  Relational Lattice is a succinct mathematical model for Relational Algebra.
It reduces the set of six classic relational algebra operators to two: natural
join and inner union. In this paper we push relational lattice theory in two
directions. First, we uncover a pair of complementary lattice operators, and
organize the model into a bilattice of four operations and four distinguished
constants. We take a notice a peculiar way bilattice symmetry is broken. Then,
we give axiomatic introduction of unary negation operation and prove several
laws, including double negation and De Morgan. Next we reduce the model back to
two basic binary operations and twelve axioms, and exhibit a convincing
argument that the resulting system is complete in model-theoretic sense. The
final parts of the paper casts relational lattice perspective onto database
dependency theory and into cylindric algebras.
