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/?member_id=8660244&id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
