On Combining Backward and Forward Chaining in Constraint Logic Programming

We address the problem of designing constraint logic languages that usefully combine backward and forward chaining in a sound and complete way. Following the approach of Constraint Logic Programming, we define a class of programming languages that generalize both Constraint Logic and Concurrent Constraint Programming. Syntactically, this class corresponds to Constraint Handling Rules with disjunctions, but differ operationally by featuring set-based semantics instead of multiset-based ones; i. e., conjunction and disjunction are idempotent. The assumption of program confluence is the crux on which both the committed choice strategy and the logical completeness of the languages rely.