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I have a couple of questions about the Venn diagrams object :

  1. Words from the binary alphabet with n letters label each region of an order-n Venn diagram. Is there any more profound connection between binary representations and say the way Venn diagrams should be laid out with respect to neighbors (Hamming distance between labels, say)?

  2. What are the consequences if we consider 'fuzzy' sets, say a type of set with a inclusion metric that is ternary (0,out),(1,inbetween),(2,in) , and we label the 'regions' of some kind of Venn diagram using words of n letters from the ternary alphabet?

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I posted a comment in the wrong place---after an answer. It might give you an idea of the complexity of these diagrams. –  Fred Kline Feb 27 '13 at 22:25

2 Answers 2

You might want to explore this article, which goes some way to addressing your questions and gives some references to follow up.

Lewis Carroll explores diagrams and methods in Symbolic Logic and the Game of Logic, but this is a less relevant and rather old fashioned treatment.

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I actually browsed through a new edition of Lewis Carroll complete works the other day in part based on this suggestion. Great illustrations, but not that much maths in the selection they presented. –  Cris Stringfellow Feb 20 '13 at 14:01
    
As I recall Carroll writes in terms of classifying syllogisms rather than boolean algebra - but he is exploring ways of presenting information, which is why I noted it - it's a treatment which predates modern methods. –  Mark Bennet Feb 20 '13 at 17:44
    
Oh yes, in the reference provided, yes. I was relating an anecdote about how a collection of his "complete" works did not include his mathematical works. –  Cris Stringfellow Feb 20 '13 at 17:55
    
Sorry - tired - astonishing! –  Mark Bennet Feb 20 '13 at 17:58
    
I just saw the modified OP. I think ternary might be doable in a Randolph diagram using a tic-tac-toe structure instead of a cross. (Interesting concept). It will be a lot of work. I was about to do a Mathematica function for the diagrams, but encountered medical issues. I'm not sure when I can get back to it. mathematica.stackexchange.com/q/18342/973 –  Fred Kline Feb 27 '13 at 11:03

Randolph diagram might be an alternative to Venn diagrams.
Randolph's paper on jstor

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Yes I like the randolph diagram idea. –  Cris Stringfellow Feb 24 '13 at 9:55

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