#LogicalGraphs • 16
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

Turning to the #InitialEquation or #LogicalAxiom whose text expression is \(``\texttt{(}~\texttt{)(}~\texttt{)}=\texttt{(}~\texttt{)}",\) Figure 8 shows the planar maps and their corresponding #DualGraphs superimposed.

Figure 8
• https://oeis.org/w/images/0/09/Logical_Graph_Figure_8_Visible_Frame.jpg

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 15
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

We have treated in some detail various forms of the #InitialEquation or #LogicalAxiom whose text expression is \(``\texttt{((}~\texttt{))}~=~".\) For comparison, let's record the plane-embedded and #TopologicalDual forms of the axiom whose text expression is \(``\texttt{(}~\texttt{)(}~\texttt{)}=\texttt{(}~\texttt{)}".\)

Figure 7 reproduces the planar form of the equation we first saw in Figure 1.

Figure 7
• https://oeis.org/w/images/b/b4/Logical_Graph_Figure_7_Visible_Frame.jpg

#Logic #Peirce