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 efficient 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 definition, 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.