Re: convergence question

On 23 Jun 2006 04:01:47 -0700, makc.the.great@xxxxxxxxx wrote:

in P(t1), Q(t2) => R(t0), what's t0(t1, t2)?

Time.

You have P at t1, rather than P for all times. If t0 is the time now, then
your trust in P(t1) would be reverse proportional to t0-t1. If all facts
are devaluating with the same speed (that's another assumption, which might
be wrong), then you could create a kind of "temporal" measure of truth by
adding a time dimension to the truth values. For example, by using
(possibility, necessity time) instead of just (possibility, necessity). You
could then try to define lattice operations on such composite objects.

Especially, composition operations, like consensus (+) and gullibility (*).
Normally, consensus: true + false = uncertain, gullibility: true * false =
contradictory. But with the time aspect it could become

(true, now) + (false, year ago) = (almost true and slightly uncertain about
false, now)

(true, now) * (false, year ago) = (almost true and slightly reserved to
false, now)

I would assume that false and true change to uncertain with the time. In
terms of possibility it would mean that pos(P) ---> 1. So nec(P) ---> 0.

Dmitry A. Kazakov wrote:
On 21 Jun 2006 06:46:35 -0700, makc.the.great@xxxxxxxxx wrote:

let's say we have some reasoning program that constantly draws out some
conclusions based on results of its own previous conclusions. what
choise of functions will guarantee that resulting values will not "flat
out" to 0 or "squeeze up" to 1 just because they have been put through
too many iterations?

This is an interesting problem. I think that there is no such function in
the following sense. The model is inadequate. The assumption that the facts
which the conclusions are inferred from are not stable. So each new
iteration can potentially add contradictions to the knowledge base.
Inference can handle contradictions either by consensus or gullibility
operations, but in the end, it will anyway decline to either "dunno" or
"rubbish". I think that the only way out is to change the model, i.e. to
give a time aspect to the knowledge. So that the inference would deal with
P(t1), Q(t2) => R(t0) rather than just P, Q => R. The model should then
describe how, say, delta t=t0-t1 influences confidence in P. The goal would
be to let more fresh facts to override old ones if they contradict each
other, or to approve each other otherwise.

--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
.

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