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Topic: ALL(F):N->R is 2OL! NOT 1OL!!!!!!
Replies: 6   Last Post: Nov 15, 2012 2:39 AM

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Graham Cooper

Posts: 4,237
Registered: 5/20/10
Re: ALL(F):N->R is 2OL! NOT 1OL!!!!!!
Posted: Nov 15, 2012 2:39 AM
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> <=  is definable using Peano Arithmetic
>
> A(n)  0 <= n
> A(m) A(n) s(m)<=s(n) -> m<=n



Other way around...
m<=n -> s(m)<=s(n)

I was thinking of PROLOG
s(m)<=s(n) :- m<n

FORWARD CHAINING

0 <= s(0) FROM AXIOM 1
0<=s(0) -> s(0)<=s(s(0)) FROM AXIOM 2

L & L->R -> R MODUS PONENS
L = 0<=s(0)
R = s(0)<=s(s(0))
==============
s(0)<=s(s(0))

Herc





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