Residuation for Soft Constraints: Lexicographic Orders and Approximation Techniques

TL;DR

This paper advances constraint programming by developing a residuated monoid of tuples using lexicographic order and introducing an approximation technique that leverages weak inverses for improved preference aggregation.

Contribution

It constructs a new residuated monoid of tuples based on lexicographic order and proposes a variant of the Mini-bucket approximation technique utilizing weak inverses.

Findings

Residuated monoid of tuples constructed using lexicographic order.

A new approximation technique exploiting weak inverses is introduced.

Enhanced preference aggregation methods for constraint programming.

Abstract

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.