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.

> 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.



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