Pei,
First, I agree that proving stuff like this is not the maximally
interesting aspect of AGI. Actually creating a thinking machine is a
lot more exciting, and that is what I'm devoting the bulk of my
attention to!!
However, the question of how much inconsistency is inevitable in an
AGI is an interesting one.
I agree with you that perfect consistency is not possible for a
finite-resources mind confronted with reasonably complex goals.
However, I also think that given a particular goal and particular
resource restrictions, by and large the smarter minds (the better
goal achievers) will be the more consistent ones (in the sense I've
defined). This seems a worthwhile conclusion, if true ... depending
on the conditions attached to the theorem once it's proved....
It implies that, in AGI design, it is worthwhile to focus on making
one's AGI consistent.
But, what's interesting is that achieving a high level of
**behavioral** logical consistency in the manner I've defined it, may
not necessarily imply having internal structures that are focused on
formal logic. It could be that the way to maximize behavioral
logical consistency given severe resource constraints, is actually
NOT to explicitly do logic at all. Or, more likely, it could be that
the way to do it is to mix explicit logic with other non-logical
mechanisms.
This is the reason why I have chosen a fairly complex definition of
consistency that has to do with what an observer could infer from the
system's behaviors, rather than a definition that assumes the system
is explicitly doing formal logic internally.
-- Ben
On Feb 3, 2007, at 8:47 PM, Pei Wang wrote:
On 2/3/07, Ben Goertzel <[EMAIL PROTECTED]> wrote:
My desire in this context is to show that, for agents that are
optimal or near-optimal at achieving the goal G under resource
restrictions R, the set of important implicit abstract expectations
associated with the agent (in goal-context G as assessed by an ideal
probabilistic observer) should come close to being consistent.
I believe your hypothesis is correct, and I agree that to prove it
will be taken as an academic achievement. However, personally I'm not
interested in it. Instead, my goal is to find a different sense of
"optimal" that is achievable by the agent even when it cannot maintain
consistent beliefs because of knowledge/resources restrictions.
I surely don't like inconsistency, but see it as inevitable in an AGI.
Pei
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