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Topic: layer logic: a new dimension to logic?
Replies: 12   Last Post: May 26, 2013 10:56 AM

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Oskar Trestone

Posts: 22
From: Germany
Registered: 9/17/11
Re: layer logic: a new dimension to logic?
Posted: May 26, 2013 10:56 AM
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Hello,

trying to use layers of layers was maybe to ambitios.

Therefore I come back to a easier way:

I will alter the following rule:
A7: layers are upstairs and for themselfes "blind":
W ( W(A,t)=v, d ) = u for t >=d ans any v = u or w or -w.

Now the truth value of "W(A,t)=v" is independant of layers (like d).

As now we see W(A,t) as a (fixed) truth value,
therefore statements about W(A,t) (like ?W(A,t)=v?) are statements about truth values an not dependant of layers.

In classic logic a statement A could be substituted by its truth value W(A),
in layer logic A this is possible for every layer t= 0,2,3, ...:
For every layer t statement A can be substituted by W(A,t).

So statements about W(A,t) are de facto classical statements
(where I use a 3rd truth value u "undefined" for symmetrical reasons).

Same with statements about all statements, all layers or about the existence of special properties.

The equality of layer statements is a meta property and easier to define:
W(A=B) = w :<-> for all t: W ( W(A,t) = W(B,t) ) = w. and W(A=B)= f else.
(if A or B are classic and no layer statements, we define W(A,0) :=u and W(A,t):= W(A) else, same for W(B,t))

Equality of layer sets:

W(M1=M2) = W ( For all t: W(xeM1,t) = W(xeM2,t) )
Exspecially: W(M=M)=w .

The succesor set m+ (for the peano axioms) is now more easy:

W(x e m+, t+1) := W ( W(x e m, t) v W(x=m) )

As a whole, layers are just used in a certain "kernel" of logic, the rest remains nearly as usual.

Looking from the perspective of layer logic it still remains a unsolved question,
why in everyday life we so rarely encounter layer effects...

Yours
Trestone



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