On Fri, May 25, 2007 at 04:00:40PM +0200, Bruno Marchal wrote:
> Le 25-mai-07, à 04:12, Russell Standish a écrit :
> > I don't think anyone yet has managed a self aware formal system,
> I would say all my work is about that. You can interpret Godel's 
> theorem, or more exactly the fact that machine can prove their own 
> provability logic, and even guess correctly the true but non provable 
> part, as a general statement of self-awareness. Sometimes, 
> self-awareness is defined more precisely by the "4" modal formula: Bp 
> -> BBp. This is a theorem for PA, but not for LRA.
> When LRA proves p, then soon or later, if not already, LRA will prove 
> Bp (that is LRA will prove that she prove p). So Bp -> BBp is true for 
> LRA, but only PA can prove such a proposition on itself.

Absolutely your work is all about that. And constructing a formal
self-aware system will just as likely come from an approach like
yours as anything else. My only statement was that it hasn't been done
already, and certainly I wasn't aware of you claiming self-awareness
already. Admittedly, I miss some of the conclusions you do make, such as the
Theatetic axioms encapsulating knowledge, and also Kripke frames being
the phenomena of time (I can see that they could be a model of time,
but that is another thing entirely).

> > although self-reproducing systems have been known since the 1950s, and
> > are popularly encountered in the form of computer viruses.
> The principle is really the same. That is what I show in my paper 
> "amoeba, planaria, and dreaming machine". self-reproduction and 
> self-awareness are a consequence of the closure of the set of partial 
> computable function for the daigonalization procedure.

Incidently, I read your Elsevier paper the other day. It has inspired
me to take a look at combinators for artificial life applications. I
discovered that Pietro Speroni di Fenizio has spent a PhD looking at
this. He was a student of Walter Banzhaf and Peter Dittrich - I met
Walter shortly before I caught up with you in Brussels in 2003. Peter
I met in the Lausanne ECAL in 1999. Are you aware of any of this work?
AFACT, he never achieved self-reproduction, which is a precursor to
evolution, but alas he didn't publish any of his code.

> bruno
> http://iridia.ulb.ac.be/~marchal/

A/Prof Russell Standish                  Phone 0425 253119 (mobile)
UNSW SYDNEY 2052                         [EMAIL PROTECTED]
Australia                                http://www.hpcoders.com.au

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