Cf: Differential Propositional Calculus • Discussion 5 http://inquiryintoinquiry.com/2021/03/21/differential-propositional-calculus-discussion-5/
Re: Peirce List https://list.iupui.edu/sympa/arc/peirce-l/2021-03/thrd1.html#00020 ::: Helmut Raulien https://list.iupui.edu/sympa/arc/peirce-l/2021-03/msg00095.html Re: Ontolog Forum https://groups.google.com/g/ontolog-forum/c/T8DAe6shKFw ::: Mauro Bertani https://groups.google.com/g/ontolog-forum/c/T8DAe6shKFw/m/zKS50rJAAwAJ <QUOTE HR:> 1. I think I like very much your Cactus Graphs. Meaning that I am in the process of understanding them, and finding it much better not to have to draw circles, but lines. 2. Less easy for me is the differential calculus. Where is the consistency between (x,y) and (x, y, z)? (x, y) means that x and y are not equal and (x, y, z) means that one of them is false. Unequality and truth/falsity for me are two concepts so different I cannot think them together or see a consistency between them. 3. What about (w, x, y, z)? </QUOTE> <QUOTE MB:> So, if I want to transform a circle into a line I have to use a function f : Bⁿ → B ? This is the base of temporal logic? I’m using f : Nⁿ → N. </QUOTE> Dear Mauro, Here I think Helmut is describing the transition from forms of enclosure on a plane sheet of paper, such as those used by Peirce and Spencer Brown, to their topological duals in the form of rooted trees. There is more detail about this transformation at the following sites. Logical Graphs • Introduction https://inquiryintoinquiry.com/2008/07/29/logical-graphs-1/ Logical Graphs • Duality : Logical and Topological https://oeis.org/wiki/Logical_Graphs#Duality:_logical_and_topological This is the first step in the process of converting planar maps to graph-theoretic data structures. Further transformations take us from trees to the more general class of cactus graphs, which implement a highly efficient family of logical primitives called “minimal negation operators”. These are described in the following article. Minimal Negation Operators https://oeis.org/wiki/Minimal_negation_operator Regards, Jon
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