Differential Logic • Overview

The previous series of blog posts on Differential Propositional Calculus brought us to the threshold of the subject without quite stepping over but I wanted to lay out the necessary ingredients in the most concrete, intuitive, and visual way possible before taking up the abstract forms.

One of my readers on Facebook told me “venn diagrams are obsolete” and of course we all know they become unwieldy 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 are a death trap on numerous conceptual and computational counts.  Still, venn diagrams do us good service 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.

At any rate, intrepid readers will have provisioned their visual imaginations fully enough at this point to pick their way through the cactus patch ahead.  The outline below links to my last, best introduction to Differential Logic, which I’ll be working to improve as I serialize it to this blog.

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 Differential Features

Transforms Expanded over Ordinary Features

Operational Representation

Part 3

Development • Field Picture

Proposition and Tacit Extension

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

cc: CyberneticsOntolog ForumPeirce ListStructural ModelingSystems Science

This entry was 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, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

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