We study here a natural situation when constraint programming can be entirely reduced to
rule-based programming. To this end we explain first how one can compute on constraint
satisfaction problems using rules represented by simple first-order formulas. Then we consider
constraint satisfaction problems that are based on predefined, explicitly given constraints.
To solve them we first derive rules from these explicitly given constraints and limit the
computation process to a repeated application of these rules, combined with labeling. We
consider two types of rule here. The first type, that we call equality rules, leads to a new
notion of local consistency, called rule consistency that turns out to be weaker than arc
consistency for constraints of arbitrary arity (called hyper-arc consistency in Marriott &
Stuckey (1998)). For Boolean constraints rule consistency coincides with the closure under the
well-known propagation rules for Boolean constraints. The second type of rules, that we call
membership rules, yields a rule-based characterization of arc consistency. To show feasibility
of this rule-based approach to constraint programming, we show how both types of rules can
be automatically generated, as CHR rules of Frühwirth (1995). This yields an implementation
of this approach to programming by means of constraint logic programming. We illustrate
the usefulness of this approach to constraint programming by discussing various examples,
including Boolean constraints, two typical examples of many valued logics, constraints dealing
with Waltz's language for describing polyhedral scenes, and Allen's qualitative approach to
temporal logic.
On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems
