Re: [agi] NARS and probability
Brad, Thanks for the encouragement. For people who cannot fully grok the discussion from the email alone, the relevant NARS references are http://nars.wang.googlepages.com/wang.semantics.pdf and http://nars.wang.googlepages.com/wang.confidence.pdf Pei On Sat, Oct 11, 2008 at 1:13 AM, Brad Paulsen [EMAIL PROTECTED] wrote: Pei, Ben G. and Abram, Oh, man, is this stuff GOOD! This is the real nitty-gritty of the AGI matter. How does your approach handle counter-evidence? How does your approach deal with insufficient evidence? (Those are rhetorical questions, by the way -- I don't want to influence the course of this thread, just want to let you know I dig it and, mostly, grok it as well). I love this stuff. You guys are brilliant. Actually, I think it would make a good publication: PLN vs. NARS -- The AGI Smack-down! A win-win contest. This is a rare treat for an old hacker like me. And, I hope, educational for all (including the participants)! Keep it coming, please! Cheers, Brad Pei Wang wrote: On Fri, Oct 10, 2008 at 8:03 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Yah, according to Bayes rule if one assumes P(bird) = P(swimmer) this would be the case... (Of course, this kind of example is cognitively misleading, because if the only knowledge the system has is Swallows are birds and Swallows are NOT swimmers then it doesn't really know that the terms involved are swallows, birds, swimmers etc. ... then in that case they're just almost-meaningless tokens to the system, right?) Well, it depends on the semantics. According to model-theoretic semantics, if a term has no reference, it has no meaning. According to experience-grounded semantics, every term in experience have meaning --- by the role it plays. Further questions: (1) Don't you intuitively feel that the evidence provided by non-swimming birds says more about Birds are swimmers than Swimmers are birds? (2) If your answer for (1) is yes, then think about Adults are alcohol-drinkers and Alcohol-drinkers are adults --- do they have the same set of counter examples, intuitively speaking? (3) According to your previous explanation, will PLN also take a red apple as negative evidence for Birds are swimmers and Swimmers are birds, because it reduces the candidate pool by one? Of course, the probability adjustment may be very small, but qualitatively, isn't it the same as a non-swimming bird? If not, then what the system will do about it? Pei On Fri, Oct 10, 2008 at 7:34 PM, Pei Wang [EMAIL PROTECTED] wrote: Ben, I see your position. Let's go back to the example. If the only relevant domain knowledge PLN has is Swallows are birds and Swallows are NOT swimmers, will the system assigns the same lower-than-default probability to Birds are swimmers and Swimmers are birds? Again, I only need a qualitative answer. Pei On Fri, Oct 10, 2008 at 7:24 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Pei, I finally took a moment to actually read your email... 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? According to Bayes rule, P(bird | swimmer) P(swimmer) = P(swimmer | bird) P(bird) So, in PLN, evidence for P(bird | swimmer) will also count as evidence for P(swimmer | bird), though potentially with a different weighting attached to each piece of evidence If P(bird) = P(swimmer) is assumed, then each piece of evidence for each of the two conditional probabilities, will count for the other one symmetrically. The intuition here is the standard Bayesian one. Suppose you know there are 1 things in the universe, and 1000 swimmers. Then if you find out that swallows are not swimmers ... then, unless you think there are zero swallows, this does affect P(bird | swimmer). For instance, suppose you think there are 10 swallows and 100 birds. Then, if you know for sure that swallows are not swimmers, and you have no other info but the above, your estimate of P(bird|swimmer) should decrease... because of the 1000 swimmers, you now know there are only 990 that might be birds ... whereas before you thought there were 1000 that might be birds. And the same sort of reasoning holds for **any** probability distribution you place on the number of things in the universe, the number of swimmers, the number of birds, the number of swallows. It doesn't matter what assumption you make, whether you look at n'th order pdf's or whatever ... the same reasoning works... From what I understand, your philosophical view is that it's
Re: [agi] NARS and probability
Pei etc.,
First high level comment here, mostly to the non-Pei audience ... then I'll
respond to some of the details:
This dialogue -- so far -- feels odd to me because I have not been
defending anything special, peculiar or inventive about PLN here.
There are some things about PLN that would be considered to fall into that
category
(e.g. the treatment of intension which uses my pattern theory, and the
treatment of quantifiers which uses third-order probabilities ... or even
the
use of indefinite truth values). Those are the things that I would expect
to be arguing about! Even more interesting would be to argue about
strategies
for controlling combinatorial explosion in inference trees, which IMO is the
truly crucial issue, more so than the particulars of the inference and
uncertainty
management formalism (though those particulars need to be workable too, if
one is to have an AI with explicit inference as a significant component).
Instead, in this dialogue, I am essentially defending the standard usage
of probability theory, which is the **least** interesting and inventive part
of
PLN. I'm defending the use of Bayes rule ... re-presenting the standard
Bayesian argument about the Hempel confirmation problem, etc.
This is rather a reversal of positions for me, as I more often these days
argue
with people who are hard-core Bayesians, who believe that explicitly doing
Bayesian inference is the key to AGI ... and my argument with them is that
a) you need to supplement probability theory with heuristics, because
otherwise
things become intractable; b) these heuristics are huge and subtle and in
fact wind up constituting a whole cognitive architecture of which explicit
probability
theory is just one component (but the whole architecture appears to the
probabilistic-reasoning component as a set of heuristic assumptions).
So anyway this is not, so far, so much of a PLN versus NARS debate as a
probability theoretic AI versus NARS debate, in the sense that none of the
more odd/questionable/fun/inventive parts of PLN are being invoked here ...
only the parts that are common to PLN and a lot of other approaches...
But anyway, back to defending Bayes and elementary probability theory in
(its application to common sense reasoning; obviously Pei is not disputing
the actual mathematics!)
Maybe in this reply I will get a chance to introduce some of the more
interesting
aspects of PLN, we'll see...
Since each inference rule usually only considers two premises, whether
the meaning of the involved concepts are rich or poor (i.e., whether
they are also involved in other statements not considered by the rule)
shouldn't matter in THAT STEP, right?
It doesn't matter in the sense of determining
what the system does in that step, but it matters in terms
of the human intuitiveness evaluation of that step, because we are
intuitively accustomed to evaluating inferences regarding rich concepts
that have a lot of links, and for which we have some intuitive understanding
of the relevant term probabilities.
Further questions:
(1) Don't you intuitively feel that the evidence provided by
non-swimming birds says more about Birds are swimmers than
Swimmers are birds?
Yes, but only because I know intuitively that swimmers are more common
in my everyday world than birds.
Please note that this issue is different from our previous debate.
Node probability have nothing to do with the asymmetry in
induction/abduction.
I don't remember our previous debate and don't have time to study my
email archives (I don't really have time to answer this email but I'm doing
it
anyway ;-) ...
