  One of the longstanding problems in universal algebra is the question of
which finite lattices are isomorphic to the congruence lattices of finite
algebras. This question can be phrased as which finite lattices can be
represented as lattices of equivalence relations on finite sets closed under
certain first order formulas. We generalize this question to a different
collection of first-order formulas, giving examples to demonstrate that our new
question is distinct. We then prove that every lattice $\m M_n$ can be
represented in this new way. [This is an extended version of a paper submitted
to \emph{Algebra Universalis}.]
