Animated Logical Graphs • 71

Re: Richard J. LiptonThe Art Of Math
Re: Animated Logical Graphs • (57)(58)(59)(60)(61)(62)(63)(64)(65)(66)(69)(70)

Our investigation has brought us to the point of seeing both a transformation group and a triadic sign relation in the duality between entitative and existential interpretations of logical graphs.

Given the level of the above abstractions it helps to anchor them in concrete structural experience.  In that spirit we’ve been pursuing the case of a group action $T : X \to X$ and a sign relation $L \subseteq O \times X \times X$ where $O$ is the set of boolean functions on two variables and $X$ is a set of logical graphs denoting those functions.  We drew up a Table combining the aspects of both structures and sorted it according to the orbits $T$ induces on $X$ and consequently on $O.$

$\text{Peirce Duality as Sign Relation} \stackrel{_\bullet}{} \text{Orbit Order}$

Resources

cc: Peirce List (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)
cc: Structural Modeling (1) (2) • Systems Science (1) (2)
cc: Cybernetics (1) (2) • Ontolog Forum (1) (2)
cc: FB | Logical GraphsLaws of Form

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