Jon Awbrey · @Inquiry
234 followers · 1733 posts · Server mathstodon.xyzCactus 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
#cellularautomata #cactussyntax #CactusLanguage #CactusCalculus #PropositionalCalculus #BooleanFunctions #LogicalGraphs #logic
Jon Awbrey · @Inquiry
173 followers · 1043 posts · Server mathstodon.xyz#MinimalNegationOperators
• https://oeis.org/wiki/Minimal_negation_operator
#Peirce #LogicalGraphs #MinimalNegations
#BooleanFunctions #PropositionalCalculus
#CactusGraphs #CactusLanguage #CactusSyntax
#cactussyntax #CactusLanguage #CactusGraphs #PropositionalCalculus #BooleanFunctions #minimalnegations #LogicalGraphs #Peirce #MinimalNegationOperators
Jon Awbrey · @Inquiry
141 followers · 656 posts · Server mathstodon.xyz
Jon Awbrey · @Inquiry
94 followers · 373 posts · Server mathstodon.xyz#cactussyntax #CactusGraphs #CactusLanguage
Jon Awbrey · @Inquiry
85 followers · 291 posts · Server mathstodon.xyz
#ThemeOneProgram • #JetsAndSharks 2
• https://inquiryintoinquiry.com/2022/08/30/theme-one-program-jets-and-sharks-2/
As we saw last time, Theme One reads the text file shown below and constructs a #CactusGraph #DataStructure in computer memory. The cactus graph represents a single #LogicalFormula in #PropositionalCalculus and that proposition embodies the #LogicalConstraints defining the Jets and Sharks #DataBase.
Jets and Sharks • Log File
• https://inquiryintoinquiry.files.wordpress.com/2022/08/theme-one-guide-e280a2-jets-and-sharks-e280a2-log-file.png
#logicalcacti #cactussyntax #Peirce #LogicalGraphs #logic #database #logicalconstraints #PropositionalCalculus #logicalformula #datastructure #cactusgraph #JetsAndSharks #ThemeOneProgram
Jon Awbrey · @Inquiry
82 followers · 269 posts · Server mathstodon.xyz
#ThemeOneProgram • #JetsAndSharks 1.4
• https://inquiryintoinquiry.com/2022/08/25/theme-one-program-jets-and-sharks-1/
Displayed below is the text expression of a #TraversalString which Theme One parses into a #CactusGraph #DataStructure in computer memory. The cactus graph represents a single #LogicalFormula in #PropositionalCalculus and this proposition embodies all the #LogicalConstraints defining the Jets and Sharks #DataBase.
#Logic #LogicalGraphs #Peirce
#CactusSyntax #LogicalCacti
#MinimalNegationOperators
#MinimalNegationOperators #logicalcacti #cactussyntax #Peirce #LogicalGraphs #logic #database #logicalconstraints #PropositionalCalculus #logicalformula #datastructure #cactusgraph #traversalstring #JetsAndSharks #ThemeOneProgram
Jon Awbrey · @Inquiry
52 followers · 171 posts · Server mathstodon.xyz
#DifferentialPropositionalCalculus • 5.6
• https://inquiryintoinquiry.com/2020/02/29/differential-propositional-calculus-5/
\(\text{Figure 8. Linear Propositions} : \mathbb{B}^3 \to \mathbb{B}\)
• https://inquiryintoinquiry.files.wordpress.com/2020/02/venn-diagrams-e280a2-p-q-r-e280a2-linear-propositions.jpg
At the bottom of Figure 8 is #VennDiagram for the #LinearProposition of rank 0, the constant \(0\) function or the everywhere false proposition, expressed in #CactusSyntax by the form \(\texttt{(}~\texttt{)}\) or in algebraic form by a simple \(0.\)
\(\text{Figure 8.4 Venn Diagram for}~\texttt{(}~\texttt{)}\)
#cactussyntax #linearproposition #venndiagram #DifferentialPropositionalCalculus