Animated Logical Graphs • 45

Re: Richard J. LiptonThe Art Of Math
Re: Animated Logical Graphs • (30)

There’s a nice interplay between geometric and logical dualities in C.S. Peirce’s graphical systems of logic, rooted in his discovery of the amphecks \textsc{Nand} and \textsc{Nnor} and flowering in his logical graphs for propositional and predicate calculus.  Peirce’s logical graphs bear the dual interpretations he dubbed entitative and existential graphs.

Here’s a Table of Boolean Functions on Two Variables, using an extension of Peirce’s graphs from trees to cacti, illustrating the duality so far as it affects propositional calculus.

\text{Boolean Functions on Two Variables}

Boolean Functions on Two Variables

Resources

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

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.

4 Responses to Animated Logical Graphs • 45

  1. Pingback: Survey of Animated Logical Graphs • 3 | Inquiry Into Inquiry

  2. Pingback: Animated Logical Graphs • 46 | Inquiry Into Inquiry

  3. Pingback: Animated Logical Graphs • 47 | Inquiry Into Inquiry

  4. Pingback: Animated Logical Graphs • 48 | Inquiry Into Inquiry

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