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echo: philos
to: WILLIAM ELLIOT
from: JOHN BOONE
date: 1998-02-01 18:08:00
subject: logic

Hello William, 
 
  You wrote to me several interesting posts.  I finally got to 
read and digest some of them. 
  One of them dealt with the logic tables of fuzzy logic. 
I will begin by quoting part of it: 
 
        The notions of fuzzy set A and B, A or B can be used for 
        multi valued propositional calculus. To wit: p, q the 
        true values of P, Q, 0<=p,q<=1. Truth value of not P 
        is 1-p, of P&Q is min(p,q), or P or Q is max(p,q).  Note 
        that P or Q equivalent not(notP and notQ) and P&Q 
        equivalent not(notP or notQ).  So does it fly? 
        Where to?  Can we take P implies Q, P->Q, to be 
        not(P & notQ) or equivalent notP or Q? 
 
  According to Kahane's book, the logic of P implies Q, 
P -> Q is (P&Q)&(P¬Q).  I wonder if this would change 
the truth values given for P -> Q.   I have not checked 
this but thought I would write and see what you get. 
  Sorry, I don't have time to write more, but I have to 
leave.  
 
Take care, 
John 
 
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