Logical Graphs • Discussion 1

Re: Laws of Form • John Mingers

JM:

I find it very frustrating not to be able to draw crosses and expressions within emails or Word documents.  Does anyone know of any software or apps that can do this?  If not, with so many computer scientists on this group, could someone produce something?

Dear John, All …

People with backgrounds in computing, combinatorics, or graph theory would immediately recognize Spencer Brown’s expressions are isomorphic to what graph theorists know and love as “trees”, more specifically “rooted trees”, with a particular manner of attaching letters to the nodes to be described later.  In those fields there’s a standard way of mapping trees to strings of parentheses and letters.  That operation is called “traversing the tree” when one passes from trees to strings and the reverse operation is called “parsing the string” when one passes from strings to trees.

The transformation of Spencer Brown’s simple closed figures in the plane or his formal expressions of “crosses” into rooted trees, together with the further transformation of those two forms to “pointer data structures” in computer memory, is discussed in the following post on my blog.

• Logical Graphs • Introduction

There’s a more formal presentation of logical graphs, working from the axioms or “initials” I borrowed with modifications from Peirce and Spencer Brown, in the following blog post.

• Logical Graphs • Formal Development

Those two pieces are combined and extended in the following article.

• Logical Graphs

The program I developed all through the 80s using those data structures in its logic module is documented so far as I’ve done to date on the following page.

• Survey of Theme One Program

Regards,
Jon

cc: Category Theory • Cybernetics • Ontolog • Structural Modeling • Systems Science
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