Tag Archives: Proof Theory

Unknown's avatar Jon Awbrey 9:44 am on May 3, 2026
Tags: , , , , , , , , , , , , , , , , , , , , , , , , Proof Theory, , , , , , ,   

Animated Logical Graphs • 2

Re: Peirce List • Jim Willgoose

It’s almost 50 years now since I first encountered the volumes of Peirce’s Collected Papers in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for Spencer Brown’s Laws of Form in the Whole Earth Catalog and I sent off for it right away.  I would spend the next decade just beginning to figure out what either one of them was talking about in the matter of logical graphs and I would spend another decade after that developing a program, first in Lisp and then in Pascal, that turned graph‑theoretic data structures formed on their ideas to good purpose as the basis of its reasoning engine.

I thought it might contribute to a number of long‑running and ongoing discussions if I could articulate what I think I learned from that experience.

So I’ll try to keep focused on that.

Resources

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

#abstraction, #amphecks, #analogy, #animata, #automated-research-tools, #boolean-algebra, #boolean-functions, #c-s-peirce, #cactus-graphs, #deduction, #differential-logic, #duality, #form, #graph-theory, #iconicity, #laws-of-form, #leibniz, #logic, #logical-graphs, #mathematics, #minimal-negation-operators, #model-theory, #peirces-law, #praeclarum-theorema, #proof-theory, #propositional-calculus, #propositional-logic, #semiotics, #spencer-brown, #theorem-proving, #topology, #visualization

Unknown's avatar Jon Awbrey 10:10 am on April 30, 2026
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Animated Logical Graphs • 1

For Your Musement …

Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce’s Alpha Graphs for propositional logic.

  • Proof Animations
    • Double Negation

      • Double Negation

    • Peirce’s Law

      • Peirce's Law

    • Praeclarum Theorema

      • Praeclarum Theorema

    • Two‑Thirds Majority Function

      • Two‑Thirds Majority Function

A full discussion of logical graphs can be found in the following article.

Additional Resources

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

#abstraction, #amphecks, #analogy, #animata, #automated-research-tools, #boolean-algebra, #boolean-functions, #c-s-peirce, #cactus-graphs, #deduction, #differential-logic, #duality, #form, #graph-theory, #iconicity, #laws-of-form, #leibniz, #logic, #logical-graphs, #mathematics, #minimal-negation-operators, #model-theory, #peirces-law, #praeclarum-theorema, #proof-theory, #propositional-calculus, #propositional-logic, #semiotics, #spencer-brown, #theorem-proving, #topology, #visualization

Unknown's avatar Jon Awbrey 11:30 am on November 15, 2025
Tags: , , , , , , Computational Complexity, , , , , , , , , , , , , , Proof Theory, , , , ,   

Survey of Animated Logical Graphs • 8

This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph‑theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.

Beginnings

Elements

Examples

Blog Series

  • Logical Graphs • Interpretive Duality • (1) • (2) • (3) • (4)
  • Logical Graphs, Iconicity, Interpretation • (1) • (2)
  • Genus, Species, Pie Charts, Radio Buttons • (1)

Excursions

Applications

Anamnesis

cc: FB | Logical Graphs • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#amphecks, #animata, #boolean-algebra, #boolean-functions, #c-s-peirce, #cactus-graphs, #computational-complexity, #constraint-satisfaction-problems, #differential-logic, #equational-inference, #graph-theory, #group-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