Constraint Propagation for Soft Constraint Satisfaction Problems: Generalization and Termination Conditions

Soft constraints based on semirings are a generalization of classical constraints, where tuples of variables’ values in each soft constraint are uniquely associated to elements from an algebraic structure called semiring. This framework is able to express, for example, fuzzy, classical, weighted, valued and over-constrained constraint problems. Classical constraint propagation has been extended and adapted to soft constraints by defining a schema for soft local consistency [BMR97]. On the other hand, in [Apt99a,Apt99b] it has been proved that most of the well known constraint propagation algorithms for classical constraints can be cast within a single schema. In this paper we combine these two schema and we show how the framework of [Apt99a,Apt99b] can be used for soft constraints. In doing so, we generalize the concept of soft local consistency, and we prove some convenient properties about its termination.