  Residuation theory concerns the study of partially ordered algebraic
structures, most often monoids, equipped with a weak inverse for the monoidal
operator. One of its area of application has been constraint programming, whose
key requirement is the presence of an aggregator operator for combining
preferences. Given a residuated monoid of preferences, the paper first shows
how to build a new residuated monoid of (possibly infinite) tuples, which is
based on the lexicographic order. Second, it introduces a variant of an
approximation technique (known as Mini-bucket) that exploits the presence of
the weak inverse.
