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Directory:Jon Awbrey/Papers/Differential Logic : Introduction (view source)
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===Cactus Language for Propositional Logic===
===Cactus Language for Propositional Logic===
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.
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.