nonmonotonic updating?
YKY (Yan King Yin, 甄景贤)
I have a question about updating NARS confidence...
Suppose we first learned that birds can fly with NARS confidence 0.8:
bird(X) -> fly(X) c1=0.9
Then we learn that penguins cannot fly and so we need to *add* this rule:
penguin(X) -> ! fly(X) c2=0.7
where c2 is "by itself" 0.7 because it is supported by a certain
number of observations (of penguins not flying).
The problem is, for the new rules to function correctly, c2 should be
> c1 (otherwise the conclusion of the second rule will not override
the first one, right?)
So, does it mean that we need to artificially decrease c1, or increase
c2? Even if we do that, we cannot ensure that the change will not
incorrectly affect *other* nonmonotonic relations related to flying.
So it seems to be a difficult problem...
Thanks in advance! =)
YKY
Pei Wang
> Hi,
>
> I have a question about updating NARS confidence...
>
> Suppose we first learned that birds can fly with NARS confidence 0.8:
> bird(X) -> fly(X) c1=0.9
> Then we learn that penguins cannot fly and so we need to *add* this rule:
> penguin(X) -> ! fly(X) c2=0.7
> where c2 is "by itself" 0.7 because it is supported by a certain
> number of observations (of penguins not flying).
>
> The problem is, for the new rules to function correctly, c2 should be
>> c1 (otherwise the conclusion of the second rule will not override
> the first one, right?)
confidence wins.
> So, does it mean that we need to artificially decrease c1, or increase
> c2? Even if we do that, we cannot ensure that the change will not
> incorrectly affect *other* nonmonotonic relations related to flying.
> So it seems to be a difficult problem...
typical birds, which may let the second statement (NARS doesn't call
it a "rule") to become the winner.
Otherwise, why should the system to prefer a low confidence statement?
A detailed discussion is in
http://www.cis.temple.edu/~pwang/Publication/reference_classes.pdf
Pei
YKY (Yan King Yin, 甄景贤)
> Not necessarily. One way is to tell the system that penguins are not
> typical birds, which may let the second statement (NARS doesn't call
> it a "rule") to become the winner.
>
> Otherwise, why should the system to prefer a low confidence statement?
>
> A detailed discussion is in
> http://www.cis.temple.edu/~pwang/Publication/reference_classes.pdf
Thanks, I think that paper of yours has some very good ideas which
I've adopted, but I'm skeptical about the case when 2 factors are
correlated, and you said the result should be the one with higher
confidence. To me it seems that any mixture of the 2 factors would be
a reasonable guess...
I'll think more about this...
YKY
YKY (Yan King Yin, 甄景贤)
case #1. When 2 factors are *independent* then it seems always
reasonable to use the weighted mixing rule (as given by you). This
much seems uncontroversial. (Although actual data can deviate
arbitrarily from this statement's prediction).
case #2. When 1 factor subsumes the other factor (ie, a subset
relation) then it seems reasonable to let the more SPECIFIC class wins
(ie, specificity principle). But in this situation (your "white
collar male" vs "male" example) you chose the one with the higher
confidence -- this may be incorrect if the higher-confidence one is
LESS specific.
So I suspect that in this case, the specificity principle still holds
(perhaps should be adjusted by the confidence in some way, since you
said that the sample sizes do matter).
case #3. When 1 factor is CONTRARY to the other, for instance, F1
implies "not F2". In this case, it seems that the one with higher
confidence shall win. Your solution seems to have mixed #2 and #3.
To give an example of #3:
Ben is usually very punctual. He promised to pick up Joshua at the
airport at 11:00pm. So we can predict that he will be there:
punctual -> at airport
But, on the other hand, if I go with Ben on a taxi ride, and we have
an accident and I clearly see that Ben died, then he cannot be at the
airport at the promised time:
dead -> ! at airport
Since a person who is dead cannot be punctual:
dead -> ! punctual
This is the underlying reason why the #3 rule should apply. And the
result is that we should choose the one with higher confidence.
That's my analysis so far.... =)
YKY
Pei Wang
> From my own observations:
>
> case #1. When 2 factors are *independent* then it seems always
> reasonable to use the weighted mixing rule (as given by you). This
> much seems uncontroversial. (Although actual data can deviate
> arbitrarily from this statement's prediction).
> case #2. When 1 factor subsumes the other factor (ie, a subset
> relation) then it seems reasonable to let the more SPECIFIC class wins
> (ie, specificity principle).
principle" works only under certain assumptions.
