Differential Logic • Comment 1

Re: Gil KalaiPivotal Variables

Just a tangential association with respect to logical influence and pivotability.  I have been exploring questions related to pivotal variables (“Differences that Make a Difference” or “Difference In ⟹ Difference Out”) via logical analogues of partial and total differentials.

For example, letting \mathbb{B} = \{ 0, 1 \}, the partial differential operator \partial_{x_i} sends a function f : \mathbb{B}^k \to \mathbb{B} with fiber F = f^{-1}(1) \subseteq \mathbb{B}^k to a function g = \partial_{x_i}f whose fiber G = g^{-1}(1) \subseteq \mathbb{B}^k consists of all the places where a change in the value of x_i makes a change in the value of f.


This entry was posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Differential Analytic Turing Automata, Differential Logic, Discrete Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Logic, Logical Graphs, Logical Influence, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pivotal Variables, Propositional Calculus, Propositional Equation Reasoning Systems, Visualization, Zeroth Order Logic and tagged , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

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