Re: All Process, No Paradox

Post   : All Process, No Paradox : 6
URL    : http://inquiryintoinquiry.com/2014/01/22/all-process-no-paradox-6/
Posted : January 22, 2014 at 9:00 pm
Author : Jon Awbrey

Re: Dick Lipton • Anti-Social Networks
http://rjlipton.wordpress.com/2014/01/22/anti-social-networks/

Re: Lou Kauffman • Iterants, Imaginaries, and Matrices
http://kauffman2013.wordpress.com/2013/12/27/iterants-imaginaries-and-matrices/

Comments I made on a blog post about computer science and social networks have a connection with the 
work in progress on this thread, so it may gain a march to append them here.

Comment 1
---------

I have been interested for a long time now in using graphs to do logic.  For that you need more than 
positive links — negative relations are more generative than positive relations.  This is analogous 
to social networks where people can “unlike” or “¬like” other people, or website networks where the 
information at one node can contradict the information at another node.  In my pursuits it turns out 
that particular species of graph-theoretic “cacti” are much more useful than the usual trees and 
unsigned graphs.

Comment 2
---------

For what it's worth, here is my somewhat dry exposition of “painted cacti” and their application to 
propositional calculus.

• Cactus Language
http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language

Painted cacti are rooted cacti with any number of symbols from a finite alphabet attached to each 
node.  In the intended interpretations these symbols (“paints”) are boolean variables.

Triangles are interesting in this context because they arise in logical case expressions.  In one of 
the customary interpretations of the cactus graphs, a rooted triangular lobe says that the values of 
the two non-root nodes are logically inequivalent.

-- 

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