Of course, this is only one among very many differences btw PLN and NARS, but I agree it's an interesting one.
I've got other stuff to do today, but I'll try to find time to answer this email carefully over the weekend. ben On Fri, Oct 10, 2008 at 5:38 PM, Pei Wang <[EMAIL PROTECTED]> wrote: > Ben, > > I agree with what you said in the previous email. > > However, since we already touched this point in the second time, there > may be people wondering what the difference between NARS and PLN > really is. > > Again let me use an example to explain why the truth-value function of > abduction/induction should be asymmetric, at least to me. Since > induction is more intuitive, I'll use it. > > The general induction rule in NARS has the following form > > M-->P <t_1> > M-->S <t_2> > ----------------- > S-->P <t_a> > P-->S <t_b> > > where each truth value has a "frequency" factor (for > positive/negative), and a "confidence" factor (for sure/unsure). > > A truth-value function is symmetric with respect to the premises, if > and only if <t_a> = <t_b> for all <t_1> and <t_2>. Last time you > mentioned the following abduction function of PLN: > s3 = s1 s2 + w (1-s1)(1-s2) > which is symmetric in this sense. > > Now, instead of discussing the details of the NARS function, I only > explain why it is not symmetric, that is, when t_a and t_b are > different. > > First, positive evidence lead to symmetric conclusions, that is, if M > support S-->P, it will also support P-->S. For example, "Swans are > birds" and "Swans are swimmers" support both "Birds are swimmers" and > "Swimmers are birds", to the same extent. > > However, the negative evidence of one conclusion is no evidence of the > other conclusion. For example, "Swallows are birds" and "Swallows are > NOT swimmers" suggests "Birds are NOT swimmers", but says nothing > about whether "Swimmers are birds". > > Now I wonder if PLN shows a similar asymmetry in induction/abduction > on negative evidence. If it does, then how can that effect come out of > a symmetric truth-function? If it doesn't, how can you justify the > conclusion, which looks counter-intuitive? > > Pei > > > > On Fri, Oct 10, 2008 at 4:57 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote: > > > > Sorry Pei, you are right, I sloppily mis-stated! > > > > What I should have said was: > > > > " > > the result that the NARS induction and abduction *strength* formulas > > each depend on **only one** of their premise truth values ... > > " > > > > Anyway, my point in that particular post was not to say that NARS is > either > > good or bad in this aspect ... but just to note that this IMO is a > > conceptually > > important point that should somehow "fall right out" of a probabilistic > > (or nonprobabilistic) derivation of NARS, rather than being achieved via > > carefully fitting complex formulas to produce it... > > > > ben g > > > > On Fri, Oct 10, 2008 at 4:48 PM, Pei Wang <[EMAIL PROTECTED]> > wrote: > >> > >> On Fri, Oct 10, 2008 at 4:24 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote: > >> > > >> > In particular, the result that NARS induction and abduction each > >> > depend on **only one** of their premise truth values ... > >> > >> Ben, > >> > >> I'm sure you know it in your mind, but this simple description will > >> make some people think that NARS is obvious wrong. > >> > >> In NARS, in induction and abduction the truth value of the conclusion > >> depends on the truth values of both premises, but in an asymmetric > >> way. It is the "frequency" factor of the conclusion that only depends > >> on the frequency of one premise, but not the other. > >> > >> Unlike deduction, the truth-value function of induction and abduction > >> are fundamentally asymmetric (on negative evidence), with respect to > >> the two premises. Actually, it is the PLN functions that looks wrong > >> to me, on this aspect. ;-) > >> > >> Pei > >> > >> > >> ------------------------------------------- > >> 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 | 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
