Differential Logic • 13

Posted on November 14, 2024 by Jon Awbrey

Transforms Expanded over Ordinary and Differential Variables

Two views of how the difference operator \mathrm{D} acts on the set of sixteen functions f : \mathbb{B} \times \mathbb{B} \to \mathbb{B} are shown below.  Table A5 shows the expansion of \mathrm{D}f over the set \{ p, q \} of ordinary variables and Table A6 shows the expansion of \mathrm{D}f over the set \{ \mathrm{d}p, \mathrm{d}q \} of differential variables.

Difference Map Expanded over Ordinary Variables

\text{Table A5.}~~ \mathrm{D}f ~\text{Expanded over Ordinary Variables}~ \{ p, q \}

Df Expanded over Ordinary Variables {p, q}

Difference Map Expanded over Differential Variables

\text{Table A6.}~~ \mathrm{D}f ~\text{Expanded over Differential Variables}~ \{ \mathrm{d}p, \mathrm{d}q \}

Df Expanded over Differential Variables {dp, dq}

Resources

cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate

This entry was posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Zeroth Order Logic and tagged , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

4 Responses to Differential Logic • 13

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