Pei, You agree that the abduction and induction "strength" formulas only rely on one of the two premises?
Is there some variable called strength that I missed? --Abram 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 > ------------------------------------------- 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