Anyway, in PLN, if we map is into ExtensionalInheritance, then the point
that
P(swimmer | Bird) P(bird) = P(bird | swimmer) P(swimmer)
lets me answer your question without even thinking much about the context.
Due to Bayes rule, in any Bayesian inference system, evidence for one of
{ P(swimmer|bird), P(bird|swimmer) } may be considered as evidence for the
other, on principle. [How that evidence is propagated through the system's
memory is another question, etc. etc.] And Bayes rule tells you how to
convert
evidence for one of these conditionals into evidence for another.
Getting back to the odd versus standard aspects of PLN, if we introduce an
odd
aspect we can model is as IntensionalInheritance, or a weighted average of
ExtensionalInheritance and IntensionalInheritance.
In the Intensional case, then for instance
bird is swimmer
comes out to mean
P(X is in PAT_swimmer | X is in PAT_bird)
where PAT_A is the fuzzy set of patterns in A.
A quick cut and paste from the PLN book, page 257, here:
***
Note a significant difference from NARS here. In NARS, it is assumed that X
inherits from Y if X extensionally inherits from Y but Y intensionally
inherits
from (inherits properties from) X. We take a different approach here. We say
that
X inherits from Y if X's members are members of Y, and the properties
associ-
Re: [agi] NARS and probability
On Fri, Oct 10, 2008 at 8:56 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Well, it depends on the semantics. According to model-theoretic semantics, if a term has no reference, it has no meaning. According to experience-grounded semantics, every term in experience have meaning --- by the role it plays. That's why I said almost-meaningless ... if those are the only relationships known to the system, then the terms in those relationships play almost no roles, hence have almost no meanings... Since each inference rule usually only considers two premises, whether the meaning of the involved concepts are rich or poor (i.e., whether they are also involved in other statements not considered by the rule) shouldn't matter in THAT STEP, right? Further questions: (1) Don't you intuitively feel that the evidence provided by non-swimming birds says more about Birds are swimmers than Swimmers are birds? Yes, but only because I know intuitively that swimmers are more common in my everyday world than birds. Please note that this issue is different from our previous debate. Node probability have nothing to do with the asymmetry in induction/abduction. For example, non-swimmer birds is negative evidence for Birds are swimmers but irrelevant to Swimmers are birds, while non-bird swimmers is negative evidence for Swimmers are birds but irrelevant to Birds are swimmers. No matter which of the two nodes is more common, you cannot have both case right. (2) If your answer for (1) is yes, then think about Adults are alcohol-drinkers and Alcohol-drinkers are adults --- do they have the same set of counter examples, intuitively speaking? Again, our intuitions for this are colored by the knowledge that there are more adults than alcohol-drinkers. As above, the two sets of counter examples are non-alcohol-drinking adult and non-adult alcohol-drinker, respectively. The fact that these two statements have different negative evidence have nothing to do with the size of the related sets (node probability). Consider high school, which has 4 years: freshman, sophomore, junior, senior. Then think about Juniors seniors are women and women are juniors seniors It seems quite intuitive to me that, in this case, the same pieces of evidence support the truth values of these two hypotheses. This is because the term probabilities of juniors and seniors and women are intuitively known to be about equal. Instead of supporting evidence, you should address refuting evidence (because that is where the issue is). For Juniors seniors are women, it is juniors seniors man, and for women are juniors seniors, it is freshman sophomore women. What I argued is: the counter evidence of statement A is B is not counter evidence of the converse statement B is A, and vice versa. You cannot explain this in both directions by node probability. (3) According to your previous explanation, will PLN also take a red apple as negative evidence for Birds are swimmers and Swimmers are birds, because it reduces the candidate pool by one? Of course, the probability adjustment may be very small, but qualitatively, isn't it the same as a non-swimming bird? If not, then what the system will do about it? Yes, in principle, PLN will behave in Hempel's confirmation paradox in a similar way to other Bayesian systems. I do find this counterintuitive, personally, and I spent a while trying to work around it ... but finally I decided that my intuition is the faulty thing. As you note, it's a very small probability adjustment in these cases, so it's not surprising if human intuition is not tuned to make such small probability adjustments in a correct or useful way... Well, actually your previous explanation is exactly the opposite of the standard Bayesian answer --- see http://en.wikipedia.org/wiki/Raven_paradox Now we have three different opinions on the relationship between statement Birds are swimmers and the evidence provided by a red apple: (1) NARS: it is irrelevant (neither positive nor negative) (2) PLN: it is negative evidence (though very small) (3) Bayesian: it is positive evidence (though very small) Everyone agrees that (2) and (3) are counterintuitive, but most people trust probability theory more than their own intuition --- after all, nobody is perfect ... :-( To me, small probability adjustments is a bad excuse. No matter how small the adjustment is, as far as it is not infinitely small, it cannot be always ignored, since it will accumulate. If all non-bird objects are taken as (either positive or negative) evidence for Birds are swimmers, then the huge number of them cannot be ignored. It is always possible to save a theory (probability theory, in this situation) if you are willing to pay the price. The problem is whether the price is too high. Pei --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed:
Re: [agi] NARS and probability
Ben, Your reply raised several interesting topics, and most of them cannot be settled down in this kind of email exchanges. Therefore, I won't address every of them here, but will propose another solution, in a separate private email. Go back to where this debate starts: the asymmetry of induction/abduction. To me, here is what the discussion has revealed so far: (1) The PLN solution is consistent with the Bayesian tradition and probability theory in general, though it is counterintuitive. (2) The NARS solution fits people's intuition, though it violates probability theory. Please note that on this topic, what is involved is not just Pei's intuition (though in some other topics, it is) --- Hempel's Paradox looks counterintuitive to everyone, including you (which you admitted) and Hempel himself, though you, Hempel, and most of the others involved in this research, choose to accept the counterintuitive conclusion, because of the belief that probability theory should be followed in commonsense reasoning. As I said before, I don't think I can change your belief in probability theory very soon. Therefore, as long as you think my above summary is fair, I've reached my goal in this round of exchange. Pei On Sat, Oct 11, 2008 at 8:45 AM, Ben Goertzel [EMAIL PROTECTED] wrote: Pei etc., First high level comment here, mostly to the non-Pei audience ... then I'll respond to some of the details: This dialogue -- so far -- feels odd to me because I have not been defending anything special, peculiar or inventive about PLN here. There are some things about PLN that would be considered to fall into that category (e.g. the treatment of intension which uses my pattern theory, and the treatment of quantifiers which uses third-order probabilities ... or even the use of indefinite truth values). Those are the things that I would expect to be arguing about! Even more interesting would be to argue about strategies for controlling combinatorial explosion in inference trees, which IMO is the truly crucial issue, more so than the particulars of the inference and uncertainty management formalism (though those particulars need to be workable too, if one is to have an AI with explicit inference as a significant component). Instead, in this dialogue, I am essentially defending the standard usage of probability theory, which is the **least** interesting and inventive part of PLN. I'm defending the use of Bayes rule ... re-presenting the standard Bayesian argument about the Hempel confirmation problem, etc. This is rather a reversal of positions for me, as I more often these days argue with people who are hard-core Bayesians, who believe that explicitly doing Bayesian inference is the key to AGI ... and my argument with them is that a) you need to supplement probability theory with heuristics, because otherwise things become intractable; b) these heuristics are huge and subtle and in fact wind up constituting a whole cognitive architecture of which explicit probability theory is just one component (but the whole architecture appears to the probabilistic-reasoning component as a set of heuristic assumptions). So anyway this is not, so far, so much of a PLN versus NARS debate as a probability theoretic AI versus NARS debate, in the sense that none of the more odd/questionable/fun/inventive parts of PLN are being invoked here ... only the parts that are common to PLN and a lot of other approaches... But anyway, back to defending Bayes and elementary probability theory in (its application to common sense reasoning; obviously Pei is not disputing the actual mathematics!) Maybe in this reply I will get a chance to introduce some of the more interesting aspects of PLN, we'll see... Since each inference rule usually only considers two premises, whether the meaning of the involved concepts are rich or poor (i.e., whether they are also involved in other statements not considered by the rule) shouldn't matter in THAT STEP, right? It doesn't matter in the sense of determining what the system does in that step, but it matters in terms of the human intuitiveness evaluation of that step, because we are intuitively accustomed to evaluating inferences regarding rich concepts that have a lot of links, and for which we have some intuitive understanding of the relevant term probabilities. Further questions: (1) Don't you intuitively feel that the evidence provided by non-swimming birds says more about Birds are swimmers than Swimmers are birds? Yes, but only because I know intuitively that swimmers are more common in my everyday world than birds. Please note that this issue is different from our previous debate. Node probability have nothing to do with the asymmetry in induction/abduction. I don't remember our previous debate and don't have time to study my email archives (I don't really have time to answer this email but I'm doing it anyway ;-)
Re: [agi] NARS and probability
Thanks Pei! This is an interesting dialogue, but indeed, I have some reservations about putting so much energy into email dialogues -- for a couple reasons 1) because, once they're done, the text generated basically just vanishes into messy, barely-searchable archives. 2) because I tend to answer emails on the fly and hastily, without putting careful thought into phrasing, as I do when writing papers or books ... and this hastiness can sometimes add confusion It would be better to further explore these issues in some other forum where the discussion would be preserved in a more easily readable form, and where the medium is more conducive to carefully-thought-out phrasings... Go back to where this debate starts: the asymmetry of induction/abduction. To me, here is what the discussion has revealed so far: (1) The PLN solution is consistent with the Bayesian tradition and probability theory in general, though it is counterintuitive. (2) The NARS solution fits people's intuition, though it violates probability theory. I don't fully agree with this summary, sorry. I agree that the PLN approach is counterintuitive in some respects (e.g. the Hempel puzzle) I also note that the more innovative aspects of PLN don't seem to introduce any new counterintuitiveness. The counterintuitiveness that is there is just inherited from plain old probability theory, it seems. However, I also feel the NARS approach is counterintuitive in some respects. One example is the fact that in NARS, induction/abduction the frequency component of the conclusion depends on only one of the premises). Another example is the lack of Bayes rule in NARS: there is loads of evidence that humans and animals intuitively reason according to Bayes rule in various situations. Which approach (PLN or NARS) is more agreeable with human intuition, on the whole, is not clear to me. And, as I argued in my prior email, this is not the most interesting issue from my point of view ... for two reasons, actually (only one of which I elaborated carefully before) 1) I'm not primarily trying to model humans, but rather trying to create a powerful AGI 2) Human intuition about human practice, does not always match human practice. What we feel like we're doing may not match what we're actually doing in our brains. This is very plainly demonstrated for instance in the area of mental arithmetic: the algorithms people think they're following, could not possibly lead to the timing-patterns that people generate when actually solving mental arithmetic problems. The same thing may hold for inference: the rules people think they're following may not be the ones they actually follow. So that intuitiveness is of significant yet limited value in figuring out what people actually do unconsciously when thinking. -- Ben G --- 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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
Ben, My summary was on the asymmetry of induction/abduction topic alone, not on NARS vs. PLN in general --- of course NARS is counterintuitive in several places! Under that restriction, I assume you'll agree with me summary. Please note that this issue is related to Hempel's Paradox, but not the same --- the former is on negative evidence, while the latter is on positive evidence. I won't address the other issues here --- as you said, they are complicated, and email discussion is not always enough. I'm looking forward to the PNL book and your future publications on the related topics. Pei On Sat, Oct 11, 2008 at 11:54 AM, Ben Goertzel [EMAIL PROTECTED] wrote: Thanks Pei! This is an interesting dialogue, but indeed, I have some reservations about putting so much energy into email dialogues -- for a couple reasons 1) because, once they're done, the text generated basically just vanishes into messy, barely-searchable archives. 2) because I tend to answer emails on the fly and hastily, without putting careful thought into phrasing, as I do when writing papers or books ... and this hastiness can sometimes add confusion It would be better to further explore these issues in some other forum where the discussion would be preserved in a more easily readable form, and where the medium is more conducive to carefully-thought-out phrasings... Go back to where this debate starts: the asymmetry of induction/abduction. To me, here is what the discussion has revealed so far: (1) The PLN solution is consistent with the Bayesian tradition and probability theory in general, though it is counterintuitive. (2) The NARS solution fits people's intuition, though it violates probability theory. I don't fully agree with this summary, sorry. I agree that the PLN approach is counterintuitive in some respects (e.g. the Hempel puzzle) I also note that the more innovative aspects of PLN don't seem to introduce any new counterintuitiveness. The counterintuitiveness that is there is just inherited from plain old probability theory, it seems. However, I also feel the NARS approach is counterintuitive in some respects. One example is the fact that in NARS, induction/abduction the frequency component of the conclusion depends on only one of the premises). Another example is the lack of Bayes rule in NARS: there is loads of evidence that humans and animals intuitively reason according to Bayes rule in various situations. Which approach (PLN or NARS) is more agreeable with human intuition, on the whole, is not clear to me. And, as I argued in my prior email, this is not the most interesting issue from my point of view ... for two reasons, actually (only one of which I elaborated carefully before) 1) I'm not primarily trying to model humans, but rather trying to create a powerful AGI 2) Human intuition about human practice, does not always match human practice. What we feel like we're doing may not match what we're actually doing in our brains. This is very plainly demonstrated for instance in the area of mental arithmetic: the algorithms people think they're following, could not possibly lead to the timing-patterns that people generate when actually solving mental arithmetic problems. The same thing may hold for inference: the rules people think they're following may not be the ones they actually follow. So that intuitiveness is of significant yet limited value in figuring out what people actually do unconsciously when thinking. -- Ben G 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/?member_id=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
