Residuation for Soft Constraints: Lexicographic Orders and Approximation Techniques

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