Interpretive Duality in Logical Graphs • 3

Posted on April 24, 2024 by Jon Awbrey

Re: Interpretive Duality in Logical Graphs • (1) • (2)

For a sense of how the choice of interpretation bears on cases beyond the bare minimum complexity let us start with the familiar example of Peirce’s law, commonly expressed in the following form.

((p \Rightarrow q) \Rightarrow p) \Rightarrow p

The following two formal equations show how Peirce’s law may be expressed in terms of logical graphs, operating under the entitative and existential interpretations, respectively.

\text{Peirce's Law} \stackrel{_\bullet}{} \text{Dual Graphs}

Peirce's Law • Dual Graphs

Resources

cc: FB | Logical Graphs • Laws of Form • Mathstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

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, Interpretive Duality, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

2 Responses to Interpretive Duality in Logical Graphs • 3

  1. Pingback: Survey of Animated Logical Graphs • 7 | Inquiry Into Inquiry

  2. Pingback: Interpretive Duality in Logical Graphs • 4 | Inquiry Into Inquiry

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