Pei, Ben, I am going to try to spell out an arguments for each side (arguing for symmetry, then for asymmetry). For Symmetry: Suppose we get negative evidence for As are Bs, such that we are tempted to say no As are Bs. We then consider the statement Bs are As, with no other info. We think, If we found a B that was an A, then we would also have found an A that was a B; I don't think any exist; so, I don't think there are any Bs that are As. Thus, evidence against As are Bs is also evidence against Bs are As. Against Symmetry: If we are counting empirical frequencies, then an A that is not a B will lower the frequency of As are Bs; however, it will not alter the frequency count for Bs are As. What this highlights for me is the idea that NARS truth values attempt to reflect the evidence so far, while probabilities attempt to reflect the world. --Abram --- 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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
On Sat, Oct 11, 2008 at 5:38 PM, Pei Wang [EMAIL PROTECTED] wrote: On Sat, Oct 11, 2008 at 4:10 PM, Abram Demski [EMAIL PROTECTED] wrote: Pei, Ben, I am going to try to spell out an arguments for each side (arguing for symmetry, then for asymmetry). For Symmetry: Suppose we get negative evidence for As are Bs, such that we are tempted to say no As are Bs. We then consider the statement Bs are As, with no other info. We think, If we found a B that was an A, then we would also have found an A that was a B; I don't think any exist; so, I don't think there are any Bs that are As. Thus, evidence against As are Bs is also evidence against Bs are As. I see your point --- it comes from the fact that As are Bs and Bs are As have the same positive evidence (both in NARS and in PLN), plus the additional assumption that no positive evidence means negative evidence. Here the problem is in the additional assumption. Indeed it is assumed both in traditional logic and probability theory that everything matters for every statement (as revealed by Hempel's Paradox). Hmm... other additional assumptions will do the job here as well, and I don't see why you mentioned the one you did. An assumption closer to the argument I gave would be The more negative evidence we've ween, the less positive evidence we should expect. --Abram --- 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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
On Sat, Oct 11, 2008 at 5:56 PM, Abram Demski [EMAIL PROTECTED] wrote: I see your point --- it comes from the fact that As are Bs and Bs are As have the same positive evidence (both in NARS and in PLN), plus the additional assumption that no positive evidence means negative evidence. Here the problem is in the additional assumption. Indeed it is assumed both in traditional logic and probability theory that everything matters for every statement (as revealed by Hempel's Paradox). Hmm... other additional assumptions will do the job here as well, and I don't see why you mentioned the one you did. An assumption closer to the argument I gave would be The more negative evidence we've ween, the less positive evidence we should expect. Yes, for this topic, your assumption may be more proper, though it is still unjustified, unless it is further assumed that the number of total amount of evidence is fixed. 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/?member_id=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
Hi, What this highlights for me is the idea that NARS truth values attempt to reflect the evidence so far, while probabilities attempt to reflect the world I agree that probabilities attempt to reflect the world . Well said. This is exactly the difference between an experience-grounded semantics and a model-theoretic semantics. I don't agree with this distinction ... unless you are construing model theoretic semantics in a very restrictive way, which then does not apply to PLN. If by model-theoretic semantics you mean something like what Wikipedia says at http://en.wikipedia.org/wiki/Formal_semantics, *** *Model-theoretic semanticshttp://en.wikipedia.org/w/index.php?title=Model-theoretic_semanticsaction=editredlink=1 * is the archetype of Alfred Tarskihttp://en.wikipedia.org/wiki/Alfred_Tarski's semantic theory of truthhttp://en.wikipedia.org/wiki/Semantic_theory_of_truth, based on his T-schema http://en.wikipedia.org/wiki/T-schema, and is one of the founding concepts of model theoryhttp://en.wikipedia.org/wiki/Model_theory. This is the most widespread approach, and is based on the idea that the meaning of the various parts of the propositions are given by the possible ways we can give a recursively specified group of interpretation functions from them to some predefined mathematical domains: an interpretationhttp://en.wikipedia.org/wiki/Interpretation_%28logic%29of first-order predicate logic http://en.wikipedia.org/wiki/First-order_predicate_logicis given by a mapping from terms to a universe of individuals http://en.wikipedia.org/wiki/Individual, and a mapping from propositions to the truth values true and false. *** then yes, PLN's semantics is based on a mapping from terms to a universe of individuals, and a mapping from propositions to truth values. On the other hand, these individuals may be for instance **elementary sensations or actions**, rather than higher-level individuals like, say, a specific cat, or the concept cat. So there is nothing non-experience-based about mapping terms into a individuals that are the system's direct experience ... and then building up more abstract terms by grouping these directly-experience-based terms. IMO, the dichotomy between experience-based and model-based semantics is a misleading one. Model-based semantics has often been used in a non-experience-based way, but that is not because it fundamentally **has** to be used in that way. To say that PLN tries to model the world, is then just to say that it tries to make probabilistic predictions about sensations and actions that have not yet been experienced ... which is certainly the case. Once again, the difference in truth-value functions is reduced to the difference in semantics, what is, what the truth-value attempts to measure. Agreed... Ben G --- 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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
On Wed, Oct 8, 2008 at 5:15 PM, Abram Demski [EMAIL PROTECTED] wrote: 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)). Note: NARS truth values are more often (I think?) represented by the pair 'f' 'c', where 'c' is computed from 'w' by the formula c=w/(w+k), where k is a fixed constant. This is of little consequence at this point, and it was more intuitive to use 'f' and 'w' (at least for me). At this stage, you are right. Since c and w fully determines each other, in principle you can use either, and w is more intuitive. However, in designing the truth-value functions, it is more convenient to use c, a real number in [0, 1], than w, which has no upper bound. Here's the math. In NARS, the operation we're interested in is taking two pools of evidence, one concerning A=X and the other concerning B=X, and combining them to calculate the evidence they lend to A=B. Now things get tricky, In my derivation, in abduction/deduction the evidence of a premise is not directly used as evidence for the conclusion. Instead, it is the premise, as a summary of its own evidences, that is used as evidence. That is, X is not a set, but an individual. Consequently, the operation doesn't taking two pools of evidence and somehow combine them into one pool (as in the revision rule). So probabilistically, we want to determine the probability of the evidence for A=X and B=X given each possible 'par' value of A=B. According to the semantics of NARS, A=X or B=X, by itself, doesn't provide evidence for A=B. Overall, it is a nice try, but given the difference in semantics between probability theory and NARS, I'm still doubtful on how far you can go in this direction. 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/?member_id=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
