From: Ben Goertzel (ben@goertzel.org)
Date: Tue May 31 2005 - 06:14:20 MDT
> >As a side comment, I also of course reject Marc
> >Geddes' suggestion that
> >Bayesian inference and deduction are unrelated.
>
> I never suggested any such thing Ben. *Of course*
> Bayesian inference and deduction are related. What I
> was doubting was whether they could be *completely*
> integreted. Can deduction be completely integrated
> into the Bayesian framework, or is there something
> (however small) amiss?
Well, I don't really know what "the Bayesian framework" means....
Logical deduction is simply the process of deriving conclusions from axioms
via repeated application of the axioms to each other....
Thus, deductions can be made based on the axioms of probability theory (from
which Bayes theorem is one deduced conclusion), or based on the axioms of
probability theory appropriately combined with other axioms (such as the
axioms of predicate logic).
The appropriate combination of predicate logic with probability theory is a
tricky issue, which we've approached in Novamente via taking a "term logic"
approach to reformulating predicate logic, which seems to simplify the
matching-up with probability theory.
> Too many people seem to think that pattern recognition
> and prediction making is sufficient for general
> intelligence. It isn't. General intelligence
> consists of a prediction system AND a goal system.
This is true, but I'm not sure what it has to do with deduction.
Clearly, the mind must (explicitly or implicitly) make inferences of the
form
"Action X in context C is likely to help me achieve goal G"
Such inferences may be made based on (explicit or implicit) deduction, and
also via probabilistic induction based on historical observations (which is
where Bayes rule comes in).
> I keep pointing out that general intelligence consists
> of *two* integrated systems: a system for
> *evaluating*/*formulating goals* and a system for
> *making predictions* Everyone seems to have focused
> on the latter and overlooked the former.
>
> What effect will a complete solution for the goal
> system have on the solution for the prediction system?
> Don't assume that these two systems are independent.
Agreed, these systems are independent.
For instance, it is key that the system's initial supergoal(s) are
formulated in a way that is amenable to flexible goal-refinement by the
system's (implicit or explicit) reasoning systems. Otherwise the goals will
be useless in actually guiding the system's behavior.
> The interaction between induction and deduction is
> clearly the weak link in the Bayesian picture.
Again, I'm not really sure what you mean by "the Bayesian picture". I'm not
sure what Eliezer means by "the Bayesian way" either, so my confusion on
this issue is not restricted to understanding *you* ;-)
-- Ben
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