Generalized Local Propagation: A Framework for Solving Constraint Hierarchies

`Constraint hierarchy' is a nonmonotonic system that allows programmers to describe over-constrained real-world problems by specifying constraints with hierarchical preferences, and has been applied to various areas. An important aspect of constraint hierarchies is the existence of e cient satisfaction algorithms based on local propagation. However, past local-propagation algorithms have been limited to multi-way equality constraints. We overcome this by reformulating constraint hierarchies with a more strict de nition, and proposing generalized local propagation as a theoretical framework for studying constraint hierarchies and local propagation. Then, we show that global semi-monotonicity in satisfying hierarchies turns out to be a practically useful property in generalized local propagation. Finally, we discuss the relevance of generalized local propagation with our previous DETAIL algorithm for solving hierarchies of multi-way equality constraints.