Tag Archives: Graph Theory

Cactus Language • Overview 3

Posted on March 7, 2025 by Jon Awbrey

In the development of Cactus Language to date the following two species of graphs have been instrumental. Painted And Rooted Cacti (PARCAI). Painted And Rooted Conifers (PARCOI). It suffices to begin with the first class of data structures, developing their … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 3 Comments

Cactus Language • Overview 2

Posted on March 6, 2025 by Jon Awbrey

In order to facilitate the use of propositions as indicator functions it helps to acquire a flexible notation for referring to propositions in that light, for interpreting sentences in a corresponding role, and for negotiating the requirements of mutual sense … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Cactus Language • Overview 1

Posted on March 1, 2025 by Jon Awbrey

Thus, what looks to us like a sphere of scientific knowledge more accurately should be represented as the inside of a highly irregular and spiky object, like a pincushion or porcupine, with very sharp extensions in certain directions, and virtually … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Riffs and Rotes • Happy New Year 2025

Posted on January 1, 2025 by Jon Awbrey

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

Posted in Algebra, Arithmetic, Combinatorics, Computation, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Recursion, Representation, Riffs and Rotes, Semiotics, Visualization | Tagged , , , , , , , , , , , , , | Leave a comment

Differential Propositional Calculus • 37

Posted on December 31, 2024 by Jon Awbrey

Foreshadowing Transformations • Extensions and Projections of Discourse And, despite the care which she took to look behind her at every moment, she failed to see a shadow which followed her like her own shadow, which stopped when she stopped, … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Differential Propositional Calculus • 36

Posted on December 30, 2024 by Jon Awbrey

Transformations of Discourse It is understandable that an engineer should be completely absorbed in his speciality, instead of pouring himself out into the freedom and vastness of the world of thought, even though his machines are being sent off to … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Differential Propositional Calculus • 35

Posted on December 29, 2024 by Jon Awbrey

Example 2. Drives and Their Vicissitudes (concl.) Applied to the example of ‑gear curves, the indexing scheme results in the data of the next two Tables, showing one period for each orbit. The states in each orbit are listed as … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Propositional Calculus • 34

Posted on December 29, 2024 by Jon Awbrey

Example 2. Drives and Their Vicissitudes (cont.) With a little thought it is possible to devise a canonical indexing scheme for the states in differential logical systems.  A scheme of that order allows for comparing changes of state in universes … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Differential Propositional Calculus • 33

Posted on December 28, 2024 by Jon Awbrey

Example 2. Drives and Their Vicissitudes (cont.) Expressed in the language of drives and gears our next Example may be described as the family of fourth‑gear curves through the fourth extension   Those are the trajectories generated subject to the … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Propositional Calculus • 32

Posted on December 28, 2024 by Jon Awbrey

I open my scuttle at night and see the far‑sprinkled systems, And all I see, multiplied as high as I can cipher, edge but      the rim of the farther systems. — Walt Whitman • Leaves of Grass Example 2. Drives … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments