Tag Archives: Visualization

Differential Logic • 4

Posted on February 8, 2026 by Jon Awbrey

Differential Expansions of Propositions Bird’s Eye View An efficient calculus for the realm of logic represented by boolean functions and elementary propositions makes it feasible to compute the finite differences and the differentials of those functions and propositions. For example, … Continue reading →

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

Differential Logic • 3

Posted on February 7, 2026 by Jon Awbrey

Cactus Language for Propositional Logic (cont.) Table 1 shows the cactus graphs, the corresponding cactus expressions, their logical meanings under the so‑called existential interpretation, and their translations into conventional notations for a sample of basic propositional forms. Table 1. Syntax … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Differential Logic • 2

Posted on February 6, 2026 by Jon Awbrey

Cactus Language for Propositional Logic The development of differential logic is facilitated by having a moderately efficient calculus in place at the level of boolean‑valued functions and elementary logical propositions.  One very efficient calculus on both conceptual and computational grounds … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Differential Logic • 1

Posted on February 5, 2026 by Jon Awbrey

Introduction Differential logic is the component of logic whose object is the description of variation — focusing on the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description.  A definition that broad naturally … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Differential Logic • Overview

Posted on February 3, 2026 by Jon Awbrey

A reader once told me “venn diagrams are obsolete” and of course we all know how unwieldy they become as our universes of discourse expand beyond four or five dimensions.  Indeed, one of the first lessons I learned when I … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Riffs and Rotes • Happy New Year 2026

Posted on January 1, 2026 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 order 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

Cactus Language • Semantics 8

Posted on November 1, 2025 by Jon Awbrey

The 16 boolean functions on two variables are shown in the following Table. As before, all boolean functions on proper subsets of the current variables are subsumed in the Table at hand.  In particular, we have the following inclusions. The … 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 , , , , , , , , , , , , , , , , | 2 Comments

Cactus Language • Semantics 7

Posted on October 30, 2025 by Jon Awbrey

A good way to illustrate the action of the conjunction and surjunction operators is to show how they can be used to construct the boolean functions on any finite number of variables.  Though it’s not much to look at let’s … 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 , , , , , , , , , , , , , , , , | 2 Comments

Cactus Language • Semantics 6

Posted on October 27, 2025 by Jon Awbrey

If one takes the view that PARCEs and PARCs amount to a pair of intertranslatable representations for the same domain of objects then denotation brackets of the form can be used to indicate the logical denotation of a sentence or … 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 , , , , , , , , , , , , , , , , | 2 Comments

Cactus Language • Semantics 5

Posted on October 14, 2025 by Jon Awbrey

Last time we reached the threshold of a potential codomain or target space for the kind of semantic function we need at this point, one able to supply logical meanings for the syntactic strings and graphs of a given cactus … 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 , , , , , , , , , , , , , , , , | 2 Comments