing this sort of issue, do you? No, none that address Cox and AI directly, but I suspect one is forthcoming perhaps from you. Yes? :) There is a literature on Cox and AI. For example, http://www.cs.cornell.edu/home/halpern/papers/cox1.pdf Pei

Re: [agi] foundations of probability theory

2007-02-02 Thread Ben Goertzel
Interpretation-wise, Cox followed Keynes pretty closely. Keynes had his own eccentric view of probability, which held among other things that a single number was not enough information to capture a judgment of uncertainty (and I agree with this). However, even so, Cox's Theorem does

Re: [agi] foundations of probability theory

2007-02-02 Thread gts
On Fri, 02 Feb 2007 15:57:24 -0500, Ben Goertzel [EMAIL PROTECTED] wrote: Interpretation-wise, Cox followed Keynes pretty closely. Keynes had his own eccentric view of probability... Although I don't yet know much about Cox, (Amazon is shipping his book to me), I have studied a bit about

Re: [agi] foundations of probability theory

2007-02-02 Thread Ben Goertzel
In Novamente, we use entities called indefinite probabilities, which are described in a paper to appear in the AGIRI Workshop Proceedings later this year... Roughly speaking an indefinite probability is a quadruple (L,U,b,N) with interpretation The probability is b that after I make N

[agi] Optimality of using probability

2007-02-02 Thread Eliezer S. Yudkowsky
Ben Goertzel wrote: Cox's axioms and de Finetti's subjective probability approach, developed in the first part of the last century, give mathematical arguments as to why probability theory is the optimal way to reason under conditions of uncertainty. However, given limited computational