Differential Logic • Overview

[Jon Awbrey]

Differential Logic • Overview
• https://inquiryintoinquiry.com/2024/11/25/differential-logic-overview-a/

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 as visible as possible the links between variant styles
of imagery in logical representation — and that is what I hoped to do in the
sketch of Differential Logic outlined below.

Note. I'll give just the links to the main topic heads below.
Please follow the link at the top of the page for the full outline.

Introduction
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Introduction

Cactus Language for Propositional Logic
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Cactus_Language_for_Propositional_Logic

Differential Expansions of Propositions
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Differential_Expansions_of_Propositions

Propositional Forms on Two Variables
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2#Propositional_Forms_on_Two_Variables

Transforms Expanded over Ordinary and Differential Variables
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2#Transforms_Expanded_over_Ordinary_and_Differential_Variables

Field Picture
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Field_Picture

Differential Fields
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Differential_Fields

Propositions and Tacit Extensions
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Propositions_and_Tacit_Extensions

Enlargement and Difference Maps
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Enlargement_and_Difference_Maps

Tangent and Remainder Maps
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3#Tangent_and_Remainder_Maps

Resources —

Logic Syllabus
• https://inquiryintoinquiry.com/logic-syllabus/

Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/

Regards,

Jon

cc: https://www.academia.edu/community/546xOz
cc: https://www.researchgate.net/post/Differential_Logic_Overview