# Re: questions on machines, belief, awareness, and knowledge

```Hi Brian,
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On 13 Sep 2012, at 22:04, Brian Tenneson wrote:

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```Bruno,

You use B as a predicate symbol for "belief" I think.
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I use for the modal unspecified box, in some context (in place of the more common "[]"). Then I use it mainly for the box corresponding to GĂ¶del's beweisbar (provability) arithmetical predicate (definable with the symbols E, A, &, ->, ~, s, 0 and parentheses. Thanks to the fact that Bp -> p is not a theorem, it can plays the role of believability for the ideally correct machines.
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What are some properties of B and is there a predicate for knowing/ being aware of that might lead to a definition for self-awareness?
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Yes, B and its variants:
B_1 p == Bp & p
B_2 p = Bp & Dt
B_3 p = Bp & Dt & t,
and others.

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btw, what is a machine and what types of machines are there?
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With comp we bet that we are, at some level, digital machine. The theory is one studied by logicians (Post, Church, Turing, etc.).
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Is there a generic description for a structure (in the math logic sense) to have a belief or to be aware; something like
```A |= "I am the structure A"
?
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Yes, by using the Dx = xx method, you can define a machine having its integral 3p plan available. But the 1p-self, given by Bp & p, does not admit any name. It is the difference between "I have two legs" and "I have a pain in a leg, even if a phantom one". G* proves them equivalent (for correct machines), but G cannot identify them, and they obeys different logic (G and S4Grz).
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Finally, on a different note, if there is a structure for which all structures can be 1-1 injected into it, does that in itself imply a sort of ultimate structure perhaps what Max Tegmark views as the level IV multiverse?
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A 1-1 map is too cheap for that, and the set structure is a too much structural flattening. Comp used the simulation, notion, at a non specifiable level substitution.
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Bruno

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

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