Abram, I finally read your long post...
> The basic idea is to treat NARS truth values as representations of a > statement's likelihood rather than its probability. The likelihood of > a statement given evidence is the probability of the evidence given > the statement. Unlike probabilities, calculating likelihoods does not > require prior beliefs; the likelihood of a statement is a direct > reflection of the evidence in favor of it. So, I thought likelihoods > were a good match for the experienced-based semantics of NARS. > > The second decision was to model inheritance statements with > probability distributions over other inheritance statements; > specifically, A=>B is the conditional probability of A=>X given B=>X > (ie, something like the probability that A will inherit B's intension) > and also the conditional x=>B given X=>A (measuring B's inheritance of > A's extension). This seems to follow from the typical description of > NARS. > > Third, I chose to have a single parameter determine this distribution, > ranging from 0 to 1. I simply called it 'par' before, although perhaps > 'strength' or something would have been more descriptive... All this is OK with me. > > > Given those three assumptions, plus the NARS formula for revision, > there is (I think) only one possible formula relating the NARS > variables 'f' and 'w' to the value of 'par': the probability density > function p(par | w, f) = par^(w*f) * (1-par)^(w*(1-f)). Why is this the only possible formula? > Here's the math. My problem with your math is that the basic approach seems to be to take the NARS formulas as the **goal**, and then reverse-engineer some formulas that will produce them as a result. This just doesn't seem the right sort of approach, to me. If you could set up a probabilistic treatment in a way that "just makes sense" given the conceptual assumptions ... and reasonable, not obviously ad-hoc mathematical assumptions ... and find that NARS then just **emerges**, then I'd be impressed!! But, coming up with complex math formulas that need to be specifically tweaked and fitted to yield NARS-type rules, doesn't satisfy me much. In particular, the result that NARS induction and abduction each depend on **only one** of their premise truth values, seems conceptually fundamental, and I'd expect your treatment to give some elegant explanation of this (whether conceptual or mathematical). If that exists in the equations you posit, I couldn't find it... So I sorta agree with Pei: nice try indeed, and interesting stuff to think about ... but it doesn't feel "right" enough that I'm moved to invest time working out the math details... -- Ben ------------------------------------------- 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
