Distributivity and residuation for lexicographic orders

Residuation theory concerns the study of partially ordered algebraic structures, most often just monoids, equipped with a weak inverse for the monoidal operator. One of its areas of application is constraint programming, whose key requirement is the presence of a distributive operator for combining preferences. The key result of the paper shows how, given a residuated monoid of preferences, to build a new residuated monoid of (possibly infinite) tuples based on lexicographic order