  Continuing with the authors concept (and results) of defining independence
for columns of a boolean and superboolean matrix, we apply this theory to
finite lattices and finite posets, introducing boolean and superboolean matrix
representations for these objects. These representations yield the new concept
of c-independent subsets of lattices and posets, for which the notion of c-rank
is determined as the cardinality of the largest c-independent subset. We
characterize this c-rank and show that c-independent subsets have a very
natural interpretation in term of the maximal chains of the Hasse diagram and
the associated partitions of the lattice. This realization has direct important
connections with chamber systems.