This is where non-monotonic logic is wrong --- if there is very little
evidence about whether penguins fly, it does not always have a higher
priority over the belief that birds fly.
> But in this situation (your "white
> collar male" vs "male" example) you chose the one with the higher
> confidence -- this may be incorrect if the higher-confidence one is
> LESS specific.
> So I suspect that in this case, the specificity principle still holds
> (perhaps should be adjusted by the confidence in some way, since you
> said that the sample sizes do matter).
of the several factors, not always the dominating one.
> case #3. When 1 factor is CONTRARY to the other, for instance, F1
> implies "not F2". In this case, it seems that the one with higher
> confidence shall win. Your solution seems to have mixed #2 and #3.
> To give an example of #3:
>
> Ben is usually very punctual. He promised to pick up Joshua at the
> airport at 11:00pm. So we can predict that he will be there:
> punctual -> at airport
> But, on the other hand, if I go with Ben on a taxi ride, and we have
> an accident and I clearly see that Ben died, then he cannot be at the
> airport at the promised time:
> dead -> ! at airport
> Since a person who is dead cannot be punctual:
> dead -> ! punctual
> This is the underlying reason why the #3 rule should apply. And the
> result is that we should choose the one with higher confidence.
Pei
YKY (Yan King Yin, 甄景贤)
> I thought I made it clear in that paper that the "specificity
> principle" works only under certain assumptions.
>
> This is where non-monotonic logic is wrong --- if there is very little
> evidence about whether penguins fly, it does not always have a higher
> priority over the belief that birds fly.
I think the analysis in your paper is correct concerning the case (ie
#2) where there is a *subset* relation between the 2 factors, F1 and
F2. In this case, your solution is an improvement over the
specificity principle, the latter can fail in some small-n cases.
This is a good thing.
But I have identified another case (#3) where there is a causal
relation between F1 and F2 (or a common cause affecting both). In
this case, the "causing factor" always wins. For example, if Ben is
dead THEN he cannot be punctual; ie, his death causes him to be
unable to be punctual. So the causing factor will win regardless of
its confidence.
To recap, there are 3 cases:
#1: independent -- weighted sum
#2: subset -- higher-confidence wins
#3: causal -- causing factor wins
YKY
Joe Geldart
How do you know that X causes Y? How do you know that X has actually
occurred?
Regards,
Joe Geldart <jgel...@gmail.com>
http://www.dur.ac.uk/j.r.c.geldart/
Pei Wang
Again, "confidence" is not another factor (like specificity, sample
size, causality, etc.), but a common measurement of them. A strong
causal relation surely favors a conclusion, though a weak one may not.
Pei
YKY (Yan King Yin, 甄景贤)
>> But I have identified another case (#3) where there is a causal
>> relation between F1 and F2 (or a common cause affecting both). In
>> this case, the "causing factor" always wins. For example, if Ben is
>> dead THEN he cannot be punctual; ie, his death causes him to be
>> unable to be punctual. So the causing factor will win regardless of
>> its confidence.
>>
>> To recap, there are 3 cases:
>> #1: independent -- weighted sum
>> #2: subset -- higher-confidence wins
>> #3: causal -- causing factor wins
>
> How do you know that X causes Y? How do you know that X has actually
> occurred?
Sorry that my reply is more than 3 months late...!
A discussion of causality and how causal relations can be learned
inductively, is discussed in Judea Pearl's book "Causality". He has
an algorithm called ID* (if I remember correctly) that learns
causality. Recently this topic is developed in even more depth in Jon
Williamson's book, "Bayesian Nets and Causality".
There is as yet no consensus of what causality really is, but it seems
to be some high-level learned concept built on top of the logic, and
thus is not part of the logic.
Nevertheless, I think causality should be used in some belief update
situations, as illustrated by my example: Ben is usually punctual,
but if Ben is dead, his death *causes* him to be immobilized, and thus
he cannot be punctual.
It seems NARS should somehow incorporate causality into its
thinking... otherwise it would be flawed as an AGI...
YKY
Pei Wang
>
> It seems NARS should somehow incorporate causality into its
> thinking... otherwise it would be flawed as an AGI...
>
Already incorporated. Read Section 5.3.3 to see my opinion on this
topic (very different from Pearl's), and see
http://code.google.com/p/open-nars/wiki/ProceduralLearning for how
NARS learns the "causal relations" as in the preconditions and
consequences of an operation.
Pei