Formal definitions of intelligence, mind, self-modifiability

From: Ben Goertzel (ben@goertzel.org)
Date: Tue Mar 05 2002 - 23:15:46 MST

Hi all,

I mentioned a week ago that I had an idea for how to mathematically
formalize the different levels of self-modifiability that I had informally
presented.

Well, I haven't had time to do a totally rigorous mathematical treatment,
but I don't know when I'll have that kind of time to devote to something
that isn't Novamente engineering.

However, I have written up a semi-mathematical paper, the last section of
which gives a formalization of the self-modifiability levels. The previous
parts of the paper give formal definitions for things like "intelligence"
and "mind", some of which are needed for the self-modifiability definitions.

I also describe herein one "AI proof of principle" -- a design for an
insanely inefficient AI system that would be intelligent if it could be run
on a powerful enough computer. This idea is close to the theory of
Solomonoff Induction.

Please note, this little article is NOT directly related to the Novamente AI
system. It gives some formalizations that have been useful to me in
thinking about Novamente, but only in a very general sense. The "AI proof
of principle" described in the article has very little to do with Novamente,
which is tremendously more complex and more efficient (it's a real AI design
not a proof of principle).

As an aside, however: The formal definition of pattern given in the paper
*is* used in Novamente in a couple of places (the system tries to
evolve/infer schema and compound relationships that are "patterns" in the
formal sense given here).

Constructive feedback will be much appreciated.

I know the definitions given here are not at all practical to compute. They
are also sufficiently complex that proving anything nontrivial about them
would be a huge pain. So I think their main role is conceptual.

The paper is at

www.goertzel.org/dynapsyc/2002/FormalTheoryIntelligence.htm

I tried to proofread all the equations, but I tend to be poor at this, so
it's possible there are a couple notational slip-ups in here..

-- Ben

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