Differential Logic • The Logic of Change and Difference
• https://inquiryintoinquiry.com/2023/08/22/differential-logic-%ce%b1/

Differential logic is the logic of variation — the logic of change and difference.

Differential logic is the component of logic whose object is the description of variation, for example, the aspects of change, difference, distribution, and diversity, in universes of discourse subject to qualitative logical description. In its formalization, differential logic treats the principles governing the use of a “differential logical calculus”, in other words, 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. This 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
• Part 1 ( https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1 )
• Part 2 ( https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2 )
• Part 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
• Part 1 ( https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1 )
• Part 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
• Part 1 ( https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1 )
• Part 2 ( https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2 )
• Part 3 ( https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3 )
• Part 4 ( https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4 )
• Part 5 ( https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_5 )

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DiscreteDynamicalSystems
#Leibniz #BooleanFunctions #BooleanDifferenceCalculus #QualitativeDynamics
#DifferentialPropositions #MinimalNegationOperators #NeuralNetworkSystems

Survey of Differential Logic • 5
• https://inquiryintoinquiry.com/2023/04/25/survey-of-differential-logic-5/

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.

Please follow the above link for the full set of resources.
Articles and blog series on the core ideas are linked below.

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
• https://inquiryintoinquiry.com/2020/02/16/differential-propositional-calculus-overview/

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
• https://inquiryintoinquiry.com/2020/03/20/differential-logic-overview/

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
• https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-2/

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativePhysics
#CactusCalculus #MinimalNegationOperators #NeuralNetworkSystems

Differential Logic and Dynamic Systems • Overview 2
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

The work pursued here is coordinated with a parallel application focusing on #NeuralNetworkSystems but the dependencies are arranged to make the present article the main and the more self-contained work, to serve as a conceptual frame and a technical background for the network project.

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativeChange

Differential Logic and Dynamic Systems • Overview
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

❝Stand and unfold yourself.❞

— Hamlet • Francisco • 1.1.2

This article develops a differential extension of propositional calculus and applies it to analyzing the temporal evolution of systems whose states are described in qualitative logical terms.

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativeChange

Differential Logic and Dynamic Systems • Overview
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

❝Stand and unfold yourself.❞

— Hamlet • Francisco • 1.1.2

This article develops a differential extension of propositional calculus and applies it to analyzing the temporal evolution of systems whose states are described in qualitative logical terms.

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativeChange

Differential Logic and Dynamic Systems • Overview
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

❝Stand and unfold yourself.❞

— Hamlet • Francisco • 1.1.2

This article develops a differential extension of propositional calculus and applies it to analyzing the temporal evolution of systems whose states are described in qualitative logical terms.

#Peirce #Logic #LogicalGraphs #DifferentialLogic #DynamicSystems
#BooleanFunctions #BooleanDifferenceCalculus #QualitativeChange