OK, we're done with AGI, time to move on to discussion of psychic powers 8-D
On Wed, Sep 24, 2008 at 12:17 PM, Pei Wang <[EMAIL PROTECTED]> wrote: > Thanks for the detailed answer. Now I'm happy, and we can turn to > something else. ;-) > > Pei > > On Wed, Sep 24, 2008 at 12:09 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote: > > > >> > >> >> I guess my previous question was not clear enough: if the only domain > >> >> knowledge PLN has is > >> >> > >> >> > Ben is an author of a book on AGI <tv1> > >> >> > This dude is an author of a book on AGI <tv2> > >> >> > >> >> and > >> >> > >> >> > Ben is odd <tv1> > >> >> > This dude is odd <tv2> > >> >> > >> >> Will the system derives anything? > >> > > >> > Yes, via making default assumptions about node probability... > >> > >> Then what are the conclusions, with their truth-values, in each of the > >> two cases? > > > > > > Without node probability tv's, PLN actually behaves pretty similarly > > to NARS in this case... > > > > If we have > > > > Ben ==> AGI-author <s1> > > Dude ==> AGI-author <s2> > > |- > > Dude ==> Ben <s3> > > > > the PLN abduction rule would yield > > > > s3 = s1 s2 + w (1-s1)(1-s2) > > > > where w is a parameter of the form > > > > w = p/ (1-p) > > > > and if we set w=1 which is a principle of indifference type > > assumption then we just have > > > > s3 = 1 - s1 - s2 + 2s1s2 > > > > In any case, regardless of w, s1=s2=1 implies s3=1 > > in this formula, which is the same answer NARS gives > > in this case (of crisp premises) > > > > Similar to NARS, PLN also gives a fairly low confidence > > to this case, but the confidence formula is a pain and I > > won't write it out here... (i.e., PLN assigns this a beta > > distribution with 1 in its support, but a pretty high variance...) > > > > So, similar to NARS, without node probability info PLN cannot > > distinguish the two inference examples I gave .. no system could... > > > > However, PLN incorporates the node probabilities when available, > > immediately and easily, without requiring knowledge of math on > > the part of the system... and it incorporates them according to Bayes > > rule which I believe the right approach ... > > > > What is counterintuitive to me is having an inference engine that > > does not immediately and automatically use the node probability info > > when it is available... > > > > As evidence about Bayesian neural population coding in the brain > suggests, > > use of Bayes rule is probably MORE cognitively primary than use of > > these other more complex inference rules... > > > > -- ben g > > > > > > p.s. > > details: > > > > In PLN, > > simple abduction consists of the inference problem: > > Given P(A), P(B), P(C), P(B|A) and P(B|C), find P(C|A). > > > > and the simplest, independence-assumption + Bayes rule based formula > > for this is > > > > abdAC:=(sA,sB,sC,sAB,sCB)->(sAB*sCB*sC/sB+(1-sAB)*(1-sBC)*sC/(1-sB)) > > > > [or, more fully including all consistency conditions, > > > > abdAC:= > > > (sA,sB,sC,sAB,sCB)->(sAB*sCB*sC/sB+(1-sAB)*(1-sBC)*sC/(1-sB))*(Heaviside(sAB-max(((sA+sB-1)/sA),0))-Heaviside(sAB-min(1,(sB/sA))))*(Heaviside(sCB-max(((sB+sC-1)/sC),0))-Heaviside(sCB-min(1,(sB/sC)))); > > > > ] > > > > (This is Maple notation...) > > > > ________________________________ > > agi | Archives | Modify Your Subscription > > > ------------------------------------------- > 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 > -- Ben Goertzel, PhD CEO, Novamente LLC and Biomind LLC Director of Research, SIAI [EMAIL PROTECTED] "Nothing will ever be attempted if all possible objections must be first overcome " - Dr Samuel Johnson ------------------------------------------- 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
