I got it from an internal source.
Pei
On Sun, Sep 28, 2008 at 8:24 PM, Brad Paulsen [EMAIL PROTECTED] wrote:
Pei,
Would you mind sharing the link (that is, if you found it on the Internet)?
Thanks,
Brad
Pei Wang wrote:
I found the paper.
As I guessed, their update operator is defined
Hmm... I didn't mean infinite evidence, only infinite time and space
with which to compute the consequences of evidence. But that is
interesting too.
The higher-order probabilities I'm talking about introducing do not
reflect inaccuracy at all. :)
This may seem odd, but it seems to me to follow
When working on your new proposal, remember that in NARS all
measurements must be based on what the system has --- limited evidence
and resources. I don't allow any objective probability that only
exists in a Platonic world or the infinite future.
Pei
On Sun, Sep 21, 2008 at 1:53 PM, Abram
--- On Sat, 9/20/08, Pei Wang [EMAIL PROTECTED] wrote:
Think about a concrete example: if from one source the
system gets
P(A--B) = 0.9, and P(P(A--B) = 0.9) = 0.5, while
from another source
P(A--B) = 0.2, and P(P(A--B) = 0.2) = 0.7, then
what will be the
conclusion when the two sources are
It has been mentioned several times on this list that NARS has no
proper probabilistic interpretation. But, I think I have found one
that works OK. Not perfectly. There are some differences, but the
similarity is striking (at least to me).
I imagine that what I have come up with is not too
Abram,
I think the best place to start, in exploring the relation between NARS
and probablity theory, is with Definition 3.7 in the paper
From Inheritance Relation to Non-Axiomatic
Logichttp://www.cogsci.indiana.edu/pub/wang.inheritance_nal.ps
[*International Journal of Approximate
Ben,
Thanks for the references. I do not have any particularly good reason
for trying to do this, but it is a fun exercise and I find myself
making the attempt every so often :).
I haven't read the PLN book yet (though I downloaded a copy, thanks!),
but at present I don't see why term
I haven't read the PLN book yet (though I downloaded a copy, thanks!),
but at present I don't see why term probabilities are needed... unless
inheritance relations A inh B are interpreted as conditional
probabilities A given B. I am not interpreting them that way-- I am
just treating
And the definition 3.7 that you mentioned *does* match up, perfectly,
when the {w+, w} truth-value is interpreted as a way of representing
the likelihood density function of the prob_inh. Easy! The challenge
is section 4.4 in the paper you reference: syllogisms. The way
evidence is spread
Well, one question is whether you want to be able to do inference like
A --B tv1
|-
B --A tv2
Doing that without term probabilities is pretty hard...
Not the way I set it up. A--B is not the conditional probability
P(B|A), but it *is* a conditional probability, so the normal Bayesian
On Sat, Sep 20, 2008 at 2:22 PM, Abram Demski [EMAIL PROTECTED] wrote:
It has been mentioned several times on this list that NARS has no
proper probabilistic interpretation. But, I think I have found one
that works OK. Not perfectly. There are some differences, but the
similarity is striking
Beside the problem you mentioned, there are other issues. Let me start
at the basic ones:
(1) In probability theory, an event E has a constant probability P(E)
(which can be unknown). Given the assumption of insufficient knowledge
and resources, in NARS P(A--B) would change over time, when
Thanks for the critique. Replies follow...
On Sat, Sep 20, 2008 at 8:20 PM, Pei Wang [EMAIL PROTECTED] wrote:
On Sat, Sep 20, 2008 at 2:22 PM, Abram Demski [EMAIL PROTECTED] wrote:
[...]
The key, therefore, is whether NARS can be FULLY treated as an
application of probability theory, by
(2) For the same reason, in NARS a statement might get different
probability attached, when derived from different evidence.
Probability theory does not have a general rule to handle
inconsistency within a probability distribution.
The same statement holds for PLN, right?
PLN handles
On Sat, Sep 20, 2008 at 9:09 PM, Abram Demski [EMAIL PROTECTED] wrote:
(1) In probability theory, an event E has a constant probability P(E)
(which can be unknown). Given the assumption of insufficient knowledge
and resources, in NARS P(A--B) would change over time, when more and
more
Think about a concrete example: if from one source the system gets
P(A--B) = 0.9, and P(P(A--B) = 0.9) = 0.5, while from another source
P(A--B) = 0.2, and P(P(A--B) = 0.2) = 0.7, then what will be the
conclusion when the two sources are considered together?
There are many approaches to
I didn't know this paper, but I do know approaches based on the
principle of maximum/optimum entropy. They usually requires much more
information (or assumptions) than what is given in the following
example.
I'd be interested to know what the solution they will suggest for such
a situation.
Pei
The approach in that paper doesn't require any special assumptions, and
could be applied to your example, but I don't have time to write up an
explanation of how to do the calculations ... you'll have to read the paper
yourself if you're curious ;-)
That approach is not implemented in PLN right
I found the paper.
As I guessed, their update operator is defined on the whole
probability distribution function, rather than on a single probability
value of an event. I don't think it is practical for AGI --- we cannot
afford the time to re-evaluate every belief on each piece of new
evidence.
You are right in what you say about (1). The truth is, my analysis is
meant to apply to NARS operating with unrestricted time and memory
resources (which of course is not the point of NARS!). So, the
question is whether NARS approaches a probability calculation as it is
given more time to use all
On Sat, Sep 20, 2008 at 11:02 PM, Abram Demski [EMAIL PROTECTED] wrote:
You are right in what you say about (1). The truth is, my analysis is
meant to apply to NARS operating with unrestricted time and memory
resources (which of course is not the point of NARS!). So, the
question is whether
On Sat, Sep 20, 2008 at 10:32 PM, Pei Wang [EMAIL PROTECTED] wrote:
I found the paper.
As I guessed, their update operator is defined on the whole
probability distribution function, rather than on a single probability
value of an event. I don't think it is practical for AGI --- we cannot
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