  The Boolean logic of subsets, usually presented as `propositional logic,' is
considered as being "classical" while intuitionistic logic and the many
sublogics and off-shoots are "non-classical." But there is another mathematical
logic, the logic of partitions, that is at the same mathmatical level as
Boolean subset logic since subsets and quotient sets (partitions or equivalence
relations) are dual to one another in the category-theoretic sense. Our purpose
here is to explore the notions of negation and implication in that other
mathematical logic of partitions.
