Correctness of Solving Query-Answering Problems Using Satisfiability Solvers

A query-answering (QA) problem is concerned with finding the set of all ground instances of a given atomic formula that are logical consequences of a specified logical formula. Recently, many kinds of problems have been solved efficiently by using satisfiability (SAT) solvers, motivating us to use SAT solvers to speed up solving a class of QA problems. Given a finite ground clause set as input, a SAT solver used in this paper generates all models of the input set that contain only atomic formulas appearing in it. A method for solving QA problems using SAT solvers is developed, based on the use of a support set to restrict the generation of ground instances of given clauses possibly with constraint atomic formulas. The correctness of the proposed method is proved.