Ben,
If we don't work out the correspondence (even approximately) between
FOL and term logic, this conversation would not be very fruitful. I
don't even know what you're doing with PLN. I suggest we try to work
it out here step by step. If your approach really makes sense to me,
you will gain another helper =) Also, this will be good for your
project's documentation.
I have some examples:
Eng: "Some philosophers are wise"
TL: +Philosopher+Wise
FOL: philosopher(X) -> wise(X)
Eng: "Romeo loves Juliet"
TL: +-Romeo* + (Loves +-Juliet*)
FOL: loves(romeo, juliet)
Eng: "Women often have long hair"
TL: ?
FOL: woman(X) -> long_hair(X)
I know your term logic is slightly different from Fred Sommers'. Can
you fill in the TL parts and also attach indefinite probabilities?
On 6/3/08, Ben Goertzel <[EMAIL PROTECTED]> wrote:
> If you attach indefinite probabilities to FOL propositions, and create
> indefinite probability formulas corresponding to standard FOL rules,
> you will have a subset of PLN
>
> But you'll have a hard time applying Bayes rule to FOL propositions
> without being willing to assign probabilities to terms ... and you'll
> have a hard time applying it to FOL variable expressions without doing
> something that equates to assigning probabilities to propositions w.
> unbound variables ... and like I said, I haven't seen any other
> adequate way of propagating pdf's through quantifiers than the one we
> use in PLN, though Halpern's book describes a lot of inadequate ways
> ;-)
Re "assigning probabilties to terms..."
"Term" in term logic is completely different from "term" in FOL. I
guess terms in term logic roughly correspond to predicates or
propositions in FOL. Terms in FOL seem to have no counterpart in term
logic......
Anyway there should be no confusion here. Propositions are the ONLY
things that can have truth values. This applies to term logic as well
(I just refreshed my memory of TL). When truth values go from { 0, 1
} to [ 0, 1 ], we get single-value probabilistic logic. All this has
a very solid and rigorous foundation, based on so-called model theory.
YKY
-------------------------------------------
agi
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