sentences:  A join-semilattice with zero is a refinement monoid if and only if it is distributive.Any abelian group is a refinement monoid.The positive cone "G+" of a partially ordered abelian group "G" is a refinement monoid if and only if "G" is an "interpolation group", the latter meaning that for any elements "a0", "a1", "b0", "b1" of "G" such that "ai ≤ bj" for all "i, j<2", there exists an element "x" of "G" such that "ai ≤ x ≤ bj" for all "i, j<2".