Animated Logical Graphs • 75

Posted on May 10, 2021 by Jon Awbrey

Re: Richard J. Lipton • The Art Of Math
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Continuing our scan of the Table in Episode 72, the next two orbits contain the logical graphs for the boolean functions f_{2}, f_{11}, f_{4}, f_{13}, in that order.  A first glance shows these two orbits have surprisingly intricate structures and relationships to each other — let’s isolate that section for a closer look.

\text{Peirce Duality} \stackrel{_\bullet}{} \text{Subtractions and Implications}

Peirce Duality • Subtractions and Implications

  • The boolean functions f_{2} and f_{4} are called subtraction functions.
  • The boolean functions f_{11} and f_{13} are called implication functions.
  • The logical graphs for f_{2} and f_{11} are dual to each other.
  • The logical graphs for f_{4} and f_{13} are dual to each other.

The values of the subtraction and implication functions for each (x, y) \in \mathbb{B} \times \mathbb{B} and the text expressions for their logical graphs are given in the following Table.

Subtractions and Implications

Resources

cc: Peirce List (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
cc: Structural Modeling (1) (2) • Systems Science (1) (2)
cc: Cybernetics (1) (2) • Ontolog Forum (1) (2)
cc: FB | Logical Graphs • Laws of Form

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