It looks like the {A} operator would have a large enough influence to
be useful. The contribution of {A} to the likelihood of A=>B would be
the probability of {A} given A=>B. {A} is the average of the two
distributions p(A=>y) and p(y=>A) for random y; A=>B is the average of
the two distributions p(A=>y | B=>y) and p(y=>B | y=>A). So, there is
significant influence, which can be calculated with the even prior
(though I lack the patience at the moment to translate that influence
to <f,w> arithmetic).
--Abram Demski
On Mon, Sep 22, 2008 at 8:25 AM, Abram Demski <[EMAIL PROTECTED]> wrote:
> It would be possible to get what you want in the setting, by allowing
> some probabilistic manipulations not done in NARS. The node
> probability you want in this case could be simulated by talking about
> the probability distribution of sentences of the form "X is the author
> of a book". We can give this a low prior probability. Since the system
> manipulates likelihoods, it won't notice; but if we manipulate
> probabilities, it would.
>
> Perhaps a more satisfying answer would be to introduce a new operator
> into the system, {A}, that simulates the node probability; or more
> specifically, it represents the average truth-value distribution of
> statements that have A on one side or the other. So, it has a 'par'
> value just like inheritance statements do. If there was evidence for a
> low par, there would be an effect in the direction you want. (It might
> be way too small, though?)
>
> --Abram
>
> On Sun, Sep 21, 2008 at 10:46 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote:
>>
>>
>> On Sun, Sep 21, 2008 at 10:43 PM, Abram Demski <[EMAIL PROTECTED]>
>> wrote:
>>>
>>> The calculation in which I sum up a bunch of pairs is equivalent to
>>> doing NARS induction + abduction with a final big revision at the end
>>> to combine all the accumulated evidence. But, like I said, I need to
>>> provide a more explicit justification of that calculation...
>>
>> As an example inference, consider
>>
>> Ben is an author of a book on AGI <tv1>
>> This dude is an author of a book on AGI <tv2>
>> |-
>> This dude is Ben <tv3>
>>
>> versus
>>
>> Ben is odd <tv1>
>> This dude is odd <tv2>
>> |-
>> This dude is Ben <tv4>
>>
>> (Here each of the English statements is a shorthand for a logical
>> relationship that in the AI systems in question is expressed in a formal
>> structure; and the notations like <tv1> indicate uncertain truth values
>> attached to logical relationships, In both NARS and PLN, uncertain truth
>> values have multiple components, including a "strength" value that denotes a
>> frequency, and other values denoting confidence measures. However, the
>> semantics of the strength values in NARS and PLN are not identical.)
>>
>> Doing these two inferences in NARS you will get
>>
>> tv3.strength = tv4.strength
>>
>> whereas in PLN you will not, you will get
>>
>> tv3.strength >> tv4.strength
>>
>> The difference between the two inference results in the PLN case results
>> from the fact that
>>
>> P(author of book on AGI) << P(odd)
>>
>> and the fact that PLN uses Bayes rule as part of its approach to these
>> inferences.
>>
>> So, the question is, in your probabilistic variant of NARS, do you get
>>
>> tv3.strength = tv4.strength
>>
>> in this case, and if so, why?
>>
>> thx
>> ben
>> ________________________________
>> agi | Archives | Modify Your Subscription
>
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agi
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