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/?member_id=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
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: 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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
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/?member_id=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
Of course, this is only one among very many differences btw PLN and NARS, but I agree it's an interesting one. I've got other stuff to do today, but I'll try to find time to answer this email carefully over the weekend. ben 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 -- 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: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription:
Re: [agi] NARS and probability
Ben, Strength? If you mean weight or confidence, this is not so. As Pei corrected, it is the *frequency* that depends on only one of the two. The strength depends on both. And, that is one feature of NARS that I don't find strange. It can be explained OK by the formula I previously proposed and now abandoned. To re-use the same metaphor I referred to before, it is as if we are trying to estimate the weight of heads and tails for a quarter when we have only partial knowledge of a series of coin flips, and partial knowledge telling us whether or not that series of flips is actually the quarter we are interested in. The 2 types of knowledge there are exactly like the 2 premises: we only want the frequency to depend on the first type of evidence, but the confidence of that frequency also depends on the 2nd type of evidence. To respond more generally to the comments... The criticism is certainly valid; I am not so worried about semantics, only about making the manipulations fit. The decision to go with likelihoods is an exception to this, but that is because I doubt that the manipulations would be easy to fit together with no resemblance in semantics... If I were taking more the approach Ben suggests, that is, making reasonable-sounding assumptions and then working forward rather than assuming NARS and working backward, I would have kept the formula from last time (justifying it with the argument mentioned above). Probably this results in a system with many similarities to NARS but differing in the exact formulas, and in the absence of the constant 'k'. --Abram 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/?member_id=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
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
Re: [agi] NARS and probability
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:
Re: [agi] NARS and probability
I meant frequency, sorry Strength is a term Pei used for frequency in some old sicsussions... If I were taking more the approach Ben suggests, that is, making reasonable-sounding assumptions and then working forward rather than assuming NARS and working backward, I would have kept the formula from last time (justifying it with the argument mentioned above). Probably this results in a system with many similarities to NARS but differing in the exact formulas, and in the absence of the constant 'k'. The exact formulas used in NARS are basically heuristics derived based on endpoint conditions, so replicating those exact formulas is really not important IMO... the key would be replicating their qualitative behavior... 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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
On Fri, Oct 10, 2008 at 5:52 PM, Ben Goertzel [EMAIL PROTECTED] wrote: I meant frequency, sorry Strength is a term Pei used for frequency in some old sicsussions... Another correction: strength is never used in any NARS publication. It was used in some Webmind documents, though I guess it must be your idea, since I never like this term. ;-) The exact formulas used in NARS are basically heuristics derived based on endpoint conditions, so replicating those exact formulas is really not important IMO... the key would be replicating their qualitative behavior... I have to say that I don't like the term heuristics, neither, since it usually refers to quick-and-dirty replacement of the real thing. I fully agree with you that what really matters is the qualitative behavior, rather than the exact formula. 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/?member_id=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
On Fri, Oct 10, 2008 at 6:01 PM, Pei Wang [EMAIL PROTECTED] wrote: On Fri, Oct 10, 2008 at 5:52 PM, Ben Goertzel [EMAIL PROTECTED] wrote: I meant frequency, sorry Strength is a term Pei used for frequency in some old sicsussions... Another correction: strength is never used in any NARS publication. It was used in some Webmind documents, though I guess it must be your idea, since I never like this term. ;-) As I recall, the use of the term (in discussions rather than publications) was your idea, *but* the context in which it was suggested was as follows. We wanted a term for a variable in the Webmind Java code that would be applicable to both NARS and PLN truth values, and would be burdened as little as possible with specific theoretical interpretation. So you suggested strength. I'm not sure why we didn't just use frequency instead. I remember you did not want to call it probability. (This was, unbelievably, 10 years ago, so I don't want to bet my right arm on the details of my recollection ... but that's how I remember it...) The exact formulas used in NARS are basically heuristics derived based on endpoint conditions, so replicating those exact formulas is really not important IMO... the key would be replicating their qualitative behavior... I have to say that I don't like the term heuristics, neither, since it usually refers to quick-and-dirty replacement of the real thing. I didn't mean anything negative via the word heuristic ... and you didn't suggest an alternative word ;-) 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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
Ben, Maybe your memory is correct --- we use strength in Webmind to keep some distance from NARS. Anyway, I don't like that term because it can be easily interpreted in several ways, while the reason I don't like probability is just the opposite --- it has a widely accepted interpretation, which is hard to bend to mean what I want the term to mean. Pei On Fri, Oct 10, 2008 at 6:58 PM, Ben Goertzel [EMAIL PROTECTED] wrote: On Fri, Oct 10, 2008 at 6:01 PM, Pei Wang [EMAIL PROTECTED] wrote: On Fri, Oct 10, 2008 at 5:52 PM, Ben Goertzel [EMAIL PROTECTED] wrote: I meant frequency, sorry Strength is a term Pei used for frequency in some old sicsussions... Another correction: strength is never used in any NARS publication. It was used in some Webmind documents, though I guess it must be your idea, since I never like this term. ;-) As I recall, the use of the term (in discussions rather than publications) was your idea, *but* the context in which it was suggested was as follows. We wanted a term for a variable in the Webmind Java code that would be applicable to both NARS and PLN truth values, and would be burdened as little as possible with specific theoretical interpretation. So you suggested strength. I'm not sure why we didn't just use frequency instead. I remember you did not want to call it probability. (This was, unbelievably, 10 years ago, so I don't want to bet my right arm on the details of my recollection ... but that's how I remember it...) The exact formulas used in NARS are basically heuristics derived based on endpoint conditions, so replicating those exact formulas is really not important IMO... the key would be replicating their qualitative behavior... I have to say that I don't like the term heuristics, neither, since it usually refers to quick-and-dirty replacement of the real thing. I didn't mean anything negative via the word heuristic ... and you didn't suggest an alternative word ;-) ben 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/?member_id=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
