Tag Archives: Differential Analytic Turing Automata

Unknown's avatar Jon Awbrey 12:48 pm on February 3, 2026
Tags: , , , , , , , , , Differential Analytic Turing Automata, , , , , , , , Indicator Functions, , , , , , , , , Topology,   

Differential Logic • Overview

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 set about implementing Peirce’s graphs and Spencer Brown’s forms on the computer is that 2‑dimensional representations of logic quickly become death traps on numerous conceptual and computational counts.

Still, venn diagrams do us good service at the outset in visualizing the relationships among extensional, functional, and intensional aspects of logic.  A facility with those connections is critical to the computational applications and statistical generalizations of propositional logic commonly used in mathematical and empirical practice.

All things considered, then, it is useful to make the links between various styles of imagery in logical representation as visible as possible.  The first few steps in that direction are set out in the sketch of Differential Logic to follow.

Part 1

Introduction

Cactus Language for Propositional Logic

Differential Expansions of Propositions

Bird’s Eye View

Worm’s Eye View

Panoptic View • Difference Maps

Panoptic View • Enlargement Maps

Part 2

Propositional Forms on Two Variables

Transforms Expanded over Ordinary and Differential Variables

Enlargement Map Expanded over Ordinary Variables

Enlargement Map Expanded over Differential Variables

Difference Map Expanded over Ordinary Variables

Difference Map Expanded over Differential Variables

Operational Representation

Part 3

Field Picture

Differential Fields

Propositions and Tacit Extensions

Enlargement and Difference Maps

Tangent and Remainder Maps

Least Action Operators

Goal-Oriented Systems

Further Reading

Document History

Document History

Differential Logic • Ontology List 2002

Dynamics And Logic • Inquiry List 2004

Dynamics And Logic • NKS Forum 2004

Resources

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

#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

Unknown's avatar Jon Awbrey 11:20 am on November 7, 2025
Tags: , , , , , , , , , Differential Analytic Turing Automata, , , , , Frankl Conjecture, , , , , , , , , , , ,   

Survey of Differential Logic • 8

This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment.

Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description.  A definition as broad as that naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models.  To the extent a logical inquiry makes use of a formal system, its differential component treats the use of a differential logical calculus — a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.

Elements

Blog Series

Architectonics

Applications

Blog Dialogs

Explorations

cc: FB | Differential Logic • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#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, #frankl-conjecture, #functional-logic, #gradient-descent, #graph-theory, #hologrammautomaton, #inquiry-driven-systems, #leibniz, #logic, #logical-graphs, #mathematics, #minimal-negation-operators, #propositional-calculus, #visualization