Animated Logical Graphs • 71

Posted on April 18, 2021 by Jon Awbrey

Re: Richard J. Lipton • The 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}

Peirce Duality as Sign Relation • 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 Graphs • Laws of Form

This entry was posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.