Constraints in computational logics
Unions of non-disjoint theories and combinations of satisfiability procedures
Theoretical Computer Science
Deciding the Word Problem in the Union of Equational Theories Sharing Constructors
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
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In this paper we outline a theoretical framework for the combination of decision procedures for the satisfiability of constraints with respect to a constraint theory. We describe a general combination method which, given a procedure that decides constraint satisfiability with respect to a constraint theory T_1 and one that decides constraint satisfiability with respect to a constraint theory T_2, is able to produce a procedure that (semi-)decides constraint satisfiability with respect to the union of T_1 and T_2. We also provide some model-theoretic conditions on the constraint language and the component constraint theories for the method to be sound and complete, with special emphasis on the case in which the signatures of of T_1 and T_2 are non-disjoint.