  A representation theorem is proved for De Morgan monoids that are (i)
semilinear, i.e., subdirect products of totally ordered algebras, and (ii)
negatively generated, i.e., generated by lower bounds of the neutral element.
Using this theorem, we prove that the De Morgan monoids satisfying (i) and (ii)
form a locally finite variety. We then prove that epimorphisms are surjective
in every variety of negatively generated semilinear De Morgan monoids. In the
process, epimorphism-surjectivity is established for several other classes as
well, including the variety of all semilinear idempotent commutative residuated
lattices and all varieties of negatively generated semilinear Dunn monoids. The
results settle natural questions about Beth-style definability for a range of
substructural logics.
