Category Archives: Cactus Graphs

Animated Logical Graphs • 3

Posted on January 26, 2015 by Jon Awbrey

Re: Peirce List • Helmut Raulien I have a little more leisure now to start climbing back into the saddle, so let me see where we left off … Try looking into the article I linked before: Logical Graphs Or … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 2

Posted on January 14, 2015 by Jon Awbrey

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 … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 1

Posted on January 8, 2015 by Jon Awbrey

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 See the following article for a full … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

All Process, No Paradox • 6

Posted on January 22, 2014 by Jon Awbrey

Re: R.J. Lipton • Anti-Social Networks Re: Lou Kauffman • Iterants, Imaginaries, Matrices Comments I made elsewhere about computer science and (anti-)social networks have a connection with the work in progress on this thread, so it may steal a march … Continue reading →

Posted in Algorithms, Amphecks, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Differential Logic, Graph Theory, Laws of Form, Logic, Logical Graphs, Lou Kauffman, Mathematics, Minimal Negation Operators, Painted Cacti, Paradox, Peirce, Process Thinking, Propositional Calculus, Spencer Brown, Systems, Time | Tagged , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Differential Analytic Turing Automata • Discussion 1

Posted on October 14, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Proving Cook’s Theorem Synchronicity Rules❢ I just started reworking an old exposition of mine on Cook’s Theorem, where I borrowed the Parity Function example from Wilf (1986), Algorithms and Complexity, and translated it … Continue reading →

Posted in Algorithms, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Differential Analytic Turing Automata, Differential Logic, Logic, Logical Graphs, Peirce, Propositional Calculus, Turing Machines | Tagged , , , , , , , , , , , | 2 Comments

The Lambda Point • 1

Posted on August 1, 2013 by Jon Awbrey

A note on the title.  From long ago discussions with Harvey Davis, one of my math professors at Michigan State.  I remember telling him of my interest in the place where algebra, geometry, and logic meet, and he quipped, “Ah … Continue reading →

Posted in Algebra, Amphecks, Boolean Algebra, C.S. Peirce, Cactus Graphs, Geometry, Graph Theory, Lambda Point, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Peirce, Propositional Calculus, Topology | Tagged , , , , , , , , , , , , , , | Leave a comment

How To Succeed In Proof Business Without Really Trying

Posted on July 15, 2013 by Jon Awbrey

Re: R.J. Lipton • Surely You Are Joking? Comment 1 Even at the mailroom entry point of propositional calculus, there is a qualitative difference between insight proofs and routine proofs.  Human beings can do either sort, as a rule, but … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Automatic Theorem Proving, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Graph Theory, Logic, Logical Graphs, Minimal Negation Operators, Model Theory, Peirce, Praeclarum Theorema, Proof Theory, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , , , | 7 Comments

Finding a Needle in a Cactus Patch

Posted on April 30, 2013 by Jon Awbrey

Re: R.J. Lipton • Sex, Lies, And Quantum Computers Don’t know much about quantum computation, but my ventures in graphical syntaxes for propositional calculus did turn up a logical operator whose evaluation process reminded me a little of the themes … Continue reading →

Posted in Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Graph Theory, Logic, Logical Graphs, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Quantum Computing, Semiotics | Tagged , , , , , , , , , , , , | 4 Comments

Praeclarum Theorema

Posted on October 5, 2008 by Jon Awbrey

The praeclarum theorema, or splendid theorem, is a theorem of propositional calculus that was noted and named by G.W. Leibniz. Continue reading →

Posted in Abstraction, Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Graph Theory, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Peirce, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , | 17 Comments

Logical Graphs • Formal Development

Posted on September 19, 2008 by Jon Awbrey

Logical graphs are next presented as a formal system by going back to the initial elements and developing their consequences in a systematic manner. Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 41 Comments