Differential Logic • The Logic of Change and Difference

[Jon Awbrey]

Differential Logic • The Logic of Change and Difference
• https://inquiryintoinquiry.com/2023/08/22/differential-logic-the-logic-of-change-and-difference/

All,

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.

A simple case of a differential logical calculus is furnished by
a “differential propositional calculus”, a formalism which augments
ordinary propositional calculus in the same way the differential
calculus of Leibniz and Newton augments the analytic geometry of
Descartes.

Resources —

Differential Logic
• https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview
1 https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1
2 https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2
3 https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3

Differential Propositional Calculus
• https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview
1 https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1
2 https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2

Differential Logic and Dynamic Systems
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview
1 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1
2 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2
3 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3
4 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4
5 https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_5

Regards,

Jon

cc: https://www.academia.edu/community/LGGE0L