I have browsed papers on Loebian embodiment, for example

Life, Mind, and Robots
The Ins and Outs of Embodied Cognition
Hybrid Neural Systems, 2000 - Springer
http://acs.ist.psu.edu/misc/dirk-files/Papers/EmbodiedCognition/Life,%20Mind%20and%20Robots_The%20Ins%20and%20Outs%20of%20Embodied%20Cognition%20.pdf

It happened that they talk not about the Loeb theorem but rather about the biologist Jacques Loeb.

Do you know why robotics people do not use the Löb theorem in practice?

Evgenii


On 20.08.2011 16:22 Bruno Marchal said the following:

On 19 Aug 2011, at 20:18, Evgenii Rudnyi wrote:

On 18.08.2011 16:24 Bruno Marchal said the following:

On 17 Aug 2011, at 20:07, meekerdb wrote:

On 8/17/2011 10:36 AM, Evgenii Rudnyi wrote:
On 16.08.2011 20:47 meekerdb said the following:
On 8/16/2011 11:03 AM, Evgenii Rudnyi wrote:
Yes, this is why in my first post, I said consider
God's Turing machine (free from our limitations). Then
it is obvious that with the appropriate tape, a
physical system can be approximated to any desired
level of accuracy so long as it is predictable. Colin
said such models of physics or chemistry are
impossible, so I hope he elaborates on what makes these
systems unpredictable.

I have to repeat that the current simulation technology
just does not scale. With it even God will not help. The
only way that I could imagine is that God's Turing
machine is based on completely different simulation
technology (this however means that our current knowledge
of physical laws and/or numerics is wrong).

Scale doesn't matter at the level of theoretical
possibility. Bruno's UD is the most inefficient possible
way to compute this universe - but he only cares that it's
possible. All universal Turing machines are equivalent so
it doesn't matter what God's is based on. Maybe you just
mean the world is not computable in the sense that it is
nomologically impossible to compute it faster than just
letting it happen.

I understand what you say. On the other hand however, it is
still good to look at the current level of simulation
technology, especially when people make predictions on what
happens in the future (in other messages the possibility of
brain simulation and talk about physico-chemical processes).

From such a viewpoint, even a level of one-cell simulation is
not reachable in the foreseeable future. Hence, in my view,
after the discussion about theoretical limits it would be
good to look at the reality. It might probably help to think
the assumptions over.

I would say that it is small practical things that force us
to reconsider our conceptions.

Evgenii

I agree with that sentiment. That's why I often try to think
of consciousness in terms of what it would mean to provide a
Mars Rover with consciousness. According to Bruno the ones
we've sent to Mars were already conscious, since their
computers were capable of Lobian logic.

I don't remember having said this. I even doubt that Mars Rover
is universal, although that might be serendipitously possible
(universality is very cheap), in which case it would be as
conscious as a human being under a high dose of salvia (a form of
consciousness quite disconnected from terrestrial realities). But
it is very probable that it is not Löbian. I don't see why they
would have given the induction axioms to Mars Rover (the
induction axioms is what gives the Löbian self-referential
power).


But clearly they did not have human-like consciousness (or
intelligence). I think it much more likely that we could make
a Mars Rover with consciousness and intelligence somewhat
similar to humans using von Neumann computers or artificial
neural nets than by trying to actually simulate a brain.

I think consciousness might be attributed to the virgin (non
programmed) universal machine, but such consciousness is really
the basic consciousness of everyone, before the contingent
differentiation on the histories. LUMs, on the contrary, have a
self-consciousness, even when basically virgin: they makes a
distinction between them and some possible independent or
transcendental reality.

No doubt the truth is a bit far more subtle, if only because
there are intermediate stage between UMs and LUMs.

When I search on Google Scholar

lobian robot

then there is only one hit (I guess that this is Bruno's thesis).
When I search however

loebian robot

there are some more hits with for example Loebian embodiment. I do
not not know what it means but in my view it would be interesting
to build a robot with a Loebian logic and research it. In my view,
it is not enough to state that there is already some consciousness
there. It would be rather necessary to research on what it actually
means. Say it has visual consciousness experience, it feels pain or
something else.

It would be interesting to see what people do in this area. For
example, "Loebian embodiment" sounds interesting and it would be
nice to find some review about it.

"Löbian machine" is an idiosyncrasy that I use as a shorter
expression for what the logicians usually describes by "a
sufficiently rich theory". I have not yet decide on how to exactly
define them.

I hesitate between a very weak sense, like any belief system
(machine, theory) close for the Löb rule (which says that you can
deduce p from Bp -> p). A stronger sense is : any belief system
having the Löb's formula in it. So it contains the "formal Löb rule":
B(Bp -> p) -> Bp.

But my current favorite definition is: any universal machine which
can prove p -> Bp for p sigma_1 (or equivalent). This I paraphrase in
 layman's language by: any universal machine which knows that she is
 universal. Sigma_1 proposition are those having the shape ExP(x)
with P decidable. You can intuit that *you* can do, by testing P(0),
P(1), P(2), ... until you find a n such that P(n).

A theorem prover which can prove all true sigma_1 proposition is
provably equivalent with a universal machine, and all universal
machine can prove (modulo modification of the language) the true
sigma_1 propositions.

PA and ZF are Löbian machine in that last sense (which implies the
weaker senses). They are emulated in the human brain of those who
study them, although they are easy to implement on computers.

A long time ago I concluded that some theorem prover, written by
Chang, also by Boyer and Moore, are Löbian. When a child grasp notion
like "anniversary", "death", "forever", "potentially infinite", they
show Löbianity.

Are humans Löbian? Hard to say, because they have a non monotonical
layer (they can retrieve old beliefs), but it is clear they have a
Löbian machine (or entity) living inside. Fear of death, fear of the
 unknown and fear of the others are typically Löbian.

Another definition: a Löbian entity is an entity whose
3-self-referential beliefs obeys to the logics G and G*. Then you can
 apply the Theaetetus theory to get the 1-knower logic, and the
1-physics, etc. They have all the same theology, but the personal
arithmetical content of the "Bp" can vary a lot.

Bruno



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




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