Considering confidence values of formulas

[Ivan V.]

Just a short question relating to truth values, if anyone is interested in discussion:

Formulas in Atomspace have two fuzzy truth values associated: probability and confidence. Now, may confidence be described as probability of probability? If so, why not to call it second order probability? And, if so, may there exist a general higher order probability notion? That would be a truth notion that may recursively apply to [initial formula], to [[initial formula] with associated truth value], and so on, producing a pattern: [...[[[initial formula] with associated truth value] with associated truth value] ...].

Is this making any sense?

Recent research documents that dr. Goertzel published around here talk about specific distinctive interpretations of probability and confidence. Those are some nice correspondence fitting ideas, but taking the above under consideration, may there exist some general, recursive interpretation that makes use only of one kind of higher order of probability?

Kind regards, and hoping not to disturb too much,

ivan

[Ben Goertzel]

Yeah this was all dealt with quite a lot in the original PLN book from
2008 or whatever... PLN confidence values are interpreted in terms of
imprecise probabilities (cf Peter Walley) and indefinite probabilities
(our own invention), which are both concise ways of describing second
order probability distributions

You can have n'th order probabilities too, I even wrote a paper once
on infinite-order probabilities and their use to model the semantics
of uncertain self-referential statements ;)

ben

> --
> You received this message because you are subscribed to the Google Groups "opencog" group.
> To unsubscribe from this group and stop receiving emails from it, send an email to opencog+u...@googlegroups.com.
> To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CAB5%3Dj6XFkCtsBNZ1N3cWDidehFAN390-qfx%2BaY3KGxQmWAcpAQ%40mail.gmail.com.



--
Ben Goertzel, PhD
http://goertzel.org

“He not busy being born is busy dying" -- Bob Dylan

[Ivan V.]

Thank you for the answer. I assume that distincting between probability and confidence (taking into account only those two orders of probability) has some benefits.

Kind regards,

ivan

To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CACYTDBc6hAWVkxkQy6vawaWyt6Qf3axwSQhd_oavFC%3DsnYOLsg%40mail.gmail.com.

[Ben Goertzel]

The confidence values are key in the belief revision formulas ... if
you have two different estimates of the same probability value from
different sources and need to know how to weight them, the confidence
values give you good weighting factors...

> To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CAB5%3Dj6Vigj-EEK5sNFQPZAUfPDTwwOxYimcPwYYOiHtsgR12HQ%40mail.gmail.com.