## Animated Logical Graphs • 50

Re: Richard J. LiptonThe Art Of Math
Re: Animated Logical Graphs • (30) (45) (46) (47) (48) (49)

In the last of our six ways of looking at the Peirce duality between entitative and existential interpretations, we consider the previous Table of Logical Graphs and Venn Diagrams sorted in Orbit Order.

Logical Graphs • Entitative and Existential Venn Diagrams • Orbit Order
$\text{Logical Graph}$ $\text{Entitative Interpretation}$ $\text{Existential Interpretation}$

$\texttt{(} ~ \texttt{)}$

$\text{true}$
$f_{15}$
$\text{false}$
$f_{0}$

$\texttt{(} x \texttt{)(} y \texttt{)}$

$\lnot x \lor \lnot y$
$f_{7}$
$\lnot x \land \lnot y$
$f_{1}$

$\texttt{(} x \texttt{)} y$

$x \Rightarrow y$
$f_{11}$
$x \nLeftarrow y$
$f_{2}$

$x \texttt{(} y \texttt{)}$

$x \Leftarrow y$
$f_{13}$
$x \nRightarrow y$
$f_{4}$

$x y$

$x \lor y$
$f_{14}$
$x \land y$
$f_{8}$

$\texttt{(} x \texttt{)}$

$\lnot x$
$f_{3}$
$\lnot x$
$f_{3}$

$x$

$x$
$f_{12}$
$x$
$f_{12}$

$\texttt{(} x \texttt{,} y \texttt{)}$

$x = y$
$f_{9}$
$x \ne y$
$f_{6}$

$\texttt{((} x \texttt{,} y \texttt{))}$

$x \ne y$
$f_{6}$
$x = y$
$f_{9}$

$\texttt{(} y \texttt{)}$

$\lnot y$
$f_{5}$
$\lnot y$
$f_{5}$

$y$

$y$
$f_{10}$
$y$
$f_{10}$

$\texttt{(} x y \texttt{)}$

$\lnot (x \lor y)$
$f_{1}$
$\lnot (x \land y)$
$f_{7}$

$\texttt{(} x \texttt{(} y \texttt{))}$

$x \nLeftarrow y$
$f_{2}$
$x \Rightarrow y$
$f_{11}$

$\texttt{((} x \texttt{)} y \texttt{)}$

$x \nRightarrow y$
$f_{4}$
$x \Leftarrow y$
$f_{13}$

$\texttt{((} x \texttt{)(} y \texttt{))}$

$x \land y$
$f_{8}$
$x \lor y$
$f_{14}$

$\text{false}$
$f_{0}$
$\text{true}$
$f_{15}$

### Resources

cc: Cybernetics Communications (1) (2)FB | Logical Graphs • Ontolog Forum (1) (2)
cc: Peirce (1) (2) (3) (4) (5) (6) (7) (8) (9) • Structural Modeling (1) (2) • Systems (1) (2)

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