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===Differential Expansions of Propositions===

===Differential Expansions of Propositions===

One of the first things that you can do, once you have a moderately efficient calculus for boolean functions or propositional logic, is to start thinking about, and even to start computing, the differentials of these functions or propositions.

An efficient calculus for boolean functions and logical propositions makes it feasible to compute the finite differences and the differentials of those functions and propositions.

Let us start with a proposition of the form <math>p ~\operatorname{and}~ q</math> that is graphed as two labels attached to a root node:

For example, consider a proposition of the form <math>{}^{\backprime\backprime} p ~\operatorname{and}~ q \, {}^{\prime\prime}</math> that is graphed as two letters attached to a root node:

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