Eliminating Variables in General Constraint Logic∗

Drawing inferences from a set of general constraint clauses is known as a difficult problem. A general approach is based on the idea of eliminating some or all variables involved. In the particular case of propositional logic, this approach leads to a simple procedure that incorporates the well-known resolution principle. The purpose of this paper is to show how the resolution principle can be extended to constraint logic where the knowledge is given as a set of constraint clauses. The result is a general variable elimination method. The paper shows that the elimination problem can always be reduced to the problem of eliminating the variable from a (conjunctive) set of atomic constraints. Variabele elimination has a number of possible applications such as satisfiability testing, hypotheses testing, constraint solving, argumentative reasoning, and many others.