  We establish a combinatorial counterpart of the Cohen-Macaulay duality on a
class of curve singularities which includes algebroid curves. For such
singularities the value semigroup and the value semigroup ideals of all
fractional ideals satisfy axioms that define so-called good semigroups and good
semigroup ideals. We prove that each good semigroup admits a canonical good
semigroup ideal which gives rise to a duality on good semigroup ideals. We show
that the Cohen-Macaulay duality and our good semigroup duality are compatible
under taking values.
