On 6/3/08, Ben Goertzel <[EMAIL PROTECTED]> wrote:
> 1) representing uncertainties in a way that leads to tractable, meaningful
> logical manipulations. Indefinite probabilities achieve this. I'm not saying
> they're the only way to achieve this, but I'll argue that single-number,
> Walley-interval, fuzzy, or full-pdf approaches are not adequate for various
> reasons.
First of all, the *tractability* of your algorithm depends on
heuristics that you design, which are separable from the underlying
probabilistic logic calculus. In your mind, these 2 things may be
mixed up.
Indefinite probabilities DO NOT imply faster inference.
Domain-specific heuristics do that.
Secondly, I have no problem at all, with using your indefinite
probability approach.
It's a laudable achievement what you've accomplished.
Thirdly, probabilistic logics -- of *any* flavor -- should
[approximately] subsume binary logic if they are sound. So there is
no reason why your logic is so different that it cannot be expressed
in FOL.
Fourthly, the approach that I'm more familiar with is interval
probability. I acknowledge that you have gone further in this
direction, and that's a good thing.
> 2) using inference rules that lead to relatively high-confidence uncertainty
> propagation. For instance term logic deduction is better for uncertain
> inference than modus ponens deduction, as detailed analysis reveals
I believe term logic is translatable to FOL -- Fred Sommers mentioned
that in his book.
> 3) propagating uncertainties meaningfully through abstract logical
> formulae involving nested quantifiers (we do this in a special way in PLN
> using third-order probabilities; I have not seen any other conceptually
> satisfactory solution)
Again, that's well done.
But are you saying that the same cannot be achieved using FOL?
> 4) most critically perhaps, using uncertain truth values within inference
> control to help pare down the combinatorial explosion
Uncertain truth values DO NOT imply faster inference. In fact, they
slow down inference wrt binary logic.
If your inference algorithm is faster than resolution, and it's sound
(so it subsumes binary logic), then you have found a faster FOL
inference algorithm. But that's not true; what you're doing is
domain-specific heuristics.
> How these questions are answered matters a LOT, and my colleagues
> and I spent years working on this stuff. It's not a matter of converting
> between equivalent formalisms.
I think one can do
indefinite probability + FOL + domain-specific heuristics
just as you can do
indefinite probability + term logic + domain-specific heuristics
but it may cost an amount of effort that you're unwilling to pay.
This is a very sad situation...
YKY
-------------------------------------------
agi
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