[Arisbe] Painted Cacti & Propositional Calculus

[Jon Awbrey]

¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤

Edgers,

Here is a more straight-line presentation of my "reflective extension"
of Peirce's logical graphs -- hereafter known as "RefLog" for short --
detailing the correspondence among four types of representation for
the 16 propositions on 2 variables (boolean functions f : B^2 -> B).
and if you are in a hurry, you could probably skip to the last one.

http://ltsc.ieee.org/logs/suo/msg02534.html
http://ltsc.ieee.org/logs/suo/msg02554.html
http://ltsc.ieee.org/logs/suo/msg02570.html
http://ltsc.ieee.org/logs/suo/msg02590.html

It may be of interest to note that this yields a different sort
of relationship between Propositional Calculus and Graph Theory,
by way of the parse-graphs for propositional expressions, which
turn out in this case to comprise a species of tree-like graphs
that are called "painted and rooted cacti" (PARC's).

To Be Continued ...

Jon Awbrey

¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