Cactus Rules
• https://oeis.org/wiki/User:Jon_Awbrey/Cactus_Rules

With an eye toward the aims of the NKS Forum I've begun to work out a translation of the “elementary cellular automaton rules” (ECARs), in effect, just the boolean functions of abstract type \(f : \mathbb{B}^3 \to \mathbb{B},\) into cactus language, and I'll post a selection of my working notes here.

#Logic #LogicalGraphs #BooleanFunctions #PropositionalCalculus
#CactusCalculus #CactusLanguage #CactusSyntax #CellularAutomata

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

#DifferentialPropositionalCalculus • 2.4
• https://inquiryintoinquiry.com/2020/02/22/differential-propositional-calculus-2/

#CactusCalculus Conventions —

The briefest expression for #LogicalTruth is the #EmptyWord, denoted \(\boldsymbol\varepsilon\) or \(\boldsymbol\lambda\) in #FormalLanguages, where it forms the #IdentityElement for #Concatenation. It may be given visible expression in this context by means of the logically equivalent form \(\texttt{((} ~ \texttt{))},\) or, especially if operating in an algebraic context, by a simple \(1.\)

#DifferentialPropositionalCalculus • 2
https://inquiryintoinquiry.com/2020/02/22/differential-propositional-calculus-2/

#CactusCalculus —

Table 6 introduces a #Syntax for #PropositionalCalculus based on 2 families of #Multigrade #LogicalConnectives.

Table 6. #Syntax and #Semantics of a Calculus for #PropositionalLogic
https://inquiryintoinquiry.files.wordpress.com/2020/02/syntax-and-semantics-of-a-calculus-for-propositional-logic.png

Related Subjects —
#Peirce #Semiotics #BooleanFunctions
#Logic #LogicalGraphs #DifferentialLogic
#GraphTheory #CactusGraphs #CactusLanguage
#MinimalNegationOperators #PaintedAndRootedCacti