Category Archives: Differential Logic

Sign Relational Manifolds • 3

Posted on November 3, 2022 by Jon Awbrey

I’m not sure when it was I first noticed the relationship between manifolds and semiotics but I distinctly recall the passage in Serge Lang’s Differential and Riemannian Manifolds which brought the triadic character of tangent vectors into high relief.  I … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Intentionality, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 6 Comments

Sign Relational Manifolds • 2

Posted on November 1, 2022 by Jon Awbrey

A sense of how manifolds are applied in practice may be gleaned from the set of excerpts linked below, from Doolin and Martin (1990), Introduction to Differential Geometry for Engineers, which I used in discussing differentiable manifolds with other participants … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 6 Comments

Sign Relational Manifolds • 1

Posted on October 31, 2022 by Jon Awbrey

Riemann’s concept of a manifold, especially as later developed, bears a close relationship to Peirce’s concept of a sign relation. I will have to wait for my present train of thought to stop at a station before I can hop … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 6 Comments

Theme One Program • Exposition 8

Posted on October 8, 2022 by Jon Awbrey

Transformation Rules and Equivalence Classes The abstract character of the cactus language relative to its logical interpretations makes it possible to give abstract rules of equivalence for transforming cacti among themselves and partitioning the space of cacti into formal equivalence … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Theme One Program • Exposition 7

Posted on September 30, 2022 by Jon Awbrey

Mathematical Structure and Logical Interpretation The main things to take away from the previous post are the following two ideas, one syntactic and one semantic. Syntax.  The compositional structures of cactus graphs and cactus expressions are constructed from two kinds of connective … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Theme One Program • Exposition 6

Posted on September 29, 2022 by Jon Awbrey

Quickly recapping the discussion so far, we started with a data structure called an idea‑form flag and adopted it as a building block for constructing a species of graph-theoretic data structures called painted and rooted cacti.  We showed how to code … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Theme One Program • Jets and Sharks 3

Posted on September 3, 2022 by Jon Awbrey

Re: Theme One Program • Jets and Sharks • (1) • (2) Example 5. Jets and Sharks (cont.) Given a representation of the Jets and Sharks universe in computer memory, we naturally want to see if the memory serves to … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Theme One Program • Jets and Sharks 2

Posted on August 30, 2022 by Jon Awbrey

Re: Theme One Program • Jets and Sharks • (1) Example 5. Jets and Sharks (cont.) As we saw last time, Theme One reads the text file shown below and constructs a cactus graph data structure in computer memory.  The cactus … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Theme One Program • Jets and Sharks 1

Posted on August 25, 2022 by Jon Awbrey

It is easy to spend a long time on the rudiments of learning and logic before getting down to practical applications — but I think we’ve circled square one long enough to expand our scope and see what the category … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Theme One Program • Motivation 6

Posted on August 20, 2022 by Jon Awbrey

Comments I made in reply to a correspondent’s questions about delimiters and tokenizing in the Learner module may be worth sharing here. In one of the projects I submitted toward a Master’s in psychology I used the Theme One program to … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments