>>> John Boone on logic 
 JB> I will begin by quoting part of it: 
 JB> The notions of fuzzy set A and B, A or B can be used for 
 JB> multi valued propositional calculus. To wit: p, q the 
 JB> true values of P, Q, 0<=p,q<=1. Truth value of not P 
 JB> is 1-p, of P&Q is min(p,q), or P or Q is max(p,q).  Note 
 JB> that P or Q equivalent not(notP and notQ) and P&Q 
 JB> equivalent not(notP or notQ).  So does it fly? 
 JB> Where to?  Can we take P implies Q, P->Q, to be 
 JB> not(P & notQ) or equivalent notP or Q? 
 JB> According to Kahane's book, the logic of P implies Q, 
 P -> Q is (P&Q)&(P¬Q).  I wonder if this would change 
 JB> the truth values given for P -> Q.   I have not checked 
 JB> this but thought I would write and see what you get. 
This cannot be so as (P&Q)&(P¬Q) is in itself a contradiction.  The two 
value true tables do check out for A -) B as indicated above.  As for the 
probalistic values, I recall checking them out for A or B = not (not A & not 
B) and it's duel A and B = not (not A or not B).
Indeed 1 - min(A, 1-B) = max (1-A, B), and as I recall I worked the truth 
tables for A -) B for three values to show you the problem with that approach 
regarding equivalence.  Namely for certain truth values of A and B, A 
equivalent B even tho A and B have different truth values.  This is where it 
doesn't fly conceptually.
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