Ah. On Fri, Oct 10, 2008 at 5:51 PM, Pei Wang <[EMAIL PROTECTED]> wrote: > Abram, > > Ben's "strength" is my "frequency". > > Pei > > On Fri, Oct 10, 2008 at 5:49 PM, Abram Demski <[EMAIL PROTECTED]> wrote: >> 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/?&; >> 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 >
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