
Re: layer logic: a new dimension to logic?
Posted:
May 26, 2013 10:56 AM


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

