#cactuslanguage — Public Fediverse posts

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

Logic Syllabus • Discussion 1
• https://inquiryintoinquiry.com/2023/06/02/logic-syllabus-discussion-1/

Re: Logic Syllabus ( https://inquiryintoinquiry.com/logic-syllabus/ )
Re: Laws of Form ( https://groups.io/g/lawsofform/topic/logic_syllabus/99218507 )
Re: John Mingers ( https://groups.io/g/lawsofform/message/2326 )

JM: ❝In a previous post you mentioned the minimal negation operator. Is there also the converse of this, i.e. an operator which is true when exactly one of its arguments is true? Or is this just XOR?❞

Yes, the “just one true” operator is a very handy tool. We discussed it earlier under the headings of “genus and species relations” or “radio button logic”. Viewed in the form of a venn diagram it describes a partition of the universe of discourse into mutually exclusive and exhaustive regions.

Reading \(\texttt{(} x_1 \texttt{,} \ldots \texttt{,} x_m \texttt{)}\) to mean just one of \(x_1, \ldots, x_m\) is false, the form \(\texttt{((} x_1 \texttt{),} \ldots \texttt{,(} x_m \texttt{))}\) means just one of \(x_1, \ldots, x_m\) is true.

For two logical variables, though, the cases “condense” or “degenerate” and saying “just one true” is the same thing as saying “just one false”.

\[\texttt{((} x_1 \texttt{),(} x_2 \texttt{))} = \texttt{(} x_1 \texttt{,} x_2 \texttt{)} = x_1 + x_2 = \mathrm{xor} (x_1, x_2).\]

There's more information on the following pages.

Minimal Negation Operators
• https://oeis.org/wiki/Minimal_negation_operator

Related Truth Tables
• https://oeis.org/wiki/Minimal_negation_operator#Truth_tables

Genus, Species, Pie Charts, Radio Buttons
• https://inquiryintoinquiry.com/2021/11/10/genus-species-pie-charts-radio-buttons-1/

Related Discussions
• https://inquiryintoinquiry.com/?s=Radio+Buttons

#Logic #LogicSyllabus #BooleanDomain #BooleanFunction #BooleanValuedFunction
#Peirce #LogicalGraph #MinimalNegationOperator #ExclusiveDisjunction #XOR
#CactusLanguage #PropositionalCalculus #RadioButtonLogic #TruthTable

Logic Syllabus • 5
• https://inquiryintoinquiry.com/logic-syllabus/

Related Articles
• https://oeis.org/wiki/Logic_Syllabus#Related_articles

Cactus Language • https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview
Futures Of Logical Graphs • https://oeis.org/wiki/Futures_Of_Logical_Graphs
Differential Propositional Calculus • https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview
Differential Logic • https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview
Differential Logic and Dynamic Systems • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview
Propositions As Types Analogy • https://oeis.org/wiki/Propositions_As_Types_Analogy
Propositional Equation Reasoning Systems • https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems
Prospects for Inquiry Driven Systems • https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems
Introduction to Inquiry Driven Systems • https://oeis.org/wiki/Introduction_to_Inquiry_Driven_Systems
Inquiry Driven Systems • Inquiry Into Inquiry • https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview

#Logic #LogicSyllabus #CactusLanguage #LogicalGraphs #DifferentialLogic
#DifferentialPropositionalCalculus #DifferentialLogicAndDynamicSystems
#PropositionsAsTypesAnalogy #PropositionalEquationReasoningSystems
#Inquiry #InquiryDrivenSystems #InquiryIntoInquiry #DynamicalSystems

Survey of Theme One Program
• https://inquiryintoinquiry.com/2023/03/30/survey-of-theme-one-program-5/

This is a Survey of resources for the Theme One Program I worked on all through the 1980s. The aim was to develop fundamental algorithms and data structures for integrating empirical learning with logical reasoning. I had earlier developed separate programs for basic components of those tasks, namely, 2-level formal language learning and propositional constraint satisfaction, the latter using an extension of C.S. Peirce's logical graphs as a syntax for propositional logic. Thus arose the question of how well it might be possible to get “empiricist” and “rationalist” modes of operation to cooperate. The long-term vision is the design and implementation of an Automated Research Tool able to double as a platform for Inquiry Driven Education.

Please follow the above link for the full set of resources. An initial sample is linked below.

Wiki Hub —

Theme One Program • Overview
• https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Overview

Documentation —

Theme One Program • Pascal Source Code
• https://www.academia.edu/5210987/Theme_One_Program_Pascal_Source_Code

Theme One Program • User Guide
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide

Theme One Program • Exposition
• https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Exposition

Applications —

Applications of a Propositional Calculator • Constraint Satisfaction Problems
• https://www.academia.edu/4727842/Applications_of_a_Propositional_Calculator_Constraint_Satisfaction_Problems

Exploratory Qualitative Analysis of Sequential Observation Data
• https://oeis.org/wiki/User:Jon_Awbrey/Exploratory_Qualitative_Analysis_of_Sequential_Observation_Data

References —

An Architecture for Inquiry • Building Computer Platforms for Discovery
• https://www.academia.edu/1270327/An_Architecture_for_Inquiry_Building_Computer_Platforms_for_Discovery

Exploring Research Data Interactively • Theme One : A Program of Inquiry
• https://www.academia.edu/1272839/Exploring_Research_Data_Interactively._Theme_One_A_Program_of_Inquiry

#Peirce #Logic #LogicalGraphs #ThemeOneProgram #IdeaProcessor
#BooleanSatisfiability #CactusLanguage #DeclarativeProgramming

#MinimalNegationOperators
• https://oeis.org/wiki/Minimal_negation_operator

#Peirce #LogicalGraphs #MinimalNegations
#BooleanFunctions #PropositionalCalculus
#CactusGraphs #CactusLanguage #CactusSyntax

@bblfish @pietercolpaert

I would suggest bumping up the genus from #Trees to #Cacti. They've got the #Lobes ...

#CactusLanguage
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview

@somedonkey @NicoleCRust

#CactusLanguage #CactusSyntax
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview

@albertcardona @NicoleCRust @complexsystems @cogneurophys @PessoaBrain @SussilloDavid @carlosbrody @Neurograce @neuralreckoning @tyrell_turing @DrYohanJohn @cian @WiringtheBrain @tdverstynen @neuralengine

I'll just tag this for later when I've had a chance to collect my thoughts.

#WinnerTakeAll #Grossberg #CompetitionCooperation
#McClelland #Rumelhart #ParallelDistributedProcessing
#CactusLanguage #LogicalGraphs #MinimalNegationOperators

@charlient

Try Cacti —

#CactusLanguage
• https://oeis.org/wiki/Cactus_Language_•_Overview

#CactusGraphs #CactusSyntax

#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 #MultigradeLogicalConnectives.

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