  We are considering the algebraic structure of the Pawlak-Brouwer-Zadeh
lattice to distinguish vagueness due to imprecision from ambiguity due to
coarseness. We show that a general class of many-valued logics useful for
reasoning about data emerges from this context. All these logics can be
obtained from a very general seven-valued logic which, interestingly enough,
corresponds to a reasoning system developed by Jaina philosophers four
centuries BC. In particular, we show how the celebrated Belnap four-valued
logic can be obtained from the very general seven-valued logic based on the
Pawlak-Brouwer-Zadeh lattice.

Logic