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

Differential Logic and Dynamic Systems • Overview 4
• https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

Logic-based systems have tended to be static in character, largely because we have lacked a proper logical analogue of differential calculus. The work laid out in this series of posts is intended to address that lack.

#Logic #DifferentialLogic #DiscreteDynamicalSystems
#LogicalTransformations #TransformationsOfDiscourse
#IntelligentSystems #InquiryDrivenSystems #Semiotics

Differential Logic and Dynamic Systems • Overview 3
• https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

Symbolic models use logical methods to describe systems and their agents in qualitative terms, deriving logical consequences of a system’s description or an agent’s state of information.

#Logic #DifferentialLogic #DiscreteDynamicalSystems
#LogicalTransformations #TransformationsOfDiscourse
#IntelligentSystems #InquiryDrivenSystems #Semiotics

Differential Logic and Dynamic Systems • Overview 2
• https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

Dynamic models take their cue from physics, using quantitative measures and differential equations to model the evolution of a system’s state through time.

#Logic #DifferentialLogic #DiscreteDynamicalSystems
#LogicalTransformations #TransformationsOfDiscourse
#IntelligentSystems #InquiryDrivenSystems #Semiotics

Differential Logic and Dynamic Systems • Overview 1
• https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

In modeling intelligent systems, whether we are trying to understand a natural system or engineer an artificial system, there has long been a tension or trade-off between dynamic paradigms and symbolic paradigms.

#Logic #DifferentialLogic #DiscreteDynamicalSystems
#LogicalTransformations #TransformationsOfDiscourse
#IntelligentSystems #InquiryDrivenSystems #Semiotics

Transformations of Discourse
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3#Transformations_of_Discourse

❝The same thing cannot, however, be said about mathematics; for here we have the new method of thought, pure intellect, the very well‑spring of the times, the fons et origo of an unfathomable transformation.❞

— Robert #Musil • #TheManWithoutQualities

#Logic #DifferentialLogic #DiscreteDynamicalSystems
#LogicalTransformations #TransformationsOfDiscourse

(3/3)

Transformations of Discourse
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3#Transformations_of_Discourse

… ❝for he no more needs to be capable of applying to his own personal soul what is daring and new in the soul of his subject than a machine is in fact capable of applying to itself the differential calculus on which it is based.❞ …

— Robert #Musil • #TheManWithoutQualities

#Logic #DifferentialLogic #DiscreteDynamicalSystems
#LogicalTransformations #TransformationsOfDiscourse

(2/3)

Survey of #DifferentialLogic
• https://inquiryintoinquiry.com/2022/11/20/survey-of-differential-logic-4/

This is a Survey of blog and wiki posts on Differential Logic, material I plan to develop toward a more compact and systematic account.

#Logic
#LogicalGraphs
#CactusLanguage
#QualitativeDynamics
#PropositionalCalculus
#LogicalTransformations
#MinimalNegationOperators
#DiscreteDynamicalSystems
#TransformationsOfDiscourse
#DifferentialPropositionalCalculus
#DifferentialAnalyticTuringAutomata

#Survey of #DifferentialLogic

• https://inquiryintoinquiry.com/2021/05/15/survey-of-differential-logic-3/

This is a Survey of blog and wiki posts on Differential Logic, material I plan to develop toward a more compact and systematic account.

#Logic
#LogicalGraphs
#CactusLanguage
#PropositionalCalculus
#MinimalNegationOperators
#DiscreteDynamicalSystems
#DifferentialPropositionalCalculus
#DifferentialAnalyticTuringAutomata