Animated Logical Graphs • 19

We have encountered the question of how to extend our formal calculus to take account of operator variables.

In the days when I scribbled these things on the backs of computer punchcards, the first thing I tried was drawing big loopy script characters, placing some inside the loops of others.  Lower case alphas, betas, gammas, deltas, and so on worked best.  Graphics like these conveyed the idea that a character-shaped boundary drawn around another space can be viewed as absent or present depending on whether the formal value of the character is unmarked or marked.  The same idea can be conveyed by attaching characters directly to the edges of graphs.

Here is how we might suggest an algebraic expression of the form {}^{\backprime\backprime} \texttt{(} q \texttt{)} {}^{\prime\prime} where the absence or presence of the operator {}^{\backprime\backprime} \texttt{(} ~ \texttt{)} {}^{\prime\prime} depends on the value of the algebraic expression {}^{\backprime\backprime} p {}^{\prime\prime}, the operator {}^{\backprime\backprime} \texttt{(} ~ \texttt{)} {}^{\prime\prime} being absent whenever p is unmarked and present whenever p is marked.

Cactus Graph (q)_p = {q,(q)}

It was obvious to me from the outset that this sort of tactic would need a lot of work to become a usable calculus, especially when it came time to feed those punchcards back into the computer.

cc: Systems ScienceStructural ModelingOntolog ForumLaws of FormCybernetics

This entry was posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

3 Responses to Animated Logical Graphs • 19

  1. Pingback: Survey of Animated Logical Graphs • 2 | Inquiry Into Inquiry

  2. Pingback: Survey of Animated Logical Graphs • 2 | Inquiry Into Inquiry

  3. Pingback: Survey of Animated Logical Graphs • 3 | Inquiry Into Inquiry

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.