Pei, I finally took a moment to actually read your email... 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? According to Bayes rule, P(bird | swimmer) P(swimmer) = P(swimmer | bird) P(bird) So, in PLN, evidence for P(bird | swimmer) will also count as evidence for P(swimmer | bird), though potentially with a different weighting attached to each piece of evidence If P(bird) = P(swimmer) is assumed, then each piece of evidence for each of the two conditional probabilities, will count for the other one symmetrically. The intuition here is the standard Bayesian one. Suppose you know there are 1 things in the universe, and 1000 swimmers. Then if you find out that swallows are not swimmers ... then, unless you think there are zero swallows, this does affect P(bird | swimmer). For instance, suppose you think there are 10 swallows and 100 birds. Then, if you know for sure that swallows are not swimmers, and you have no other info but the above, your estimate of P(bird|swimmer) should decrease... because of the 1000 swimmers, you now know there are only 990 that might be birds ... whereas before you thought there were 1000 that might be birds. And the same sort of reasoning holds for **any** probability distribution you place on the number of things in the universe, the number of swimmers, the number of birds, the number of swallows. It doesn't matter what assumption you make, whether you look at n'th order pdf's or whatever ... the same reasoning works... From what I understand, your philosophical view is that it's somehow wrong for a mind to make some assumption about the pdf underlying the world around it? Is that correct? If so I don't agree with this... I think this kind of assumption is just part of the inductive bias with which a mind approaches the world. The human mind may well have particular pdf's for stuff like birds and trees wired into it, as we evolved to deal with these things. But that's not really the point. The inductive bias may be much more abstract -- ultimately, it can just be an occam bias that biases the mind to prior distributions (over the space of procedures for generating prior distributions for handling specific cases) that are simplest according to some wired-in simplicity measure So again we get back to basic differences in philosophy... -- Ben G --- 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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
Ben, I see your position. Let's go back to the example. If the only relevant domain knowledge PLN has is Swallows are birds and Swallows are NOT swimmers, will the system assigns the same lower-than-default probability to Birds are swimmers and Swimmers are birds? Again, I only need a qualitative answer. Pei On Fri, Oct 10, 2008 at 7:24 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Pei, I finally took a moment to actually read your email... 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? According to Bayes rule, P(bird | swimmer) P(swimmer) = P(swimmer | bird) P(bird) So, in PLN, evidence for P(bird | swimmer) will also count as evidence for P(swimmer | bird), though potentially with a different weighting attached to each piece of evidence If P(bird) = P(swimmer) is assumed, then each piece of evidence for each of the two conditional probabilities, will count for the other one symmetrically. The intuition here is the standard Bayesian one. Suppose you know there are 1 things in the universe, and 1000 swimmers. Then if you find out that swallows are not swimmers ... then, unless you think there are zero swallows, this does affect P(bird | swimmer). For instance, suppose you think there are 10 swallows and 100 birds. Then, if you know for sure that swallows are not swimmers, and you have no other info but the above, your estimate of P(bird|swimmer) should decrease... because of the 1000 swimmers, you now know there are only 990 that might be birds ... whereas before you thought there were 1000 that might be birds. And the same sort of reasoning holds for **any** probability distribution you place on the number of things in the universe, the number of swimmers, the number of birds, the number of swallows. It doesn't matter what assumption you make, whether you look at n'th order pdf's or whatever ... the same reasoning works... From what I understand, your philosophical view is that it's somehow wrong for a mind to make some assumption about the pdf underlying the world around it? Is that correct? If so I don't agree with this... I think this kind of assumption is just part of the inductive bias with which a mind approaches the world. The human mind may well have particular pdf's for stuff like birds and trees wired into it, as we evolved to deal with these things. But that's not really the point. The inductive bias may be much more abstract -- ultimately, it can just be an occam bias that biases the mind to prior distributions (over the space of procedures for generating prior distributions for handling specific cases) that are simplest according to some wired-in simplicity measure So again we get back to basic differences in philosophy... -- Ben G 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/?member_id=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
Yah, according to Bayes rule if one assumes P(bird) = P(swimmer) this would be the case... (Of course, this kind of example is cognitively misleading, because if the only knowledge the system has is Swallows are birds and Swallows are NOT swimmers then it doesn't really know that the terms involved are swallows, birds, swimmers etc. ... then in that case they're just almost-meaningless tokens to the system, right?) On Fri, Oct 10, 2008 at 7:34 PM, Pei Wang [EMAIL PROTECTED] wrote: Ben, I see your position. Let's go back to the example. If the only relevant domain knowledge PLN has is Swallows are birds and Swallows are NOT swimmers, will the system assigns the same lower-than-default probability to Birds are swimmers and Swimmers are birds? Again, I only need a qualitative answer. Pei On Fri, Oct 10, 2008 at 7:24 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Pei, I finally took a moment to actually read your email... 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? According to Bayes rule, P(bird | swimmer) P(swimmer) = P(swimmer | bird) P(bird) So, in PLN, evidence for P(bird | swimmer) will also count as evidence for P(swimmer | bird), though potentially with a different weighting attached to each piece of evidence If P(bird) = P(swimmer) is assumed, then each piece of evidence for each of the two conditional probabilities, will count for the other one symmetrically. The intuition here is the standard Bayesian one. Suppose you know there are 1 things in the universe, and 1000 swimmers. Then if you find out that swallows are not swimmers ... then, unless you think there are zero swallows, this does affect P(bird | swimmer). For instance, suppose you think there are 10 swallows and 100 birds. Then, if you know for sure that swallows are not swimmers, and you have no other info but the above, your estimate of P(bird|swimmer) should decrease... because of the 1000 swimmers, you now know there are only 990 that might be birds ... whereas before you thought there were 1000 that might be birds. And the same sort of reasoning holds for **any** probability distribution you place on the number of things in the universe, the number of swimmers, the number of birds, the number of swallows. It doesn't matter what assumption you make, whether you look at n'th order pdf's or whatever ... the same reasoning works... From what I understand, your philosophical view is that it's somehow wrong for a mind to make some assumption about the pdf underlying the world around it? Is that correct? If so I don't agree with this... I think this kind of assumption is just part of the inductive bias with which a mind approaches the world. The human mind may well have particular pdf's for stuff like birds and trees wired into it, as we evolved to deal with these things. But that's not really the point. The inductive bias may be much more abstract -- ultimately, it can just be an occam bias that biases the mind to prior distributions (over the space of procedures for generating prior distributions for handling specific cases) that are simplest according to some wired-in simplicity measure So again we get back to basic differences in philosophy... -- Ben G 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 -- 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: 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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
