General properties and termination conditions for soft constraint propagation

Soft constraints based on semirings are a generalization of classical constraints, where tuples of variables' values in each soft constraint are 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 constraint propagation [8]. On the other hand, in [1-3] it has been proven 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 schemas and we provide a more general framework where the schema of [3] can be used for soft constraints. In doing so, we generalize the concept of soft constraint propagation, and we provide new sufficient and independent conditions for its termination.