Jon Awbrey · @Inquiry
96 followers · 414 posts · Server mathstodon.xyz#LogicalGraphs • 12
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality
#Duality • Logical and Topological
Once we make the connection between one of #Peirce's #AlphaGraphs and its character string expression it's not too big a leap to see how the character string codes up the structure of the topological #DualGraph in the space of #RootedTrees.
#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory
#ProofTheory #modeltheory #graphtheory #BooleanFunctions #PropositionalCalculus #lawsofform #spencerbrown #logic #rootedtrees #dualgraph #alphagraphs #Peirce #duality #LogicalGraphs
Jon Awbrey · @Inquiry
96 followers · 390 posts · Server mathstodon.xyz#LogicalGraphs • 9
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality
From the #AlphaGraph and its text expression we turn to representing their common form in computer memory, where it can be manipulated with the greatest of ease. We begin by transforming the alpha graph into its #TopologicalDual. Planar regions of the alpha graph are mapped into points of the #DualGraph and boundaries between those planar regions are mapped into lines between those points.
#topologicalduality #logic #dualgraph #topologicaldual #alphagraph #LogicalGraphs