On Fri, Oct 10, 2008 at 8:03 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Yah, according to Bayes rule if one assumes P(bird) = P(swimmer) this would be the case... (Of course, this kind of example is cognitively misleading, because if the only knowledge the system has is Swallows are birds and Swallows are NOT swimmers then it doesn't really know that the terms involved are swallows, birds, swimmers etc. ... then in that case they're just almost-meaningless tokens to the system, right?) Well, it depends on the semantics. According to model-theoretic semantics, if a term has no reference, it has no meaning. According to experience-grounded semantics, every term in experience have meaning --- by the role it plays. Further questions: (1) Don't you intuitively feel that the evidence provided by non-swimming birds says more about Birds are swimmers than Swimmers are birds? (2) If your answer for (1) is yes, then think about Adults are alcohol-drinkers and Alcohol-drinkers are adults --- do they have the same set of counter examples, intuitively speaking? (3) According to your previous explanation, will PLN also take a red apple as negative evidence for Birds are swimmers and Swimmers are birds, because it reduces the candidate pool by one? Of course, the probability adjustment may be very small, but qualitatively, isn't it the same as a non-swimming bird? If not, then what the system will do about it? Pei On Fri, Oct 10, 2008 at 7:34 PM, Pei Wang [EMAIL PROTECTED] wrote: Ben, I see your position. Let's go back to the example. If the only relevant domain knowledge PLN has is Swallows are birds and Swallows are NOT swimmers, will the system assigns the same lower-than-default probability to Birds are swimmers and Swimmers are birds? Again, I only need a qualitative answer. Pei On Fri, Oct 10, 2008 at 7:24 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Pei, I finally took a moment to actually read your email... 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? According to Bayes rule, P(bird | swimmer) P(swimmer) = P(swimmer | bird) P(bird) So, in PLN, evidence for P(bird | swimmer) will also count as evidence for P(swimmer | bird), though potentially with a different weighting attached to each piece of evidence If P(bird) = P(swimmer) is assumed, then each piece of evidence for each of the two conditional probabilities, will count for the other one symmetrically. The intuition here is the standard Bayesian one. Suppose you know there are 1 things in the universe, and 1000 swimmers. Then if you find out that swallows are not swimmers ... then, unless you think there are zero swallows, this does affect P(bird | swimmer). For instance, suppose you think there are 10 swallows and 100 birds. Then, if you know for sure that swallows are not swimmers, and you have no other info but the above, your estimate of P(bird|swimmer) should decrease... because of the 1000 swimmers, you now know there are only 990 that might be birds ... whereas before you thought there were 1000 that might be birds. And the same sort of reasoning holds for **any** probability distribution you place on the number of things in the universe, the number of swimmers, the number of birds, the number of swallows. It doesn't matter what assumption you make, whether you look at n'th order pdf's or whatever ... the same reasoning works... From what I understand, your philosophical view is that it's somehow wrong for a mind to make some assumption about the pdf underlying the world around it? Is that correct? If so I don't agree with this... I think this kind of assumption is just part of the inductive bias with which a mind approaches the world. The human mind may well have particular pdf's for stuff like birds and trees wired into it, as we evolved to deal with these things. But that's not really the point. The inductive bias may be much more abstract -- ultimately, it can just be an occam bias that biases the mind to prior distributions (over the space of procedures for generating prior distributions for handling specific cases) that are simplest according to some wired-in simplicity measure So again we get back to basic differences in philosophy... -- Ben G agi | Archives | Modify Your Subscription --- agi Archives:
Re: [agi] NARS and probability
On Fri, Oct 10, 2008 at 8:29 PM, Pei Wang [EMAIL PROTECTED] wrote: On Fri, Oct 10, 2008 at 8:03 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Yah, according to Bayes rule if one assumes P(bird) = P(swimmer) this would be the case... (Of course, this kind of example is cognitively misleading, because if the only knowledge the system has is Swallows are birds and Swallows are NOT swimmers then it doesn't really know that the terms involved are swallows, birds, swimmers etc. ... then in that case they're just almost-meaningless tokens to the system, right?) Well, it depends on the semantics. According to model-theoretic semantics, if a term has no reference, it has no meaning. According to experience-grounded semantics, every term in experience have meaning --- by the role it plays. That's why I said almost-meaningless ... if those are the only relationships known to the system, then the terms in those relationships play almost no roles, hence have almost no meanings... Further questions: (1) Don't you intuitively feel that the evidence provided by non-swimming birds says more about Birds are swimmers than Swimmers are birds? Yes, but only because I know intuitively that swimmers are more common in my everyday world than birds. That illustrates why it's confusing to use commonsense terms in artificially isolated inference examples. (I take that expository strategy in the PLN book too, but it can be misleading.) (2) If your answer for (1) is yes, then think about Adults are alcohol-drinkers and Alcohol-drinkers are adults --- do they have the same set of counter examples, intuitively speaking? Again, our intuitions for this are colored by the knowledge that there are more adults than alcohol-drinkers. Consider high school, which has 4 years: freshman, sophomore, junior, senior. Then think about Juniors seniors are women and women are juniors seniors It seems quite intuitive to me that, in this case, the same pieces of evidence support the truth values of these two hypotheses. This is because the term probabilities of juniors and seniors and women are intuitively known to be about equal. (3) According to your previous explanation, will PLN also take a red apple as negative evidence for Birds are swimmers and Swimmers are birds, because it reduces the candidate pool by one? Of course, the probability adjustment may be very small, but qualitatively, isn't it the same as a non-swimming bird? If not, then what the system will do about it? Yes, in principle, PLN will behave in Hempel's confirmation paradox in a similar way to other Bayesian systems. I do find this counterintuitive, personally, and I spent a while trying to work around it ... but finally I decided that my intuition is the faulty thing. As you note, it's a very small probability adjustment in these cases, so it's not surprising if human intuition is not tuned to make such small probability adjustments in a correct or useful way... -- 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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
On Fri, Oct 10, 2008 at 4:24 PM, Ben Goertzel [EMAIL PROTECTED] wrote:
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?
Let's see... let's call the function we're looking for L(f,w). To
satisfy NARS revision it must have the property L(f1,w1)*L(f2,w2)=L{
(w1*f1+w2*f2)/(w1+w2) , w1+w2 }. Taking f1=f2 and w1=w2, we have:
L(f,w)^2=L{ (2*w*f)/(2*w) , 2*w}
L(f,w)^2=L{ f, 2*w}
That establishes that the function is exponential in w, but that's a
far cry from proving the uniqueness of the formula I gave. I should
not have asserted so boldly...
--Abram
---
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=8660244id_secret=114414975-3c8e69
Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
This seems loosely related to the ideas in 5.10.6 of the PLN book, Truth
Value Arithmetic ...
ben
On Fri, Oct 10, 2008 at 9:04 PM, Abram Demski [EMAIL PROTECTED] wrote:
On Fri, Oct 10, 2008 at 4:24 PM, Ben Goertzel [EMAIL PROTECTED] wrote:
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?
Let's see... let's call the function we're looking for L(f,w). To
satisfy NARS revision it must have the property L(f1,w1)*L(f2,w2)=L{
(w1*f1+w2*f2)/(w1+w2) , w1+w2 }. Taking f1=f2 and w1=w2, we have:
L(f,w)^2=L{ (2*w*f)/(2*w) , 2*w}
L(f,w)^2=L{ f, 2*w}
That establishes that the function is exponential in w, but that's a
far cry from proving the uniqueness of the formula I gave. I should
not have asserted so boldly...
