Hana Rudova. Constraints with variables' annotations and constraint 
hierarchies. In Branislav Rovan, editor, SOFSEM'98: Theory and Practice of 
Informatics, pages 409-418. Springer-Verlag LNCS 1521, November 1998.

Abstract:
Variables'~annotations in over-constrained problems enable to express 
preferences for optimal solution selection using preferences on variables.
The basic interpretation of variables'~annotations is presented and
correspondence with hierarchical CSP is described. New local comparator for
constraint hierarchy is proposed and used for solving constraints with
variables'~annotations. The relationships between standard locally-better
comparator and the new one are clarified. The potential application areas of
variables'~annotations are also mentioned.