Cf: All Process, No Paradox • 6 https://inquiryintoinquiry.com/2014/01/22/all-process-no-paradox-6/
Re: R.J. Lipton • Anti-Social Networks https://rjlipton.wpcomstaging.com/2014/01/22/anti-social-networks/ Re: Lou Kauffman • Iterants, Imaginaries, Matrices https://kauffman2013.wordpress.com/2013/12/27/iterants-imaginaries-and-matrices/ All, Comments I made elsewhere about computer science and (anti-)social networks have a connection with the work in progress on this thread, so it may steal 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. The logical situation is analogous to social networks where people can “unlike” or “¬like” other people or website networks where the information at one node may 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 garden variety trees and unsigned graphs. Comment 2 ========= For what it’s worth, here is my exposition of “painted cacti” and their application to propositional calculus. Cactus Language • Overview https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview Part 1 • Syntax https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_1 Part 2 • Generalities About Formal Grammars https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_2 Part 3 • Stylistics, Mechanics, Semantics https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3 A “painted cactus” is a rooted cactus with any number of symbols from a finite alphabet attached to each node. In their ordinary logical interpretations these symbols (“paints”) stand for boolean variables. Triangles are interesting in computational contexts because they arise in case-breakdown expressions. In one of the common interpretations of cactus graphs, a rooted triangular lobe says the values of the two non-root nodes are logically inequivalent. Resources ========= Futures Of Logical Graphs https://oeis.org/wiki/Futures_Of_Logical_Graphs Propositional Equation Reasoning Systems https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems Regards, Jon
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