--Abram
---
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: 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=8660244id_secret=114414975-3c8e69
Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
On Fri, Oct 10, 2008 at 8:56 PM, Ben Goertzel [EMAIL PROTECTED] wrote: [. . .] Yes, in principle, PLN will behave in Hempel's confirmation paradox in a similar way to other Bayesian systems. I do find this counterintuitive, personally, and I spent a while trying to work around it ... but finally I decided that my intuition is the faulty thing. As you note, it's a very small probability adjustment in these cases, so it's not surprising if human intuition is not tuned to make such small probability adjustments in a correct or useful way... Well, to take the extreme, suppose we had observe our first crow and seen that it was black, but later learn that it is in fact the only crow in existence. The probability adjustment is neither small nor counterintuitive! Anyway, perhaps I can try to shed some light on the broader exchange? My route has been to understand A is B as not P(A|B), but instead P(A is X | B is X) plus the extensional equivalent... under this light, the negative evidence presented by two statements B is C and A is not C reduces the frequency of A is B, but does not obviously have any bearing on B is A. (Perhaps it does have some indirect bearing, for example through some rule of inversion... but of course the system is not yet even well-defined, so I'll not speculate.) --- 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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
By the way, thanks for all the comments... I'll probably shift gears as you both suggest, if I choose to continue further. --Abram On Fri, Oct 10, 2008 at 10:02 PM, Abram Demski [EMAIL PROTECTED] wrote: On Fri, Oct 10, 2008 at 8:56 PM, Ben Goertzel [EMAIL PROTECTED] wrote: [. . .] Yes, in principle, PLN will behave in Hempel's confirmation paradox in a similar way to other Bayesian systems. I do find this counterintuitive, personally, and I spent a while trying to work around it ... but finally I decided that my intuition is the faulty thing. As you note, it's a very small probability adjustment in these cases, so it's not surprising if human intuition is not tuned to make such small probability adjustments in a correct or useful way... Well, to take the extreme, suppose we had observe our first crow and seen that it was black, but later learn that it is in fact the only crow in existence. The probability adjustment is neither small nor counterintuitive! Anyway, perhaps I can try to shed some light on the broader exchange? My route has been to understand A is B as not P(A|B), but instead P(A is X | B is X) plus the extensional equivalent... under this light, the negative evidence presented by two statements B is C and A is not C reduces the frequency of A is B, but does not obviously have any bearing on B is A. (Perhaps it does have some indirect bearing, for example through some rule of inversion... but of course the system is not yet even well-defined, so I'll not speculate.) --- 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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
Abram, Anyway, perhaps I can try to shed some light on the broader exchange? My route has been to understand A is B as not P(A|B), but instead P(A is X | B is X) plus the extensional equivalent... under this light, the negative evidence presented by two statements B is C and A is not C reduces the frequency of A is B, but does not obviously have any bearing on B is A. (Perhaps it does have some indirect bearing, for example through some rule of inversion... but of course the system is not yet even well-defined, so I'll not speculate.) The way we deal with intension in PLN is a little different.. We define a fuzzy set A_PAT associated with a term A, and then the degree of membership of W in A_PAT is of the form x*y where x is a term measuring the simplicity of W relative to A and y = [P(W | A) - P(W)]^+ (where []^+ denotes the positive part) We can then measure P( A_PAT | B_PAT) and so forth... -- 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=8660244id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
Re: [agi] NARS and probability
Pei, Ben G. and Abram, Oh, man, is this stuff GOOD! This is the real nitty-gritty of the AGI matter. How does your approach handle counter-evidence? How does your approach deal with insufficient evidence? (Those are rhetorical questions, by the way -- I don't want to influence the course of this thread, just want to let you know I dig it and, mostly, grok it as well). I love this stuff. You guys are brilliant. Actually, I think it would make a good publication: PLN vs. NARS -- The AGI Smack-down! A win-win contest. This is a rare treat for an old hacker like me. And, I hope, educational for all (including the participants)! Keep it coming, please! Cheers, Brad Pei Wang wrote: On Fri, Oct 10, 2008 at 8:03 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Yah, according to Bayes rule if one assumes P(bird) = P(swimmer) this would be the case... (Of course, this kind of example is cognitively misleading, because if the only knowledge the system has is Swallows are birds and Swallows are NOT swimmers then it doesn't really know that the terms involved are swallows, birds, swimmers etc. ... then in that case they're just almost-meaningless tokens to the system, right?) Well, it depends on the semantics. According to model-theoretic semantics, if a term has no reference, it has no meaning. According to experience-grounded semantics, every term in experience have meaning --- by the role it plays. Further questions: (1) Don't you intuitively feel that the evidence provided by non-swimming birds says more about Birds are swimmers than Swimmers are birds? (2) If your answer for (1) is yes, then think about Adults are alcohol-drinkers and Alcohol-drinkers are adults --- do they have the same set of counter examples, intuitively speaking? (3) According to your previous explanation, will PLN also take a red apple as negative evidence for Birds are swimmers and Swimmers are birds, because it reduces the candidate pool by one? Of course, the probability adjustment may be very small, but qualitatively, isn't it the same as a non-swimming bird? If not, then what the system will do about it? Pei On Fri, Oct 10, 2008 at 7:34 PM, Pei Wang [EMAIL PROTECTED] wrote: Ben, I see your position. Let's go back to the example. If the only relevant domain knowledge PLN has is Swallows are birds and Swallows are NOT swimmers, will the system assigns the same lower-than-default probability to Birds are swimmers and Swimmers are birds? Again, I only need a qualitative answer. Pei On Fri, Oct 10, 2008 at 7:24 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Pei, I finally took a moment to actually read your email... 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? According to Bayes rule, P(bird | swimmer) P(swimmer) = P(swimmer | bird) P(bird) So, in PLN, evidence for P(bird | swimmer) will also count as evidence for P(swimmer | bird), though potentially with a different weighting attached to each piece of evidence If P(bird) = P(swimmer) is assumed, then each piece of evidence for each of the two conditional probabilities, will count for the other one symmetrically. The intuition here is the standard Bayesian one. Suppose you know there are 1 things in the universe, and 1000 swimmers. Then if you find out that swallows are not swimmers ... then, unless you think there are zero swallows, this does affect P(bird | swimmer). For instance, suppose you think there are 10 swallows and 100 birds. Then, if you know for sure that swallows are not swimmers, and you have no other info but the above, your estimate of P(bird|swimmer) should decrease... because of the 1000 swimmers, you now know there are only 990 that might be birds ... whereas before you thought there were 1000 that might be birds. And the same sort of reasoning holds for **any** probability distribution you place on the number of things in the universe, the number of swimmers, the number of birds, the number of swallows. It doesn't matter what assumption you make, whether you look at n'th order pdf's or whatever ... the same reasoning works... From what I understand, your philosophical view is that it's somehow wrong for a mind to make some assumption about the pdf underlying the world around it? Is that correct? If so I don't agree with this... I think this kind of assumption is just part of the inductive bias with which a mind approaches the world. The human mind may well have particular pdf's for stuff like birds and trees wired into it, as we evolved to deal with these things. But that's not really
