Tag Archives: Group Theory

Differential Logic and Dynamic Systems • Overview

Posted on March 4, 2023 by Jon Awbrey

In modeling intelligent systems, whether we are trying to understand a natural system or engineer an artificial system, there has long been a tension or trade‑off between dynamic paradigms and symbolic paradigms.  Dynamic models take their cue from physics, using … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Riffs and Rotes • Happy New Year 2023

Posted on January 1, 2023 by Jon Awbrey

No information is lost by dropping the terminal 1s.  Thus we may write the following form. The article referenced below tells how forms like these correspond to a family of digraphs called riffs and a family of graphs called rotes.  … Continue reading →

Posted in Algebra, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , , | Leave a comment

Differential Logic and Dynamic Systems • Discussion 7

Posted on February 9, 2022 by Jon Awbrey

Re: Differential Logic and Dynamic Systems • Intentional Propositions Re: FB | Differential Logic • Marius V. Constantin Marius Constantin asks about the logical value of an intention which is not carried out. MVC: I have in my intention to … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Peirce’s 1870 “Logic of Relatives” • Comment 3

Posted on February 3, 2022 by Jon Awbrey

In passing to more complex combinations of relative terms and the extensional relations they denote, as we began to do in Comments 10.6 and 10.7, I used words like composite and composition along with the usual composition sign to describe … Continue reading →

Posted in C.S. Peirce, Category Theory, Differential Logic, Duality, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Logical Matrices, Mathematics, Peirce, Peirce's Categories, Predicate Calculus, Propositional Calculus, Relation Theory, Semiotics, Sign Relations, Teridentity, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Peirce’s 1870 “Logic of Relatives” • Discussion 5

Posted on January 8, 2022 by Jon Awbrey

Re: Conceptual Graphs • Peiyuan Zhu PZ: I’m studying imprecise probabilities which initially works as an extension in Boole’s Laws of Thoughts.  It seems like Boole was solving a set of algebraic equations for probabilities where some of the probabilities … Continue reading →

Posted in C.S. Peirce, Category Theory, Differential Logic, Duality, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Logical Matrices, Mathematics, Peirce, Peirce's Categories, Predicate Calculus, Propositional Calculus, Relation Theory, Semiotics, Sign Relations, Teridentity, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Peirce’s 1870 “Logic of Relatives” • Discussion 4

Posted on December 15, 2021 by Jon Awbrey

Re: Peirce’s 1870 “Logic of Relatives” • Proto-Graphical Syntax Re: FB | Ancient Logic • Henning Engebretsen HE: What’s your point, it’s obviously too graphical, but perhaps you are driving at something else.  Explain? Dear Henning, My aim here is … Continue reading →

Posted in C.S. Peirce, Category Theory, Differential Logic, Duality, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Logical Matrices, Mathematics, Peirce, Peirce's Categories, Predicate Calculus, Propositional Calculus, Relation Theory, Semiotics, Sign Relations, Teridentity, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Peirce’s 1870 “Logic of Relatives” • Discussion 3

Posted on December 10, 2021 by Jon Awbrey

All other sciences without exception depend upon the principles of mathematics;  and mathematics borrows nothing from them but hints. C.S. Peirce • “Logic of Number” A principal intention of this essay is to separate what are known as algebras of … Continue reading →

Posted in C.S. Peirce, Category Theory, Differential Logic, Duality, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Logical Matrices, Mathematics, Peirce, Peirce's Categories, Predicate Calculus, Propositional Calculus, Relation Theory, Semiotics, Sign Relations, Teridentity, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Riffs and Rotes • 59281

Posted on September 5, 2021 by Jon Awbrey

Re: Persiflage • 59281 Numberfile • What’s Special About 59,281? If is prime then the decimal expansion of repeats, so it makes sense to talk about the “average” of the digits of   The average can be bigger than equal … Continue reading →

Posted in Arithmetic, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , , | Leave a comment

Differential Logic and Dynamic Systems • Discussion 6

Posted on June 14, 2021 by Jon Awbrey

Re: Differential Logic and Dynamic Systems • Discussions • (4) • (5) Re: Laws of Form • Lyle Anderson LA: Have you ever done any statistical analysis of data, or any of the statistical sciences such as the Theory of … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Differential Logic and Dynamic Systems • Discussion 5

Posted on June 13, 2021 by Jon Awbrey

Re: Differential Logic and Dynamic Systems • Discussion 4 Re: Laws of Form • Lyle Anderson (1) (2) Last time I mentioned a few old writings I thought might serve to smooth the transition from “Differential Propositional Calculus” to the … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments