  We show that for every quasivariety K of structures (where both functions and
relations are allowed) there is a semilattice S with operators such that the
lattice of quasi-equational theories of K (the dual of the lattice of
sub-quasivarieties of K) is isomorphic to Con(S,+,0,F). As a consequence, new
restrictions on the natural quasi-interior operator on lattices of
quasi-equational theories are found.

Rings and Algebras;Logic