Category Archives: Proof Theory

Charles Sanders Peirce, George Spencer Brown, and Me • 20

Posted on September 16, 2025 by Jon Awbrey

Re: Laws of Form • James Bowery JB: I’m interested in those who have approached the notion of self‑duality from the meta‑perspective of switching perspectives between Directed Cyclic Graphs of NiNAND and NiNOR gates (Ni for N‑Inputs à la boolean … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Analytic Turing Automata, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Charles Sanders Peirce, George Spencer Brown, and Me • 19

Posted on September 10, 2025 by Jon Awbrey

Re: Laws of Form • James Bowery JB: I’m interested in those who have approached the notion of self‑duality from the meta‑perspective of switching perspectives between Directed Cyclic Graphs of NiNAND and NiNOR gates (Ni for N‑Inputs à la boolean … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Analytic Turing Automata, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Charles Sanders Peirce, George Spencer Brown, and Me • 18

Posted on September 7, 2025 by Jon Awbrey

Re: Laws of Form • James Bowery JB: I’m interested in those who have approached the notion of self‑duality from the meta‑perspective of switching perspectives between Directed Cyclic Graphs of NiNAND and NiNOR gates (Ni for N‑Inputs à la boolean … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Analytic Turing Automata, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Charles Sanders Peirce, George Spencer Brown, and Me • 17

Posted on August 22, 2025 by Jon Awbrey

Re: Laws of Form • James Bowery JB: I’m interested in those who have approached the notion of self‑duality from the meta‑perspective of switching perspectives between Directed Cyclic Graphs of NiNAND and NiNOR gates (Ni for N‑Inputs à la boolean … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Analytic Turing Automata, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Survey of Animated Logical Graphs • 8

Posted on May 2, 2025 by Jon Awbrey

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 Logical Graphs … Continue reading →

Posted in 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 | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 77 Comments

Transformations of Logical Graphs • Discussion 1

Posted on May 22, 2024 by Jon Awbrey

Re: Laws of Form • Mauro Bertani Dear Mauro, The couple of pages linked below give the clearest and quickest introduction I’ve been able to manage so far when it comes to the elements of logical graphs, at least, in … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Interpretive Duality, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Transformations of Logical Graphs • 14

Posted on May 21, 2024 by Jon Awbrey

Semiotic Transformations Re: Transformations of Logical Graphs • (8) • (9) • (10) • (11) • (12) • (13) Completing our scan of the Table in Episode 8, the last orbit up for consideration contains the logical graphs for the boolean … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Interpretive Duality, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Transformations of Logical Graphs • 13

Posted on May 18, 2024 by Jon Awbrey

Semiotic Transformations Re: Transformations of Logical Graphs • (8) • (9) • (10) • (11) • (12) Continuing our scan of the Table in Episode 8, the next orbit contains the logical graphs for the boolean functions and The boolean … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Interpretive Duality, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Transformations of Logical Graphs • 12

Posted on May 16, 2024 by Jon Awbrey

Semiotic Transformations Re: Transformations of Logical Graphs • (8) • (9) • (10) • (11) Re: Interpretive Duality as Sign Relation • Orbit Order Taking from our wallets an old schedule of orbits, let’s review the classes of logical graphs … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Interpretive Duality, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Transformations of Logical Graphs • 11

Posted on May 15, 2024 by Jon Awbrey

Semiotic Transformations Re: Transformations of Logical Graphs • (8) • (9) • (10) Continuing our scan of the Table in Episode 8, the next two orbits contain the logical graphs for the boolean functions in that order.  A first glance … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Interpretive Duality, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments