Re: Interpretive Duality in Logical Graphs • (1) • (2) • (3)

Last time we took up Peirce’s law, and saw how it might be expressed in two different ways, under the entitative and existential interpretations, respectively.  The next thing to do is see how our choice of interpretation bears on the patterns of proof we might find.  A sense of the possibilities may be gotten by displaying the two styles of proof in parallel columns, as shown below.

For convenience, the formal axioms and a few theorems of frequent use are linked below.

• Axiom I₁ • Condense/Protract
• Axiom I₂ • Cancel/Elicit
• Axiom J₁ • Delete/Insert
• Axiom J₂ • Collect/Distribute
• C₁ • Double Negation Theorem • Reflect/Reflect
• C₂ • Generation Theorem • Regenerate/Degenerate
• C₃ • Dominant Form Theorem • Quit/Quip

Resources

• Logical Graphs • First Impressions
• Logical Graphs • Formal Development

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