Re: [agi] fuzzy logic necessary?
On 8/7/06, Pei Wang [EMAIL PROTECTED] wrote: At the beginning, I also believed that first-order predicate logic (FOPL) plus probability theory and fuzzy logic is the way to go, like many others in the field. It is only after I ran into many problems, that I began to build my alternative, NARS. For its difference from FOPL, see http://www.cogsci.indiana.edu/farg/peiwang/PUBLICATION/wang.cognitive_mathematical.pdf Your paper raised many important issues. Let's talk about the confirmation paradox. Once I was lurking on the SL4 list when Eliezer and Ben debated it at length. My take is that there is entirely no need to talk about a thing like p(forallX raven(X) - black(X)). The logical statement S = forall X raven(X)-black(X) is an implication. As such, it depends on whether all ravens are black.Theimplication iseither true or false. There's no such thing as partially imply. SoS is either T or F. p(S) is either 1 or 0, correspondingly. It is not very meaningful to talk about an implication being probabilistically true, because the implication is about all ravens. What we need to do is to assign probabilities to events only. For example, we can meaningfully talk about the chance of the next sampled raven being black ornot. For example p(next_raven_being_black) = 90%. That is an event, not a logical statement. Then, Hempel's paradox entirely does not surface. A logical statement like all ravens are black is either true or false. That's it. If you want to make so-called probabilistic statements, you can say eg 10% of peopleare homosexual, where the number 10% is associated with people, not the statement. Only objects and events can be associated with probabilities. If I say somepeople are homosexual, using some as a fuzzy quantifier, then that statement is true with p = 1. There is never any need to assign a probability to a logical statement. I'm still reading your paper, more onit later... YKY To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
[agi] confirmation paradox
To assign truth-values (your probability) to events only is not enough for AGI, though you are right that you cannot really assign them to universal statements, which are binary by defintion. To me, the general statements (your implication) in empirical science and everyday life are not universal statements, so can be multi-valued. See http://www.cogsci.indiana.edu/pub/wang.induction.ps for more. Pei On 8/8/06, Yan King Yin [EMAIL PROTECTED] wrote: On 8/7/06, Pei Wang [EMAIL PROTECTED] wrote: At the beginning, I also believed that first-order predicate logic (FOPL) plus probability theory and fuzzy logic is the way to go, like many others in the field. It is only after I ran into many problems, that I began to build my alternative, NARS. For its difference from FOPL, see http://www.cogsci.indiana.edu/farg/peiwang/PUBLICATION/wang.cognitive_mathematical.pdf Your paper raised many important issues. Let's talk about the confirmation paradox. Once I was lurking on the SL4 list when Eliezer and Ben debated it at length. My take is that there is entirely no need to talk about a thing like p(forall X raven(X) - black(X)). The logical statement S = forall X raven(X)-black(X) is an implication. As such, it depends on whether all ravens are black. The implication is either true or false. There's no such thing as partially imply. So S is either T or F. p(S) is either 1 or 0, correspondingly. It is not very meaningful to talk about an implication being probabilistically true, because the implication is about all ravens. What we need to do is to assign probabilities to events only. For example, we can meaningfully talk about the chance of the next sampled raven being black or not. For example p(next_raven_being_black) = 90%. That is an event, not a logical statement. Then, Hempel's paradox entirely does not surface. A logical statement like all ravens are black is either true or false. That's it. If you want to make so-called probabilistic statements, you can say eg 10% of people are homosexual, where the number 10% is associated with people, not the statement. Only objects and events can be associated with probabilities. If I say some people are homosexual, using some as a fuzzy quantifier, then that statement is true with p = 1. There is never any need to assign a probability to a logical statement. I'm still reading your paper, more on it later... YKY To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED] --- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
Re: [agi] confirmation paradox
On 8/8/06, Pei Wang [EMAIL PROTECTED] wrote: To assign truth-values (your probability) to events only is not enough for AGI, though you are right that you cannot really assign them to universal statements, which are binary by defintion. To me, the general statements (your implication) in empirical science and everyday life are not universal statements, so can be multi-valued. See http://www.cogsci.indiana.edu/pub/wang.induction.ps for more. I think Richard's point is pertinent here: very often probabilities or NTVs are inappropriate or inapplicable. For example what birds can flyreally meanin the AGI is birds can fly, with exceptions. The exception is implicit in the nonmonotonic reasoning system. That is the furthest we can go. It's not meaningful to attribute a number to the statement birds can fly. Why not? Well, the difficulty is that we cannot come up with a well-defined interpretation of the NTV. For example, we can define the NTVbyp =if you randomly sample a bird in the real world, the chance of it being able to fly. But we can also define p = if you randomly name a bird species, the chance of that species being able to fly. See?The NTV has got to be precisely defined, but the additional information required to define it is not contained within the simple statement birds can fly. In other words, for the simple statement birds can fly, the best we can say is that it may have exceptions. It is far better to assign numbers whenthe statement has explicit numerical content, eg the average Chinese person is about 5'7 tall (I made this up). So we can always assignnumbers explicitly, and avoid assigning NTVs implicitly. A further example is: S1 = The fall of the Roman empire is due to Christianity. S2 = The fall of the Roman empire is due to lead poisoning. I'm not surewhether S1 or S2 is more true. But thequestion is how can you define the meaning of the NTV associated with S1 or S2? Ifwe can't, why not just leave these statements as non-numerical? YKY To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
