Automatic Combinability of Rewriting-Based Satisfiability Procedures

We address the problems of combining satisfiability procedures and consider two combination scenarios: (i) the combination within the class of rewriting-based satisfiability procedures and (ii) the Nelson-Oppen combination of rewriting-based satisfiability procedures and arbitrary satisfiability procedures. In each scenario, we use meta-saturation, which schematizes saturation of the set containing the axioms of a given theory and an arbitrary set of ground literals, to syntactically decide sufficient conditions for the combinability of rewriting-based satisfiability procedures. For (i), we give a sufficient condition for the modular termination of meta-saturation. When meta-saturation for the union of theories halts, it yields a rewriting-based satisfiability procedure for the union. For (ii), we use meta-saturation to prove the stable infiniteness of the component theories and deduction completeness of their rewriting-based satisfiability procedures. These properties are important to establish the correctness of the Nelson-Oppen combination method and to obtain an efficient implementation.