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===Differential Expansions of Propositions===

===Differential Expansions of Propositions===

An efficient calculus for the realm of logic represented by boolean functions and elementary propositions makes it feasible to compute the finite differences and the differentials of those functions and propositions.

An efficient calculus for the realm of logic represented by boolean functions and elementary propositions makes it feasible to compute the finite differences and the differentials of those functions and propositions.

If the form of the above statement reminds you of De Morgan's rule, it is no accident, as differentiation and negation turn out to be closely related operations.  Indeed, one can find discussions of logical difference calculus in the Boole–De Morgan correspondence and Peirce also made use of differential operators in a logical context, but the exploration of these ideas has been hampered by a number of factors, not the least of which has been the lack of a syntax that was adequate to handle the complexity of expressions that evolve.

If the form of the above statement reminds you of De Morgan's rule, it is no accident, as differentiation and negation turn out to be closely related operations.  Indeed, one can find discussions of logical difference calculus in the Boole–De Morgan correspondence and Peirce also made use of differential operators in a logical context, but the exploration of these ideas has been hampered by a number of factors, not the least of which has been the lack of a syntax that was adequate to handle the complexity of expressions that evolve.

Let us run through the initial example again, this time attempting to interpret the formulas that develop at each stage along the way.

Let us run through the initial example again, this time attempting to interpret the formulas that develop at each stage along the way.