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