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'''''NOTE.'''  This section is currently under construction.  In the meantime, see [[Logical Graph]].''

'''''NOTE.'''  This section is currently under construction.  In the meantime, see [[Logical Graph]].''

The development of differential logic is greatly facilitated by having a conceptually efficient calculus in place at the level of [[boolean-valued functions]] and elementary logical propositions.  A calculus that is very efficient from both conceptual and computational standpoints is based on just two types of logical connectives, both of variable <math>k\!</math>-ary scope:

The development of differential logic is greatly facilitated by having a conceptually efficient calculus in place at the level of [[boolean-valued functions]] and elementary logical propositions.  A calculus that is very efficient from both conceptual and computational standpoints is based on just two types of logical connectives, both of variable <math>k\!</math>-ary scope.  The formulas of this calculus map into a species of graph-theoretical structures called ''painted and rooted cacti'' (PARCs) that lend visual representation to their functional structure and smooth the path to efficient computation.

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| The first kind of propositional expression takes the form of a parenthesized sequence of propositional expressions, <math>\texttt{(} e_1 \texttt{,} e_2 \texttt{,} \ldots \texttt{,} e_{k-1} \texttt{,} e_k \texttt{)},</math> and is taken to indicate that exactly one of the propositions <math>e_1, e_2, \ldots, e_{k-1}, e_k</math> is false, in other words, that their [[minimal negation]] is true.

| The first kind of propositional expression takes the form of a parenthesized sequence of propositional expressions, <math>\texttt{(} e_1 \texttt{,} e_2 \texttt{,} \ldots \texttt{,} e_{k-1} \texttt{,} e_k \texttt{)},</math> and is taken to indicate that exactly one of the propositions <math>e_1, e_2, \ldots, e_{k-1}, e_k</math> is false, in other words, that their [[minimal negation]] is true. A clause of this form may also be exhibited as a graph-theoretical structure calle

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