I have still been doing some work... FYI, the formula in my most recent proposal still isn't quite right, that's pretty obvious now. The right formula can be found by solving a differential eqn, but I am no good at this, and of course there may not be a solution to it... if I could just prove there was *some* solution w/o needing to find it! Anyway, maybe I will post more soon??
--Abram On Wed, Oct 1, 2008 at 7:30 PM, Brad Paulsen <[EMAIL PROTECTED]> wrote: > > Ben wrote: "I remain convinced that probability theory is a proper > foundation for uncertain inference in an AGI context, whereas Pei remains > convinced of the opposite....So, this is really the essential issue, rather > than the particularities of the algebra..." > > But, please, don't stop discussing that algebra. This is the most fun I've > had on an e-mail list in years! > > Cheers, > Brad > > Ben Goertzel wrote: >> >> >> On Tue, Sep 23, 2008 at 9:28 PM, Pei Wang <[EMAIL PROTECTED] >> <mailto:[EMAIL PROTECTED]>> wrote: >> >> On Tue, Sep 23, 2008 at 7:26 PM, Abram Demski <[EMAIL PROTECTED] >> <mailto:[EMAIL PROTECTED]>> wrote: >> > Wow! I did not mean to stir up such an argument between you two!! >> >> Abram: This argument has been going on for about 10 years, with some >> "on" periods and "off" periods, so don't feel responsible for it --- >> you just raised the right topic in the right time to turn it "on" >> again. ;-) >> >> >> >> Correct ... Pei and I worked together on the same AI project for a few >> years >> (1998-2001) and had related arguments in person many times during that >> period, >> and have continued the argument off and on over email... >> >> It has been an interesting and worthwhile discussion, from my view any way, >> but neither of us has really convinced the other... >> >> I remain convinced that probability theory is a proper foundation for >> uncertain >> inference in an AGI context, whereas Pei remains convinced of the >> opposite ... >> >> So, this is really the essential issue, rather than the particularities >> of the >> algebra... >> >> The reason this is a subtle point is roughly as follows (in my view, Pei's >> surely differs). >> >> I think it's mathematically and conceptually clear that for a system >> with unbounded >> resources probability theory is the right way to reason. However if >> you look >> at Cox's axioms >> >> http://en.wikipedia.org/wiki/Cox%27s_theorem >> >> you'll see that the third one (consistency) cannot reasonably be expected of >> a system with severely bounded computational resources... >> >> So the question, conceptually, is: If a cognitive system can only >> approximately >> obey Cox's third axiom, then is it really sensible for the system to >> explicitly >> approximate probability theory ... or not? Because there is no way for >> the system >> to *exactly* follow probability theory.... >> >> There is not really any good theory of what reasoning math a system should >> (implicitly or explicitly) emulate given limited resources... Pei has >> his hypothesis, >> I have mine ... I'm pretty confident I'm right, but I can't prove it ... >> nor can he >> prove his view... >> >> Lacking a comprehensive math theory of these things, the proof is gonna be >> in the pudding ... >> >> And, it is quite possible IMO that both approaches can work, though they >> will >> not fit into the same AGI systems. That is, an AGI system in which NARS >> would >> be an effective component, would NOT necessarily >> look the same as an AGI system in which PLN would be an effective >> component... >> >> Along these latter lines: >> One thing I do like about using a reasoning system with a probabilistic >> foundation >> is that it lets me very easily connect my reasoning engine with other >> cognitive >> subsystems also based on probability theory ... say, a Hawkins style >> hierarchical >> perception network (which is based on Bayes nets) ... MOSES for >> probabilistic >> evolutionary program learning etc. Probability theory is IMO a great >> "lingua >> franca" for connecting different AI components into an integrative whole... >> >> -- Ben G >> >> >> ------------------------------------------------------------------------ >> *agi* | Archives <https://www.listbox.com/member/archive/303/=now> >> <https://www.listbox.com/member/archive/rss/303/> | Modify >> <https://www.listbox.com/member/?&;> >> Your Subscription [Powered by Listbox] <http://www.listbox.com> >> > > > ------------------------------------------- > agi > Archives: https://www.listbox.com/member/archive/303/=now > RSS Feed: https://www.listbox.com/member/archive/rss/303/ > Modify Your Subscription: https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com > ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
