`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 in various areas. An important aspect of constraint
hierarchies is that there are efficient satisfaction algorithms; local-propagation-based
algorithms, for example, are efficient enough to realize interactive user interfaces. However,
past local propagation algorithms have been limited to multi-way equality constraints.
In this research, we reformulate constraint hierarchies with a more strict
definition, and propose generalized local propagation as a theoretical framework for
studying local propagation and constraint hierarchies. Then, we show that a property
called global semi-monotonicity in satisfying hierarchies turns out to be a practically
useful property in generalized local propagation. Finally, we give an overview of an algorithm
for solving hierarchies of multi-way equality and inequality constraints, which
has been actually implemented.